Soil mechanics and foundations by dr. b.c. punmia ashok kumar jain- b.c. punmia- arun kr. jain
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7 SOIL MECHANICS AND FOUNDATIONS.
R=2R 273)
where R is measured below the high flood level (HEFL).
‘Scour level = HEL. -R =HFL.-2R 2274)
The grip lengih is taken as {A below the scour level according to the code of
practice of the Indian Roads Congress and as }A in Railway practice. This means that
the depth of foundation should be at last IR below HFL according to IRC code, and
LER below HEL according to Railway practice . I is futher recommended that the minimum
depth of embedment below the scour level should not be less than 2.0 m for piers and
abument with arches and 1.2 m for piers and abutments supporting other types of superstructure.
‘According co Terzaghi and Peck, the ultimate bearing capacity can be determined
from the following expression:
= Op + 2aRf, Dy 27.9
Qe = aR? (1.2 cNe + yDy Ny + 0.67RN,) so(27.6)
where No, Na Mis Terzaghi's bearing capacity factors
Re radius of well
depth of well (depth of foundation)
fis average skin friction
27.4. FORCES ACTING ON A WELL FOUNDATION
In addition to the self-weight and buoyancy, a well carries the dead load of the
super-sinicture, bearings pier and is liable 10 the following horizontal forces
(0) bracking and tactive effort of the moving vehicles.
i) force on account of resistance of the bearings against movement due 10
variation of temperature,
iil) force on account of water current,
@) wind. foctes,
(9 seismic forces,
Gf) earth pressure,
(i) centrifugal forces,
The magnitude, direction and point of application of all the above forces can be
found under the worst possible combinations and they can be replaced by two horizontal
forces, P and Q and a single vertical force W as shown in Fig. 27.3.
P= Resultant of all horizontal forces in the direction across the pier.
Q- Resultant of all horizontal forces in the direction along the pies
We Resultant of all vertical forces.
‘The analysis is done on the following assumptions (Banerjee and Gangopadhyay, 1960):
R=2R 273)
where R is measured below the high flood level (HEFL).
‘Scour level = HEL. -R =HFL.-2R 2274)
The grip lengih is taken as {A below the scour level according to the code of
practice of the Indian Roads Congress and as }A in Railway practice. This means that
the depth of foundation should be at last IR below HFL according to IRC code, and
LER below HEL according to Railway practice . I is futher recommended that the minimum
depth of embedment below the scour level should not be less than 2.0 m for piers and
abument with arches and 1.2 m for piers and abutments supporting other types of superstructure.
‘According co Terzaghi and Peck, the ultimate bearing capacity can be determined
from the following expression:
= Op + 2aRf, Dy 27.9
Qe = aR? (1.2 cNe + yDy Ny + 0.67RN,) so(27.6)
where No, Na Mis Terzaghi's bearing capacity factors
Re radius of well
depth of well (depth of foundation)
fis average skin friction
27.4. FORCES ACTING ON A WELL FOUNDATION
In addition to the self-weight and buoyancy, a well carries the dead load of the
super-sinicture, bearings pier and is liable 10 the following horizontal forces
(0) bracking and tactive effort of the moving vehicles.
i) force on account of resistance of the bearings against movement due 10
variation of temperature,
iil) force on account of water current,
@) wind. foctes,
(9 seismic forces,
Gf) earth pressure,
(i) centrifugal forces,
The magnitude, direction and point of application of all the above forces can be
found under the worst possible combinations and they can be replaced by two horizontal
forces, P and Q and a single vertical force W as shown in Fig. 27.3.
P= Resultant of all horizontal forces in the direction across the pier.
Q- Resultant of all horizontal forces in the direction along the pies
We Resultant of all vertical forces.
‘The analysis is done on the following assumptions (Banerjee and Gangopadhyay, 1960):
WELL FOUNDATIONS m
1. The well is acted upon by an uni
directional horizontal force P in a direction across
the pier.
2. The well is founded in sandy stratum.
3. The resultant unit pressure on soil at
any depth is in simple proportion to horizontal
displacement
4. The ratio between contact pressure and
corresponding displacement is independent of the
pressure.
5. The cocffcien of vertical subgrade
reaction has the same value for every point
of surface acted upon by contact pressure
“The analysis that follows Is that suggested
by Banerjee and Gangopadhyay (1960).
27.5. ANALYSIS OF WELL FOUNDATION
1. Horizontal soll reactions. When a rigid
well, embedded in sand, stars moving parallel FIG, 273. FORCES ON A WELL.
to its original position, under the action of a
horizontal force P, it transforms the soil on
‘one side to passive state of plastic equilibrium and the other side into active sae. Assuming
that the well movement p, is sufficient to mobilise fully the active and passive earth pressure,
te resultant unit pressure at a depth z below the surface
is given by RATES) 073)
where y=unit weight of soil
Ky. Ka = co-efficient of passive
and active earth pressure, and depend
upon the angle of internal friction 9,
and angle of wall friction 6.
Let p be the load per unit arca
of vertical surface of sand and p be
{te corresponding displacement. Assum-
ing that p, is the displacement required
to increase the value of resultant unit
pressure form zero to py, we have.
=p hak &
om Lon Dor) KO
073)
Rig wat
Wy
A
UA
FIG. 224. EFFECT OF WAI
MOVEMENT.
1. The well is acted upon by an uni
directional horizontal force P in a direction across
the pier.
2. The well is founded in sandy stratum.
3. The resultant unit pressure on soil at
any depth is in simple proportion to horizontal
displacement
4. The ratio between contact pressure and
corresponding displacement is independent of the
pressure.
5. The cocffcien of vertical subgrade
reaction has the same value for every point
of surface acted upon by contact pressure
“The analysis that follows Is that suggested
by Banerjee and Gangopadhyay (1960).
27.5. ANALYSIS OF WELL FOUNDATION
1. Horizontal soll reactions. When a rigid
well, embedded in sand, stars moving parallel FIG, 273. FORCES ON A WELL.
to its original position, under the action of a
horizontal force P, it transforms the soil on
‘one side to passive state of plastic equilibrium and the other side into active sae. Assuming
that the well movement p, is sufficient to mobilise fully the active and passive earth pressure,
te resultant unit pressure at a depth z below the surface
is given by RATES) 073)
where y=unit weight of soil
Ky. Ka = co-efficient of passive
and active earth pressure, and depend
upon the angle of internal friction 9,
and angle of wall friction 6.
Let p be the load per unit arca
of vertical surface of sand and p be
{te corresponding displacement. Assum-
ing that p, is the displacement required
to increase the value of resultant unit
pressure form zero to py, we have.
=p hak &
om Lon Dor) KO
073)
Rig wat
Wy
A
UA
FIG. 224. EFFECT OF WAI
MOVEMENT.
m SOL MECHANICS AND FOUNDATIONS
6. Evaluation of moment M, produced by P,
mp
120;
7. Evaluation of vertical reaction R : Modulus of vertical subgrade reaction is
= Dy de = BL apt 4D, 0? + Di 227.19)
where pe vertical deflection of soil corresponding to vertical reaction P = py
an an
R=2)" pacar)” api de
% o
or B= kB (27.20)
8. Evaluation of moment M, produced at the base due to vertical soil reaction p
‘The rotation of the well is also resisted by a moment M, acting at the base on
account of the downward deflection of the toc and upward deflection of the heel. Fig.
27.8 shows the rotation of the base, with displacement p, at the ends. Let p be the
defleetion at a distance x from the centre O of the base.
a oe]
FIG. 278 ROTATION OF BASE.
Meg a2)
This moment acts in clockwise direction for the present case of Fig. 27.5 (a).
9. Evaluation of mp, on the basis of maximum soil pressure
If no plastic low is allowed in the soil, horizontal soil reaction p at any depth
must not exceed (Poma for that depih, given by
(dea = 12 (Kp ~ Ke) 21.22)
E Ko (27.23)
6. Evaluation of moment M, produced by P,
mp
120;
7. Evaluation of vertical reaction R : Modulus of vertical subgrade reaction is
= Dy de = BL apt 4D, 0? + Di 227.19)
where pe vertical deflection of soil corresponding to vertical reaction P = py
an an
R=2)" pacar)” api de
% o
or B= kB (27.20)
8. Evaluation of moment M, produced at the base due to vertical soil reaction p
‘The rotation of the well is also resisted by a moment M, acting at the base on
account of the downward deflection of the toc and upward deflection of the heel. Fig.
27.8 shows the rotation of the base, with displacement p, at the ends. Let p be the
defleetion at a distance x from the centre O of the base.
a oe]
FIG. 278 ROTATION OF BASE.
Meg a2)
This moment acts in clockwise direction for the present case of Fig. 27.5 (a).
9. Evaluation of mp, on the basis of maximum soil pressure
If no plastic low is allowed in the soil, horizontal soil reaction p at any depth
must not exceed (Poma for that depih, given by
(dea = 12 (Kp ~ Ke) 21.22)
E Ko (27.23)
WELL FOUNDATIONS E
is in contact with soil and the remaining portion is only held by skin friction. A three-point
support of the cutting edge resting on a log may be assumed for design purposes. The
load coming on the cutting edge is unceruin as a considerable part of it is borne by
skin friction, Another factor of uncertainty is in regard to the effective depth of the well
curb, since the entre well acts as a deep girder to resist torsion and bending. Since the
Toad is occasional, working stress upto 99% of yield stress may be permitted, The well
‘curb has also to withstand stress due to sand blows, as well as due to light blasting
required when boulder obstrucis the sinking of the well
Cutting edge. The cutting edge should have as sharp an angle as practicable for
koifing into the soil without making it too weak to resist the various stresses induced by
boulders, blows, blasting. etc. An angle to the vertical of 30°, or a slope of 1 horizontal
10 2 vertical has been found satisfactory in practice. In concrete caissons, the lower portion
of the cutting edge is wrapped with 12 mm steel plates which are anchored to the concrete
by means of steel straps. A sharp vertical edge is generally provided along the outside
face of the caisson. Such an edge facilitates the rate of sinking and prevents air leakage
in the case of pneumatic casissons,
Steining thickness. The thickness of steining is designed in such a way Wat at all
stages the well can be sunk under its own weight, as the need for weighting with kendedge
takes time and retards progress considerably. For a circular well with outer diameter D
and thickness 1 of the steining. we have
Self-weight per unit height= x (D- 01 p
Skin friction force per unit weight = xD 1
where paunit weight of concrete or masonry of the steining
‘y= unit skin friction
Equating the vo. we ger m(D-mp=nD iy
From which SE] 07:46)
Ik wl be see from tis equation at for given value of sin fico, de using
ictus comes cue o be Mest Wi ices, vale of iter of th vel. THs br
however. comary 1 the nal race of providing gene ticks of ching wih ice
diameter of te’ well a given in te folios ule:
D (outside diameter of well 1 (steining thickness)
3m 0.75 m
sm 120 m
Tm 2.00 m
‘This is so because large diameter wells are taken deeper and the skin friction increases
with depth. Moreover, for deeper wells, water is invariably met with and the effective
selfsweight is reduced by buoyancy in the portion of the well below water level, and bence
larger steining thickness is required.
is in contact with soil and the remaining portion is only held by skin friction. A three-point
support of the cutting edge resting on a log may be assumed for design purposes. The
load coming on the cutting edge is unceruin as a considerable part of it is borne by
skin friction, Another factor of uncertainty is in regard to the effective depth of the well
curb, since the entre well acts as a deep girder to resist torsion and bending. Since the
Toad is occasional, working stress upto 99% of yield stress may be permitted, The well
‘curb has also to withstand stress due to sand blows, as well as due to light blasting
required when boulder obstrucis the sinking of the well
Cutting edge. The cutting edge should have as sharp an angle as practicable for
koifing into the soil without making it too weak to resist the various stresses induced by
boulders, blows, blasting. etc. An angle to the vertical of 30°, or a slope of 1 horizontal
10 2 vertical has been found satisfactory in practice. In concrete caissons, the lower portion
of the cutting edge is wrapped with 12 mm steel plates which are anchored to the concrete
by means of steel straps. A sharp vertical edge is generally provided along the outside
face of the caisson. Such an edge facilitates the rate of sinking and prevents air leakage
in the case of pneumatic casissons,
Steining thickness. The thickness of steining is designed in such a way Wat at all
stages the well can be sunk under its own weight, as the need for weighting with kendedge
takes time and retards progress considerably. For a circular well with outer diameter D
and thickness 1 of the steining. we have
Self-weight per unit height= x (D- 01 p
Skin friction force per unit weight = xD 1
where paunit weight of concrete or masonry of the steining
‘y= unit skin friction
Equating the vo. we ger m(D-mp=nD iy
From which SE] 07:46)
Ik wl be see from tis equation at for given value of sin fico, de using
ictus comes cue o be Mest Wi ices, vale of iter of th vel. THs br
however. comary 1 the nal race of providing gene ticks of ching wih ice
diameter of te’ well a given in te folios ule:
D (outside diameter of well 1 (steining thickness)
3m 0.75 m
sm 120 m
Tm 2.00 m
‘This is so because large diameter wells are taken deeper and the skin friction increases
with depth. Moreover, for deeper wells, water is invariably met with and the effective
selfsweight is reduced by buoyancy in the portion of the well below water level, and bence
larger steining thickness is required.
m SOIL MECHANICS AND FOUNDATIONS
use of phawrah Jhams is effective. When power winches are available clayey strata can
alo be succesflly excavated with the help of big grabs having tempered sos tet
As the well sinks decper, the skin friction on the sides progrestvely increases. To
‘overcome the inessed skin freon and the loss in weight of the well des to buoyancy.
ditional loading known as enedge is applied on the well
Pumping out the water fom inside the weil is effective in sinking of well under
ceruin conditions. Pumping should be discouraged in the inital stage. Usless the well has
gone deep enough or has passed through a ring of clayey stain so that chances of tts
And shis are minimised during this process. Complete dewatering. should not be allowed
when the well has been sunk to about 10 m depth. Sinking thereafter should be done
by grabbing. chseling, applying kemiedge and using gelignte charges. Only when these
meiods have failed, dowatering. may be allowed upio depressed water level of 5 m and
fot mare
On certain occasions a well is struck up and normal method of kentledge and dredging
fal to sink it further. In such a case frictional resistance developed on its outer periphery
reduced considerably by forcing jet of water on the outer face of the weil around.
This method is effective in case Me well is being sunk in sand strata
4. Tits and Shifts, The primary aim in well sinking is to sink them stright and
at the correct positon, Suitable precautions should be taken to avoid tks and shi. Alo
proper records of is and shis should be maimained and measure should be taken 10
counteract tits and shifts, The precsutions to avoid tits and shifts are as follows
1. The outer surface of the well curb and steining should be as regular and sooth
as possible.
2. The radius of curb should be kept 2 10 4 cm larger than the ouside radius
of weil seining
3. The cuting edge of the curb should be of unfrom thickness and sharpness since
the sharper edge has a grater tendency of sinking than a blunt cdge.
4. The dredging should be done uniformly on all sides in a circular well and in
etn pockets of a twin well, The dls and shits of well, if any, must be carefully checked
and recorded. The correct measurement of the tts at any stage is pethaps one of the
most important field observations required during well sinking.
AS soon as tlt exceeds 1 in 200, the sinking should be supervised with special
care and recifying measures should be inmedinely taken. Any of the following measures
can usefully be employed to counteract the tilts in the well during sinking operations
(D Regulation of grabbing. Uncqual dredging causes tilts and hence if higher side
is grabbed more by regulating the dredging, the tilt can be rectified (Fig. 27.12. (a)].
This method is not very effective when the well has been sunk lo a great depth. In that
case, a hole in the steining of the well is made on the higher side, and by hocks, the
rope of the grab is pulled towards higher side to the maximum possible extent (Fig. 27.12
(6)]. The hole is made near the ground level. The well may be dewatered if possible
and open excavation on the higher side is carried out.
use of phawrah Jhams is effective. When power winches are available clayey strata can
alo be succesflly excavated with the help of big grabs having tempered sos tet
As the well sinks decper, the skin friction on the sides progrestvely increases. To
‘overcome the inessed skin freon and the loss in weight of the well des to buoyancy.
ditional loading known as enedge is applied on the well
Pumping out the water fom inside the weil is effective in sinking of well under
ceruin conditions. Pumping should be discouraged in the inital stage. Usless the well has
gone deep enough or has passed through a ring of clayey stain so that chances of tts
And shis are minimised during this process. Complete dewatering. should not be allowed
when the well has been sunk to about 10 m depth. Sinking thereafter should be done
by grabbing. chseling, applying kemiedge and using gelignte charges. Only when these
meiods have failed, dowatering. may be allowed upio depressed water level of 5 m and
fot mare
On certain occasions a well is struck up and normal method of kentledge and dredging
fal to sink it further. In such a case frictional resistance developed on its outer periphery
reduced considerably by forcing jet of water on the outer face of the weil around.
This method is effective in case Me well is being sunk in sand strata
4. Tits and Shifts, The primary aim in well sinking is to sink them stright and
at the correct positon, Suitable precautions should be taken to avoid tks and shi. Alo
proper records of is and shis should be maimained and measure should be taken 10
counteract tits and shifts, The precsutions to avoid tits and shifts are as follows
1. The outer surface of the well curb and steining should be as regular and sooth
as possible.
2. The radius of curb should be kept 2 10 4 cm larger than the ouside radius
of weil seining
3. The cuting edge of the curb should be of unfrom thickness and sharpness since
the sharper edge has a grater tendency of sinking than a blunt cdge.
4. The dredging should be done uniformly on all sides in a circular well and in
etn pockets of a twin well, The dls and shits of well, if any, must be carefully checked
and recorded. The correct measurement of the tts at any stage is pethaps one of the
most important field observations required during well sinking.
AS soon as tlt exceeds 1 in 200, the sinking should be supervised with special
care and recifying measures should be inmedinely taken. Any of the following measures
can usefully be employed to counteract the tilts in the well during sinking operations
(D Regulation of grabbing. Uncqual dredging causes tilts and hence if higher side
is grabbed more by regulating the dredging, the tilt can be rectified (Fig. 27.12. (a)].
This method is not very effective when the well has been sunk lo a great depth. In that
case, a hole in the steining of the well is made on the higher side, and by hocks, the
rope of the grab is pulled towards higher side to the maximum possible extent (Fig. 27.12
(6)]. The hole is made near the ground level. The well may be dewatered if possible
and open excavation on the higher side is carried out.
m SOIL. MECHANICS AND FOUNDATIONS
In larger size wells to be sunk to great depths, eccentric loading may be as much
as 400 to 600 tonnes with an eccentricity of 3 10 4 m. In such a case a welded frame
bracket is used as shown in (Fig, 27.12 (ol.
Ki) Water jeting or digging pit outside the higher side of the well. In this method,
water jet is forced on the outer faces of the well, towards the higher side so that skin
friction is reduced towards the higher side. The method if used alone is not very effective
but provides a contributory effect if used with other methods.
(is) Excavation under the cutting edge. A filled well generally. refuses 10 straighten
‘on account of unbroken stiff strata on the higher side of the well. In such a case, the
well is dewatered, if possible and safe, an open excavation is done below the cutting edge
of the higher side. If dewatering is unsafe, divers should be sem to loosen the strata
€ Providing temporary obstacles below the cutting edge. In some cases wooden
sleeper pieces are put temporarily below the curing edge of the well on the lower side
to avoid further tlt of the well while various expedients are being tempted to rectify the
ü [Fig. 27.12 (@]. Hooking the cutting edge on the lower side of the weil with the
help of the steel wire rope. pulled. and kept strained by steam which also has a similar
effet (Fig. 27.12 (ol.
(vi) Pulling the well. This method is effective only in early stages of sinking. The
Well is pulled towards the higher side by placing one or more steel ropes round the well with
vertical sleepers packed in between to distribute the pressure over larger areas of well
stcining. The pulling of ropes may be carried out by winches [Fig. 27.12 (IL
(vit) Sruting the well. This method is used to avoid any further increase in the
Gilt of the well rather than rectifying it. The well is strutted on its tilted side with suitable
logs of wood. The well steining is given covering plate to distribute pressure. The other
ces of the logs rest against firm and non-yielding base by driving piles ete. Wood pieces
are Kept ready to be inserted and fixed in the gaps caused by the tilts of the well being
rectified
(ii) Pushing by jacks. The well may be pushed by force applied by hydraulic oF
mechanical jack on the tilted side of the wells
27.9. PNEUMATIC CAISSONS
Pneumatic caissons are closed at the top and open (during construction) atthe bottom,
‘The essential feature of a pneumatic caisson is that compressed air is used to exclude or remove
water from the working chamber at the bottom, and the excavations are thus carried out
in dry conditions. The method of construction of prcumatic caisson is similar to that for
open calssons (wells) except that the working chamber is kept airtight, In order that sub-soil
water may not enter the working chamber, the pressure of air in the shaft is kept just
higher than that of the water at that depth, However, the maximum pressure is timited
from the considerations of health of persons who work inside the chamber. Normally, the
tolerable air pressure under which a man can work is limited 10 3.5 kg/cm
Let h be the height of water, at any stage of working. Then air pressure p required
10 exclude water is given by
In larger size wells to be sunk to great depths, eccentric loading may be as much
as 400 to 600 tonnes with an eccentricity of 3 10 4 m. In such a case a welded frame
bracket is used as shown in (Fig, 27.12 (ol.
Ki) Water jeting or digging pit outside the higher side of the well. In this method,
water jet is forced on the outer faces of the well, towards the higher side so that skin
friction is reduced towards the higher side. The method if used alone is not very effective
but provides a contributory effect if used with other methods.
(is) Excavation under the cutting edge. A filled well generally. refuses 10 straighten
‘on account of unbroken stiff strata on the higher side of the well. In such a case, the
well is dewatered, if possible and safe, an open excavation is done below the cutting edge
of the higher side. If dewatering is unsafe, divers should be sem to loosen the strata
€ Providing temporary obstacles below the cutting edge. In some cases wooden
sleeper pieces are put temporarily below the curing edge of the well on the lower side
to avoid further tlt of the well while various expedients are being tempted to rectify the
ü [Fig. 27.12 (@]. Hooking the cutting edge on the lower side of the weil with the
help of the steel wire rope. pulled. and kept strained by steam which also has a similar
effet (Fig. 27.12 (ol.
(vi) Pulling the well. This method is effective only in early stages of sinking. The
Well is pulled towards the higher side by placing one or more steel ropes round the well with
vertical sleepers packed in between to distribute the pressure over larger areas of well
stcining. The pulling of ropes may be carried out by winches [Fig. 27.12 (IL
(vit) Sruting the well. This method is used to avoid any further increase in the
Gilt of the well rather than rectifying it. The well is strutted on its tilted side with suitable
logs of wood. The well steining is given covering plate to distribute pressure. The other
ces of the logs rest against firm and non-yielding base by driving piles ete. Wood pieces
are Kept ready to be inserted and fixed in the gaps caused by the tilts of the well being
rectified
(ii) Pushing by jacks. The well may be pushed by force applied by hydraulic oF
mechanical jack on the tilted side of the wells
27.9. PNEUMATIC CAISSONS
Pneumatic caissons are closed at the top and open (during construction) atthe bottom,
‘The essential feature of a pneumatic caisson is that compressed air is used to exclude or remove
water from the working chamber at the bottom, and the excavations are thus carried out
in dry conditions. The method of construction of prcumatic caisson is similar to that for
open calssons (wells) except that the working chamber is kept airtight, In order that sub-soil
water may not enter the working chamber, the pressure of air in the shaft is kept just
higher than that of the water at that depth, However, the maximum pressure is timited
from the considerations of health of persons who work inside the chamber. Normally, the
tolerable air pressure under which a man can work is limited 10 3.5 kg/cm
Let h be the height of water, at any stage of working. Then air pressure p required
10 exclude water is given by
m6 SOI. MECHANICS AND FOUNDATIONS
inside the well. The air lock may rest on rubber seals just above the cutting edge. The
number of air locks may vary from one 10 three. Geserally, two air locks are used —
one for sending men inside and the other for moving the excavated material with the help
of a much bucket and hoisting rope.
3. After properly placing the air lock in position, so that direct air entry is sealed,
water is pumped out from the bottom and air pressure is gradually increased so that fresh
water does not enter the working chamber.
4. Labourers are then sent down to the working chamber, through the appropriate
air lock. In order to prevent leakage of air, arrangement of double gates is provided.
‘The person enters the first gate, where pressure is atmospheric, The first door is closed
and pressure is gradually increased to make it equal to the one in the working chamber.
‘The height of working chamber is kept about 2 m, with proper lighting arrangement. Air
is supplied through the air inlet pipe connected to an air compressor.
5. Excavation is carried out in the working chamber by the labourers sent down
Hough air lock. The excavated material is sent up through the muck buckets lifted up
by a hoisting rope operated by winch drum, through the air lock. In order to assist sinking.
air pressure may be reduced for a short while, Sometimes, explosives may be employed
im which case it is essential to make arrangements for the immediate removal of fall fumes.
6. When the caisson bottom has reached the desired level, concrete seal (or plug)
is made by concreting upto the underside roof of the working chamber. Sufficient air pressure
is maimained to force the concrete against the bottom surface ill it hardens.
7. Air locks are removed, well ls filled with sand or water (or even kept empty).
‘The well cap is then formed on lis top as usual
inside the well. The air lock may rest on rubber seals just above the cutting edge. The
number of air locks may vary from one 10 three. Geserally, two air locks are used —
one for sending men inside and the other for moving the excavated material with the help
of a much bucket and hoisting rope.
3. After properly placing the air lock in position, so that direct air entry is sealed,
water is pumped out from the bottom and air pressure is gradually increased so that fresh
water does not enter the working chamber.
4. Labourers are then sent down to the working chamber, through the appropriate
air lock. In order to prevent leakage of air, arrangement of double gates is provided.
‘The person enters the first gate, where pressure is atmospheric, The first door is closed
and pressure is gradually increased to make it equal to the one in the working chamber.
‘The height of working chamber is kept about 2 m, with proper lighting arrangement. Air
is supplied through the air inlet pipe connected to an air compressor.
5. Excavation is carried out in the working chamber by the labourers sent down
Hough air lock. The excavated material is sent up through the muck buckets lifted up
by a hoisting rope operated by winch drum, through the air lock. In order to assist sinking.
air pressure may be reduced for a short while, Sometimes, explosives may be employed
im which case it is essential to make arrangements for the immediate removal of fall fumes.
6. When the caisson bottom has reached the desired level, concrete seal (or plug)
is made by concreting upto the underside roof of the working chamber. Sufficient air pressure
is maimained to force the concrete against the bottom surface ill it hardens.
7. Air locks are removed, well ls filled with sand or water (or even kept empty).
‘The well cap is then formed on lis top as usual
Machine Foundations
28.1. SOIL DYNAMICS
Soil dynamics is defined as that constituent part of soil mechanics which deals with
soil under dynamic conditions. It studies the effect of forces on soil in any way associated
with causing motions in soil as well as with the mutual dynamic interaction of the foundation
and soil (Jumikis. 1969). Most of the motions encountered in soil dynamics work are those
of vibracion, plane lincar motion, motion brought about by impact, shock, elastic. waves,
and seismic’ action of geophysical forces
“The design of foundations of turbines, motors, generators compressors, forge hammers
and other machines, having a rhythmic application of unbalanced forces require special knowledge
of theory of harmonic vibrations. Inertial forces of rotting elements of machines contribute,
besides their static loads, additional dynamic loads. The machinery vibration influences adversely
the foundation supporting soil by densifying it which may ia tum, casue differential setlement
of soil and foundation,
28.2. THE MASS SPRING SYSTEM
In soil dynamics problems, the analysis may be convenienily carried out by a single
equivalent mass supported by a perfectly elastic system —the soil being replaced by the
spring. Fig. 28.1 shows mass-spring system (or spring-
mass system), in which the weight Wamg may be
associated with the weight of the vibrating vibrator
‘foundations. The elastic spring represents the real
sol support. Such a system has six degrees of freedom,
and has thus six natural frequencies.
Free-Vibrations. Let the mass spring system
be set to vibration by an extemal force which is
in removed. The system will continue to oxcillate
Wefigitely with the same frequency and amplitude
if external force or internal friction is absent. The
time for one complete oscillation of the mass is
called the free period and the distance up or down
from the equilibrium position is called the amplitude, FIG. 281, MASSSPRING SYSTEM.
om
28.1. SOIL DYNAMICS
Soil dynamics is defined as that constituent part of soil mechanics which deals with
soil under dynamic conditions. It studies the effect of forces on soil in any way associated
with causing motions in soil as well as with the mutual dynamic interaction of the foundation
and soil (Jumikis. 1969). Most of the motions encountered in soil dynamics work are those
of vibracion, plane lincar motion, motion brought about by impact, shock, elastic. waves,
and seismic’ action of geophysical forces
“The design of foundations of turbines, motors, generators compressors, forge hammers
and other machines, having a rhythmic application of unbalanced forces require special knowledge
of theory of harmonic vibrations. Inertial forces of rotting elements of machines contribute,
besides their static loads, additional dynamic loads. The machinery vibration influences adversely
the foundation supporting soil by densifying it which may ia tum, casue differential setlement
of soil and foundation,
28.2. THE MASS SPRING SYSTEM
In soil dynamics problems, the analysis may be convenienily carried out by a single
equivalent mass supported by a perfectly elastic system —the soil being replaced by the
spring. Fig. 28.1 shows mass-spring system (or spring-
mass system), in which the weight Wamg may be
associated with the weight of the vibrating vibrator
‘foundations. The elastic spring represents the real
sol support. Such a system has six degrees of freedom,
and has thus six natural frequencies.
Free-Vibrations. Let the mass spring system
be set to vibration by an extemal force which is
in removed. The system will continue to oxcillate
Wefigitely with the same frequency and amplitude
if external force or internal friction is absent. The
time for one complete oscillation of the mass is
called the free period and the distance up or down
from the equilibrium position is called the amplitude, FIG. 281, MASSSPRING SYSTEM.
om
m SOIL. MECHANICS AND FOUNDATIONS
Fig. 282 (0) shows a simple spring with a spring constant k kg/m. When a weight
W is attached to it (without any vibrations), it extends by an amount 5, [Fig. 28.2 (DJ
‘The static deflection 8, of the apring is given by
4)
FIG. 282. FREE VIBRATIONS.
IF the the spring mass system is pulled down, by an external force, by a maximum
distance ag of A, (called the ample), and then released, the whole system vibrates
With a certain frequency. Let < be the displacement of the mass at any instant, with respect
lo the equilibrium position, the force F, in the spring (t) is then given by
Fink Gt delt Weiz 082)
‘The force acts in the opposite direction to the motion at any instant. The gravity
force W acts downward. Hence when the motion is downward, the net downward force
is equal to W4~(W+ ko). This must be equal to mass x acceleration, Hence, we get
Was
w-w+t)= Y
CALE
wer
Métipe 283 0)
or ete? 283 a)
‘which is usually writen as mi +R
Were memass of the vibrating body
Y = acceleration
Eq, 28.3 is called the equation of motion, which is similar to the following standard
equation of motion
283)
we
Frofz=
‘where oy = natural frequency of the system.
Comparing Eqs, 283 and 28.4,
084)
Fig. 282 (0) shows a simple spring with a spring constant k kg/m. When a weight
W is attached to it (without any vibrations), it extends by an amount 5, [Fig. 28.2 (DJ
‘The static deflection 8, of the apring is given by
4)
FIG. 282. FREE VIBRATIONS.
IF the the spring mass system is pulled down, by an external force, by a maximum
distance ag of A, (called the ample), and then released, the whole system vibrates
With a certain frequency. Let < be the displacement of the mass at any instant, with respect
lo the equilibrium position, the force F, in the spring (t) is then given by
Fink Gt delt Weiz 082)
‘The force acts in the opposite direction to the motion at any instant. The gravity
force W acts downward. Hence when the motion is downward, the net downward force
is equal to W4~(W+ ko). This must be equal to mass x acceleration, Hence, we get
Was
w-w+t)= Y
CALE
wer
Métipe 283 0)
or ete? 283 a)
‘which is usually writen as mi +R
Were memass of the vibrating body
Y = acceleration
Eq, 28.3 is called the equation of motion, which is similar to the following standard
equation of motion
283)
we
Frofz=
‘where oy = natural frequency of the system.
Comparing Eqs, 283 and 28.4,
084)
MACHINE FOUNDATIONS m
If fy is the natural frequency of the system in eyes per second, we have
00 1 4e
A VE cpctesses. 1428.6)
283. VIBRATING SPRING-MASS SYSTEM WITH DAMPING
IF the spring mas system de provided with
Tio
RL ee oe oe nd |
Saree LL er
Ga os cil. ees waka tat
W¿-(W+koP=cita mi
eee
Comparing this with the standard equation
for
028.8)
28.9)
FIG. 28.3. VIBRATING SPRING MASS
SYSTEM WITH DAMPING
Eq. 28.8 is the standard differential equation which can be solved by puting
et RT ER «(28.10 0)
Putting these in Eq. 28.7, we got
E] 28.10)
or m+e+k=0
428.11)
Hence dant V0 and
“Three cases may arise from Eq. 28.11 :
Cae (D Rea, Unna}
Case (ii) Zero, if =o)
Case (ip Imaginary or complex if a <a?
Case (il) gives a value of
If fy is the natural frequency of the system in eyes per second, we have
00 1 4e
A VE cpctesses. 1428.6)
283. VIBRATING SPRING-MASS SYSTEM WITH DAMPING
IF the spring mas system de provided with
Tio
RL ee oe oe nd |
Saree LL er
Ga os cil. ees waka tat
W¿-(W+koP=cita mi
eee
Comparing this with the standard equation
for
028.8)
28.9)
FIG. 28.3. VIBRATING SPRING MASS
SYSTEM WITH DAMPING
Eq. 28.8 is the standard differential equation which can be solved by puting
et RT ER «(28.10 0)
Putting these in Eq. 28.7, we got
E] 28.10)
or m+e+k=0
428.11)
Hence dant V0 and
“Three cases may arise from Eq. 28.11 :
Cae (D Rea, Unna}
Case (ii) Zero, if =o)
Case (ip Imaginary or complex if a <a?
Case (il) gives a value of
sm SOIL MECHANICS AND FOUNDATIONS
Eq. 28.11 for case (i) reduces 10 e* "0, indicating that for this condition there
will be no oscillation, but only a rapid retum back to the equilibrium postion of the
mass [Fig28:4 (b)). The value of c for this condition is called critical damping. «.
cam VE = 2k (28.12)
For case (9, the radical is real (mM>0,) , and ¢22Vmk.
ai
Nal
Heu tom (O. ace VED! extn
Eq. 28.13 shows that z is not a periodic function of time. Therefore, the motion,
When m0 >0 is not a vibration, because it can only approach the equilirium postion
st 6, However, the viscous resistance is so pronounced that the weight set in motion
fiom its equilibrium does not vibrate but creeps gradually tack to the equilibrium position
at time infinity (Fig. 284 (al. For case di) when <oz à
wi-ui- is positive or c<2 Vik
Let 2, and A, be the two
roots of Eq. 28.11 : à 1
h==ntod 0814 0)
and
he
-nosi 08.14 6)
Now Eq, 28.10 (a) gives — —
two particular solutions of Eq. (Cate e" 0. (Were fn we,
288. Also, the sum or dif.
ference of these two solutions mal-
‘plied by any constant is also a
solution +
A
arte) y
815 0)
Ge Qty get
a artes)
08.15 D)
where G, and €, are constants.
Subsituing the valves of
By 2309 dao Ba 28.14, an FIG. 28.4. TIME DISPLACEMENT CURVES FOR
simplifying, we get OS TDAMPED. VIBRATIONS
AS
ae Gé" sn os and Gets
Summation of 2, +2,» 2 renders the general solution of Eq. 28.8 in the following form.
Eq. 28.11 for case (i) reduces 10 e* "0, indicating that for this condition there
will be no oscillation, but only a rapid retum back to the equilibrium postion of the
mass [Fig28:4 (b)). The value of c for this condition is called critical damping. «.
cam VE = 2k (28.12)
For case (9, the radical is real (mM>0,) , and ¢22Vmk.
ai
Nal
Heu tom (O. ace VED! extn
Eq. 28.13 shows that z is not a periodic function of time. Therefore, the motion,
When m0 >0 is not a vibration, because it can only approach the equilirium postion
st 6, However, the viscous resistance is so pronounced that the weight set in motion
fiom its equilibrium does not vibrate but creeps gradually tack to the equilibrium position
at time infinity (Fig. 284 (al. For case di) when <oz à
wi-ui- is positive or c<2 Vik
Let 2, and A, be the two
roots of Eq. 28.11 : à 1
h==ntod 0814 0)
and
he
-nosi 08.14 6)
Now Eq, 28.10 (a) gives — —
two particular solutions of Eq. (Cate e" 0. (Were fn we,
288. Also, the sum or dif.
ference of these two solutions mal-
‘plied by any constant is also a
solution +
A
arte) y
815 0)
Ge Qty get
a artes)
08.15 D)
where G, and €, are constants.
Subsituing the valves of
By 2309 dao Ba 28.14, an FIG. 28.4. TIME DISPLACEMENT CURVES FOR
simplifying, we get OS TDAMPED. VIBRATIONS
AS
ae Gé" sn os and Gets
Summation of 2, +2,» 2 renders the general solution of Eq. 28.8 in the following form.
MACHINE FOUNDATIONS m
2e €" [Cy sin or + C cos weil
‘The quantity in the bracket represents the simple harmonic motion of the case of
vibration without damping while e" is the damping term. Fig. 28.4 (c) shows the time
displacement curve for this case. The peroid T of the damped vibration is given by
2x
Vel 28.17)
The term oy is called the frequency of damped vibrations.
or 28.18)
28.4, FORCED VIBRATIONS
Forced vibrations of a system are generated and sustained by the application of an
‘external periodic movement of the foundation of the system. Forced vibrations constiute
the most importar type of vibration in machine foundation design. We shall consider the
case of forced vibrations with damping. Generally, for oscillating machinery (where the
machinery vibrates because an unbalanced rotational force exists) the force can be expressed
as a sine or cosine function, such as Fasin or. The equation of motion for such a case
may be writen as
mi + c+ de Fe sin or 28.19)
“ sinus 08.9 à
Te soon of Ge above quon may be sumed ia de flowing forms
Loi mars baled 82 0)
By scie fernen, we ein
Endes of B carat „and
E = - do! cos of ~ Ba? sin or 428.20 0)
Substituing into Eq. 28.19 (a), we get
(Ae? con ot = Bo na + E Co sin a Do os 4 E a cos ar no = En ot
lea
Bain he ef of nar both sits,
“uen à ano
Sims, equing te ‘oes of cos wt both ids,
a+ Ets Lace csm»
Solving Eqs. 28.22 (a) and (b) for coefficients A and B, we get
2e €" [Cy sin or + C cos weil
‘The quantity in the bracket represents the simple harmonic motion of the case of
vibration without damping while e" is the damping term. Fig. 28.4 (c) shows the time
displacement curve for this case. The peroid T of the damped vibration is given by
2x
Vel 28.17)
The term oy is called the frequency of damped vibrations.
or 28.18)
28.4, FORCED VIBRATIONS
Forced vibrations of a system are generated and sustained by the application of an
‘external periodic movement of the foundation of the system. Forced vibrations constiute
the most importar type of vibration in machine foundation design. We shall consider the
case of forced vibrations with damping. Generally, for oscillating machinery (where the
machinery vibrates because an unbalanced rotational force exists) the force can be expressed
as a sine or cosine function, such as Fasin or. The equation of motion for such a case
may be writen as
mi + c+ de Fe sin or 28.19)
“ sinus 08.9 à
Te soon of Ge above quon may be sumed ia de flowing forms
Loi mars baled 82 0)
By scie fernen, we ein
Endes of B carat „and
E = - do! cos of ~ Ba? sin or 428.20 0)
Substituing into Eq. 28.19 (a), we get
(Ae? con ot = Bo na + E Co sin a Do os 4 E a cos ar no = En ot
lea
Bain he ef of nar both sits,
“uen à ano
Sims, equing te ‘oes of cos wt both ids,
a+ Ets Lace csm»
Solving Eqs. 28.22 (a) and (b) for coefficients A and B, we get
on SOIL MECHANICS AND FOUNDATIONS
Folk ma’
a Be RAM ag 23 by
17 + (cay ma + (Co?
Substiuring these in Eq. 28.20 (a), we get the solution in the form
Foco Fo (kmo!) sin ot
coso (28:24)
(ca + (= mu Y (a+ k= may
“The equation represents the components due to forced vibrations with the period of
T= E. The frequency fo vibrations (in cycles per second) à
given by
E 28.25 a)
“Tie natural frequency of vibration, as defined carter, is given by
28.25 b)
and 0825 ©
‘Substituting in
Peco
write = 2 008 $...08.26 D)
we get 22 2: (in 4 cos wtcos à sin of)mzs sin (044) am
where the angle 6 is termed as the phase angle between the exciting force and the motion
of vi
ing mass,
[Noting that these terms represent a pair of vectors which must be added to obtain
the displacement, the solution for the displacement due to the forced vibrations of Eq.
28.24 becomes
VOTE resin or + 9) (28.28)
Subsuing the values of A and B, and noting from Eg. 28.12 that
or et 28.29 b)
sin (or +) 830 0)
2830 0)
The maximum deflection ¿mas is thus given by
Folk ma’
a Be RAM ag 23 by
17 + (cay ma + (Co?
Substiuring these in Eq. 28.20 (a), we get the solution in the form
Foco Fo (kmo!) sin ot
coso (28:24)
(ca + (= mu Y (a+ k= may
“The equation represents the components due to forced vibrations with the period of
T= E. The frequency fo vibrations (in cycles per second) à
given by
E 28.25 a)
“Tie natural frequency of vibration, as defined carter, is given by
28.25 b)
and 0825 ©
‘Substituting in
Peco
write = 2 008 $...08.26 D)
we get 22 2: (in 4 cos wtcos à sin of)mzs sin (044) am
where the angle 6 is termed as the phase angle between the exciting force and the motion
of vi
ing mass,
[Noting that these terms represent a pair of vectors which must be added to obtain
the displacement, the solution for the displacement due to the forced vibrations of Eq.
28.24 becomes
VOTE resin or + 9) (28.28)
Subsuing the values of A and B, and noting from Eg. 28.12 that
or et 28.29 b)
sin (or +) 830 0)
2830 0)
The maximum deflection ¿mas is thus given by
MACHINE FOUNDATIONS m
lk
ete een
Vee gfe]
bu o, te déc of stag
a
Ed ad IF ma «(28,31 a)
CIN
me Aime mamma de af em
ating 45-255 ue more fuer or danie anplfcaion factor
Pa faro pony rato ns
Lo T T
TPE HY Y
Fig. 28.5 shows a plot between Leo
the magnification factor andthe fe-
Fe Le) for var:
user rao {= Le 2) for va
== damping ratio, we get
ain
ous values of damping ratio F | 4
Prom Fig. 28.5, itis obser
that magnification factor suddenly E quo. 7
Shoots up fr ie vale ofr between
0.60 1.5. Atr = 1, resonance occurs le
for an undamped condition. Even
fee dumped condor, Ge me P
fenton Tor (md ecos the um
linde) is maximum at r < 1 . Thus, 2
these ares show heft amp.
ing on shifting the frequency for E
Magrieaton ato y
maximum amplification away from Lal]
(he natural foundation frequency. The fo oe E
aim of the designer should be such Free to
that the frequency ratio f/f, is either FIG, 285. AMPLITUDE FREQUENCY RELATIONSHIP
less than 0.6 or more than 1.5. How FOR DAMPED FORCED VIBRATIONS.
ever, the frequency / of the machine is always constant, and a foundation engineer has
10 manipulate the nual frequency f, ofthe machine foundation system by suitably proportioning
it
lk
ete een
Vee gfe]
bu o, te déc of stag
a
Ed ad IF ma «(28,31 a)
CIN
me Aime mamma de af em
ating 45-255 ue more fuer or danie anplfcaion factor
Pa faro pony rato ns
Lo T T
TPE HY Y
Fig. 28.5 shows a plot between Leo
the magnification factor andthe fe-
Fe Le) for var:
user rao {= Le 2) for va
== damping ratio, we get
ain
ous values of damping ratio F | 4
Prom Fig. 28.5, itis obser
that magnification factor suddenly E quo. 7
Shoots up fr ie vale ofr between
0.60 1.5. Atr = 1, resonance occurs le
for an undamped condition. Even
fee dumped condor, Ge me P
fenton Tor (md ecos the um
linde) is maximum at r < 1 . Thus, 2
these ares show heft amp.
ing on shifting the frequency for E
Magrieaton ato y
maximum amplification away from Lal]
(he natural foundation frequency. The fo oe E
aim of the designer should be such Free to
that the frequency ratio f/f, is either FIG, 285. AMPLITUDE FREQUENCY RELATIONSHIP
less than 0.6 or more than 1.5. How FOR DAMPED FORCED VIBRATIONS.
ever, the frequency / of the machine is always constant, and a foundation engineer has
10 manipulate the nual frequency f, ofthe machine foundation system by suitably proportioning
it
MACHINE FOUNDATIONS us
or vo NV 28.34 b)
vine Meee of van al
Min ve of te pur sol man
Uvas. de i of eig Body ol mc Ye demi ex
as ya enue I dp on go and ce by soe af he Doe oa
Of Ke nec en aol byte Casi) pops of he sl cp.
‘We all ne eee mets dema he nel ey fanion
soit gem 1) Beets cl) Balken Race cd, ©) Pas
247. BARKEN'S METIOD
Barken suggested the following equation for the natural frequency of system
oe VE ess à
noce reis of die sia compro i
cont aa of fon i ll
insane of mc a Baie
The amplitude of displacement is given by
£
mai (1-7)
we denia mim dicen
2835 0)
Freins force à r= frequency tio = À.
‘The above formulae for natural frequency takes no account of the mass of soil vibrating
‘with the foundations.
Barken gave (he following equation for the co-efficient of elastic uniform compression
of soil, obtained from the solution of theory of elasticity problem concerning the distribution
fof normal stresses under the base contact arca of a rigid plate :
El
Gal 28.36)
m 128.36)
where E= Young's modulus of soll; y= Poisson's ratio
‘Thus, C, depends not only on clastic constants E and jt but also on size of the
base contact area of foundation. The co-effeicient C, changes in inverse proportion 40 the
square root of the base area of the foundation :
Ga far
m. Ya 28.37)
Table 28.1 gives the recommended value of C, for A= 10m, for various soil.
or vo NV 28.34 b)
vine Meee of van al
Min ve of te pur sol man
Uvas. de i of eig Body ol mc Ye demi ex
as ya enue I dp on go and ce by soe af he Doe oa
Of Ke nec en aol byte Casi) pops of he sl cp.
‘We all ne eee mets dema he nel ey fanion
soit gem 1) Beets cl) Balken Race cd, ©) Pas
247. BARKEN'S METIOD
Barken suggested the following equation for the natural frequency of system
oe VE ess à
noce reis of die sia compro i
cont aa of fon i ll
insane of mc a Baie
The amplitude of displacement is given by
£
mai (1-7)
we denia mim dicen
2835 0)
Freins force à r= frequency tio = À.
‘The above formulae for natural frequency takes no account of the mass of soil vibrating
‘with the foundations.
Barken gave (he following equation for the co-efficient of elastic uniform compression
of soil, obtained from the solution of theory of elasticity problem concerning the distribution
fof normal stresses under the base contact arca of a rigid plate :
El
Gal 28.36)
m 128.36)
where E= Young's modulus of soll; y= Poisson's ratio
‘Thus, C, depends not only on clastic constants E and jt but also on size of the
base contact area of foundation. The co-effeicient C, changes in inverse proportion 40 the
square root of the base area of the foundation :
Ga far
m. Ya 28.37)
Table 28.1 gives the recommended value of C, for A= 10m, for various soil.
w SOIL MECHANICS AND FOUNDATIONS
TABLE 28. RECOMMENDED DESIGN VALUES OF THE CO-EFFICIENT OF
ELASTIC UNIFORM COMPRESSION Cy (BARKES, 1962)
EJ sa Pi ander =
gp econ ef ste | compresion Cu Me
cepo sou gent) |
1 [Weak oie (ys and sky cays
sand, ia psc sae, clayey, and sy)
mois ms
tw laminae of organi st ad peat |
1 [Sol of mesi sei (ays and sity]
flay wand, cine oe pia ar 1535 3
and)
IM Song soil (ays and sity cays wi |
Isands of hard consimency. gravels and] 33-8 | 510
[vel sand, loess and lesa sols)
w Rocks Greer tan $ Greater tan 10
288. BULB OF PRESSURE CONCEPT
‘The calculations of aural frequency by Marken took no account of the mass of
soil vibrating, But the work done by DEGEBO indicates that when a vibrating load acts
on a soil, a certain mass of sol ranging from 4 10 5 times the vibratory load partiipaes
in the vibration, Balakrishna and Nagra} (1960) proposed the halb of pressure concept of
calculating the apparent mass of soil participating in the vibration. According lo ths, the
vibrating mass of soil is assumed to be contained by the boundary of a pressure bulb.
For the purpose of simplicity, the load acting on any surface is replaced by an equivalent
concentrated’ load acting at the mass centre of the original area. IF 7 is the uni weight
of the soil in Jeu. ft, then according lo the pressure bulb concept, the apparent mass
‘of the soil is the mass enclosed by che pressure bulb of intensity o, Tisq. A. such that
ely 2838)
For example, if the unit weight of soll is 110 Ieu.f., the apparent mass of the
soil will be the mass of the soil comained by a pressure bulb of intensity 110 Ih
fi From Boussinesq analysis, the verical stress 0; at a depih z and radial distance
0 is given by
soars 2
Hence lyl=oa7s = (28.39)
In the above equation [y| and W, are known,
Hence z= diameter of the pressure bulb is known.
Weis W, of sted (2) y | ET” es
It should be noted that Eq. 28.40 is not dimensionally homogencous, and is applicable
only in F.P.S. units, where W, and W, are in pounds and y is Ihsicu. ft
3
TABLE 28. RECOMMENDED DESIGN VALUES OF THE CO-EFFICIENT OF
ELASTIC UNIFORM COMPRESSION Cy (BARKES, 1962)
EJ sa Pi ander =
gp econ ef ste | compresion Cu Me
cepo sou gent) |
1 [Weak oie (ys and sky cays
sand, ia psc sae, clayey, and sy)
mois ms
tw laminae of organi st ad peat |
1 [Sol of mesi sei (ays and sity]
flay wand, cine oe pia ar 1535 3
and)
IM Song soil (ays and sity cays wi |
Isands of hard consimency. gravels and] 33-8 | 510
[vel sand, loess and lesa sols)
w Rocks Greer tan $ Greater tan 10
288. BULB OF PRESSURE CONCEPT
‘The calculations of aural frequency by Marken took no account of the mass of
soil vibrating, But the work done by DEGEBO indicates that when a vibrating load acts
on a soil, a certain mass of sol ranging from 4 10 5 times the vibratory load partiipaes
in the vibration, Balakrishna and Nagra} (1960) proposed the halb of pressure concept of
calculating the apparent mass of soil participating in the vibration. According lo ths, the
vibrating mass of soil is assumed to be contained by the boundary of a pressure bulb.
For the purpose of simplicity, the load acting on any surface is replaced by an equivalent
concentrated’ load acting at the mass centre of the original area. IF 7 is the uni weight
of the soil in Jeu. ft, then according lo the pressure bulb concept, the apparent mass
‘of the soil is the mass enclosed by che pressure bulb of intensity o, Tisq. A. such that
ely 2838)
For example, if the unit weight of soll is 110 Ieu.f., the apparent mass of the
soil will be the mass of the soil comained by a pressure bulb of intensity 110 Ih
fi From Boussinesq analysis, the verical stress 0; at a depih z and radial distance
0 is given by
soars 2
Hence lyl=oa7s = (28.39)
In the above equation [y| and W, are known,
Hence z= diameter of the pressure bulb is known.
Weis W, of sted (2) y | ET” es
It should be noted that Eq. 28.40 is not dimensionally homogencous, and is applicable
only in F.P.S. units, where W, and W, are in pounds and y is Ihsicu. ft
3
m SOIL MECHANICS AND FOUNDATIONS.
TABLE 282. VALUE OF &% ANDE
Salome Be are) | D (arcano | D Gen) (eit)
Dene sa and geval o CE] 113
Den sen o wos 458
Laos sant o mu 0714
Loue dy snd 1 aus ass
Dene sity snd a 0-40 2040
Ch. sensi 56 — 105 1-2 ons —023
hy. silt plaie 2-5 153 ous 02
Cay, west ph ua 153 ois = 023
‘The spring constant for the truncated pyramid is calculated by first of all determining
de surface deformation 8, given by following infinite integral :
= de
lara 28:44 0)
o f ers ess »
where 1m (a 2b) sh; on ma 0845)
The equivalen sol spring constant Ain che ventcal plane & given by
=F (by definition)
2 — (28,46)
Epa, Gem) (en) Gm,
If the base of foundation is circular, a truncated cone wil be considered in the place
of truncated prism, and the above expression will be modified as under :
= dm
af —a_ Br
Dirt END:
men me meet; beams of de fatto
The values of k are determined by curves of Fig. 28,7 in which £ is given by
the equation
‘k= 0% (Gor rectangular base) 28.48)
and k= FDA (for circular base of dia. 5), (28:48 a)
For given values of St and © ratios, 22 i determined from the cuves, and mus
2 is known, Then A is calelated from Eq, 28.38.
TABLE 282. VALUE OF &% ANDE
Salome Be are) | D (arcano | D Gen) (eit)
Dene sa and geval o CE] 113
Den sen o wos 458
Laos sant o mu 0714
Loue dy snd 1 aus ass
Dene sity snd a 0-40 2040
Ch. sensi 56 — 105 1-2 ons —023
hy. silt plaie 2-5 153 ous 02
Cay, west ph ua 153 ois = 023
‘The spring constant for the truncated pyramid is calculated by first of all determining
de surface deformation 8, given by following infinite integral :
= de
lara 28:44 0)
o f ers ess »
where 1m (a 2b) sh; on ma 0845)
The equivalen sol spring constant Ain che ventcal plane & given by
=F (by definition)
2 — (28,46)
Epa, Gem) (en) Gm,
If the base of foundation is circular, a truncated cone wil be considered in the place
of truncated prism, and the above expression will be modified as under :
= dm
af —a_ Br
Dirt END:
men me meet; beams of de fatto
The values of k are determined by curves of Fig. 28,7 in which £ is given by
the equation
‘k= 0% (Gor rectangular base) 28.48)
and k= FDA (for circular base of dia. 5), (28:48 a)
For given values of St and © ratios, 22 i determined from the cuves, and mus
2 is known, Then A is calelated from Eq, 28.38.
MACHINE FOUNDATIONS m
“Tl z
os
CR -
i i |
E 3
le 20 de
B Eso
o
“ «PH Z
os
n 0081 2 + are
FIG. 28.7. EQUIVALENT SOIL SPRING CONSTANT FOR HORIZONTAL SURFACE.
Pauw developed expression for apparent soil mass m, by equating the kinetic energy
of the effected zone to the kinetic energy of a mass assumed to be concentrated at the
base of the foundation. Following is final form of the expression :
mei (oo de fas Cy a Bon Eh
(Note. The above treatment is valid only if the machine foundation has only one
degree of freedom. ie, for the vibrations taking place in the vertical directon, In the
‘general case, however, the foundation may be considered as a mass having six degrees
of freetom, namely, displacments in the dictions of the tree coordine axes and rotons
about each of these axes.)
After having determined the equiva-
lent spring constant k and apparent soil mass os
mn. the natural frequency of oscillations,
and the amplitude of vibrations are deter- gay 19
mined from the following equations : =" b 20)
PEN Br:
mV mem so]
¿to lineal clan) (28.34 0)
FIG. 288 DETERMINATION OF FACTOR Cu
“Tl z
os
CR -
i i |
E 3
le 20 de
B Eso
o
“ «PH Z
os
n 0081 2 + are
FIG. 28.7. EQUIVALENT SOIL SPRING CONSTANT FOR HORIZONTAL SURFACE.
Pauw developed expression for apparent soil mass m, by equating the kinetic energy
of the effected zone to the kinetic energy of a mass assumed to be concentrated at the
base of the foundation. Following is final form of the expression :
mei (oo de fas Cy a Bon Eh
(Note. The above treatment is valid only if the machine foundation has only one
degree of freedom. ie, for the vibrations taking place in the vertical directon, In the
‘general case, however, the foundation may be considered as a mass having six degrees
of freetom, namely, displacments in the dictions of the tree coordine axes and rotons
about each of these axes.)
After having determined the equiva-
lent spring constant k and apparent soil mass os
mn. the natural frequency of oscillations,
and the amplitude of vibrations are deter- gay 19
mined from the following equations : =" b 20)
PEN Br:
mV mem so]
¿to lineal clan) (28.34 0)
FIG. 288 DETERMINATION OF FACTOR Cu
MACHINE FOUNDATIONS su
á Ber
REE
Example 28.2. Assuming resonance 10 have occured a ¿he frequency of 22 eylessecond
in a vertical Mbration of a tes block, 1.0% 1.0 x 1.0 m she, determine the coeficent
Of elastic uniform in compresion (C,). The weight of oscilator ts 62 Ag and the force
produced by it at 12 cycles per second is 100 kg. Also compuge the maximum amplitude
in vertical direcion at 12 cyclesiecond.
Solution. Où = 2a 2 x 22 Ade
Mass of vibrtor= 2 = 63
5.
Mass of foundation block (concrete) = 1-14 1:40 x 1000
me 6342487 = 251 ; A =comtace area of foundations = 1 m?
Substituting these in the expression for 0%,
o + ve ger @ax22)=
or Ca= (An) (251) = 4.76 x 10" kg/m
Anuplitude Ar
noe (=P)
where Fes total load produced in vertical direction = 100 kg
pa
BJ -03
metres =3% 10" cm.
me2sl ; Oy=2n(Q2)=442 ; P=
. 100
“251 G4m (1-03)
Example 28,3. The resonance of a test block 2 m x I m x J m occurred at
25 ocleshec in the vertical direction. The other data are as follows
Weight of oscillator = 62 kg. Vertical unbalanced force = 0.5 tonnes. Unit weight of
soil = 1.71/m°. Calculate the apparent mass of soil by Balakrishna Rao method.
Seaton. From Ex. 2800109 ¿ny [2755] y
3 4
Wi =1otal load in lbs (ie. weight of machine + foundation + unbalanced force)
Weight of foundation block = 2 x 1 x 2.4 x 100 = 4800. kg
Weight of oscilator=62 kg : Vertical unbalanced force = 500. kg
á Ber
REE
Example 28.2. Assuming resonance 10 have occured a ¿he frequency of 22 eylessecond
in a vertical Mbration of a tes block, 1.0% 1.0 x 1.0 m she, determine the coeficent
Of elastic uniform in compresion (C,). The weight of oscilator ts 62 Ag and the force
produced by it at 12 cycles per second is 100 kg. Also compuge the maximum amplitude
in vertical direcion at 12 cyclesiecond.
Solution. Où = 2a 2 x 22 Ade
Mass of vibrtor= 2 = 63
5.
Mass of foundation block (concrete) = 1-14 1:40 x 1000
me 6342487 = 251 ; A =comtace area of foundations = 1 m?
Substituting these in the expression for 0%,
o + ve ger @ax22)=
or Ca= (An) (251) = 4.76 x 10" kg/m
Anuplitude Ar
noe (=P)
where Fes total load produced in vertical direction = 100 kg
pa
BJ -03
metres =3% 10" cm.
me2sl ; Oy=2n(Q2)=442 ; P=
. 100
“251 G4m (1-03)
Example 28,3. The resonance of a test block 2 m x I m x J m occurred at
25 ocleshec in the vertical direction. The other data are as follows
Weight of oscillator = 62 kg. Vertical unbalanced force = 0.5 tonnes. Unit weight of
soil = 1.71/m°. Calculate the apparent mass of soil by Balakrishna Rao method.
Seaton. From Ex. 2800109 ¿ny [2755] y
3 4
Wi =1otal load in lbs (ie. weight of machine + foundation + unbalanced force)
Weight of foundation block = 2 x 1 x 2.4 x 100 = 4800. kg
Weight of oscilator=62 kg : Vertical unbalanced force = 500. kg
se SOIL MECHANICS AND FOUNDATIONS
Tot Wye $862 kg =11,800 Ib 5 ve 1.7 me 106 I ft
4 angy{ 04775 «11900 PA
win $x og REO 77 21500 10 = 9750 bg
9750 5
me ER gp kg /m
Example 284. Deion the fanden fr a ga ago vi a ma oder ont
veta ring pos Jr de Joa du
1. Total weight of engine = 4500 kg.
2. Speed of rotation = 260 rpm.
3. Unbalanced vertical force = 1 tonne
4. Bee mesons of de eagle “im #25
3. Bien of mech bse don pond aim
Weak silty sand exists 10 a depth of 0.5 m followed by a dense sand toa depth
of 6 m. The unit weight of moist sand is 1,7 1/ m.
Selen. La te ze of heck be 133m a e be of he mui, ani
2x 3m ats aan. La be bight of cn ck be 20 m0 atk pens
Ln ow te part
Weight of the Gia aes)
Ts stow 6 aes Oe vo of mice. Hrs sio)
Toa mue of mate ant fountain, m= 225445 5199 25270 tg
La à fit ante te ving coms À
26445 ase N >
= 6980 kg/m? y= 127 Um = 1700 kg/m
x 2x 24 tonnes = 27.6 1
Unit soil pressure 4
le het. 50,
Equivalent surcharge = h 8 = 4500» 27 m
ah
Now af.
Assuming a= 1 and taking b=2 m
35
re
ass: 4
From Table 282, assume, P=4.6% 10°kg/m!/m
From Fig. 28.7, when 9=1.35 und $
9435
aaa dis
La BOL = ASK) = 644 10" kam
175
75, we get
Tot Wye $862 kg =11,800 Ib 5 ve 1.7 me 106 I ft
4 angy{ 04775 «11900 PA
win $x og REO 77 21500 10 = 9750 bg
9750 5
me ER gp kg /m
Example 284. Deion the fanden fr a ga ago vi a ma oder ont
veta ring pos Jr de Joa du
1. Total weight of engine = 4500 kg.
2. Speed of rotation = 260 rpm.
3. Unbalanced vertical force = 1 tonne
4. Bee mesons of de eagle “im #25
3. Bien of mech bse don pond aim
Weak silty sand exists 10 a depth of 0.5 m followed by a dense sand toa depth
of 6 m. The unit weight of moist sand is 1,7 1/ m.
Selen. La te ze of heck be 133m a e be of he mui, ani
2x 3m ats aan. La be bight of cn ck be 20 m0 atk pens
Ln ow te part
Weight of the Gia aes)
Ts stow 6 aes Oe vo of mice. Hrs sio)
Toa mue of mate ant fountain, m= 225445 5199 25270 tg
La à fit ante te ving coms À
26445 ase N >
= 6980 kg/m? y= 127 Um = 1700 kg/m
x 2x 24 tonnes = 27.6 1
Unit soil pressure 4
le het. 50,
Equivalent surcharge = h 8 = 4500» 27 m
ah
Now af.
Assuming a= 1 and taking b=2 m
35
re
ass: 4
From Table 282, assume, P=4.6% 10°kg/m!/m
From Fig. 28.7, when 9=1.35 und $
9435
aaa dis
La BOL = ASK) = 644 10" kam
175
75, we get
" MACHINE FOUNDATIONS
From Fig, 288, Wien 10135 m0 fe, Sat.
cts = Senna
NN re =
a: 64.4 x 10%
eae VE cre BEAMER
Te omg log ee me à 020 #0
£- vo
‘The amplitude of vibration is determined from
ES
CIS
where Fo=dynamic load = 1000 kg. Assume © =0.15
As
1
4a x 107% 097
where = $Q+25)4275 m à ze depih below ground surface =1 m
(or fe 1800 rpm)
= 284 200366 09 cm. Hence te fondu i sf,
28.10. DYNAMIC ANALYSIS OF BLOCK FOUNDATIONS
‘The methods of Pauw and Balakrishna Rao are based on the assumption that a certain
mass of soil participates in the vibration with Ce foundation. Barkea's method is based
on liner spring theory. The method neglects the effects of damping and participating soil
mass, Barken's method is very much used in design offices. A summary of various formula
are given below :
1. Equation of Motion : In the general case, the foundation may be considered
as a mass having six degrees of freedom—displacements in the three conordinate axes (2,
y. 2) and rotation about each of these axes (Fig. 28.9). The rotations about y, z and
x-axes are respectively known as rocking, yawing and pitching. Let us first consider the
From Fig, 288, Wien 10135 m0 fe, Sat.
cts = Senna
NN re =
a: 64.4 x 10%
eae VE cre BEAMER
Te omg log ee me à 020 #0
£- vo
‘The amplitude of vibration is determined from
ES
CIS
where Fo=dynamic load = 1000 kg. Assume © =0.15
As
1
4a x 107% 097
where = $Q+25)4275 m à ze depih below ground surface =1 m
(or fe 1800 rpm)
= 284 200366 09 cm. Hence te fondu i sf,
28.10. DYNAMIC ANALYSIS OF BLOCK FOUNDATIONS
‘The methods of Pauw and Balakrishna Rao are based on the assumption that a certain
mass of soil participates in the vibration with Ce foundation. Barkea's method is based
on liner spring theory. The method neglects the effects of damping and participating soil
mass, Barken's method is very much used in design offices. A summary of various formula
are given below :
1. Equation of Motion : In the general case, the foundation may be considered
as a mass having six degrees of freedom—displacements in the three conordinate axes (2,
y. 2) and rotation about each of these axes (Fig. 28.9). The rotations about y, z and
x-axes are respectively known as rocking, yawing and pitching. Let us first consider the
as SOIL MECHANICS AND FOUNDATIONS
3. Stiffaess of clastic supports
(a) Soil base. The values of ku. k, and key for the elastic support of soil are
given by the following expressions
For vertical motion : kı= C, A (28.66 0)
For horizontal (sliding) motion: kı= Ce (28.666)
For rocking motion : lay = Col, (28.66 c)
‘Thus, knowing Cu, the values of # , k and hy cam be computed
(0) Elastic pads. I, however, the foundation block is supported on elastic pad
of contact area A and thickness 1, then the values of the stffiness factors are given by
‘the following expressions +
For veia mon + ten EA „a0 0
For hat (ng mein 2897 à
For ring atin: oy E 860 à
where E= modulus of elasticity of the pad material
Ge shear modulus of the pad material
(c) Steel spring, If the foundation 8 =
aca CS E
das the diameter of spring wire, D
as the diameter of spring coil, n as s
‘the number of windings in each coil,
‘Aas height of each coil and G as the =o
‘hear modulus of the material, the stiffness
factors are given by the following ex-
pressions: 1
For vertical motion, 3
keel DE 28.68 a) |
A &
If there are N springs in the col, 204
the resultan vertical sufIess will be?
Nk, 134
For horizontal motion (siding mo-
ion), :
el — ]
[oes a {1+ 922 a} | i
a CNT 20
28.68.) i
FIG. 26.10 VALUE OF COEFFICIENT «.
3. Stiffaess of clastic supports
(a) Soil base. The values of ku. k, and key for the elastic support of soil are
given by the following expressions
For vertical motion : kı= C, A (28.66 0)
For horizontal (sliding) motion: kı= Ce (28.666)
For rocking motion : lay = Col, (28.66 c)
‘Thus, knowing Cu, the values of # , k and hy cam be computed
(0) Elastic pads. I, however, the foundation block is supported on elastic pad
of contact area A and thickness 1, then the values of the stffiness factors are given by
‘the following expressions +
For veia mon + ten EA „a0 0
For hat (ng mein 2897 à
For ring atin: oy E 860 à
where E= modulus of elasticity of the pad material
Ge shear modulus of the pad material
(c) Steel spring, If the foundation 8 =
aca CS E
das the diameter of spring wire, D
as the diameter of spring coil, n as s
‘the number of windings in each coil,
‘Aas height of each coil and G as the =o
‘hear modulus of the material, the stiffness
factors are given by the following ex-
pressions: 1
For vertical motion, 3
keel DE 28.68 a) |
A &
If there are N springs in the col, 204
the resultan vertical sufIess will be?
Nk, 134
For horizontal motion (siding mo-
ion), :
el — ]
[oes a {1+ 922 a} | i
a CNT 20
28.68.) i
FIG. 26.10 VALUE OF COEFFICIENT «.
MACHINE FOUNDATIONS
28.12. INDIAN STANDARD CODE OF PRACTICE FOR DESIGN OF
FOUNDATION FOR IMPACT TYPE MACHINES
‘The design requirements of the impact types machines, such as drop and forge hammers,
are different than those of the reciprocating type machines discussed above. IS : 2974
Can 1)
type machines, Fi
Definitions.
1966 covers the design requiremens for the foundations of these heavy impact
28.13 showns some typical sections of the foundations for these machines.
( Anvil: Anvil is a base-block for a hammer on which material is
forged into shape by repeated striking of the wp. (ii) Tup: Tup is a weighted block which
sirikes the material being forged on the anvil. (
concrete on which the anvil rests. (iv) Provective cushioning layer Goint Jy )
elastic cushioning of suitable material and hick-
ness provided between the anvil and the foun-
dation block in order to prevent bouncing
of anvil and creation of large impact stresses
and consequent damages (O the top surface
of the concrete in the foundation block. (4)
Foundation support (joint J ) : I is a support
for resting the foundation block. The block
may rest directly on ground or on a resilient
‘mounting such as timber sleepers, springs cork
layer es. The block may also be supported
on pile foundations.
Design Criteria (1) The stresses produced
at the time of impact in the foundation base
Gol, timber, sleeper, cork, spring elements
or piles) should be within 0.8 times allowable
static stresses,
(2) The design of the entre foundation
system should be such that the centres of
gravity of the anvil, and of the foundation
block. as well as the joints at whieh the
resultants of forces in the elastic joints
4 and Jy act, coincide with the line of
fall of the hammer mp. While determining
the centre of gravity of the foundation block,
the weight of the frame of the up could
also be considered.
©) The maximum vesical vibrational
amplinde of the foundation block should not
be more than 1.2 mm. In case of foundations
on sand below the ground water. he permissible
amplitude should not be more than 0.8 mm.
Foundation block : It is a mass of reinforced
Mois an
(© Fura rest o le
FIG. 28.13. DIFFERENT TYPES OF FOUNDATION
‘SUPPORTS FOR IMPACT TYPE MACHINES.
28.12. INDIAN STANDARD CODE OF PRACTICE FOR DESIGN OF
FOUNDATION FOR IMPACT TYPE MACHINES
‘The design requirements of the impact types machines, such as drop and forge hammers,
are different than those of the reciprocating type machines discussed above. IS : 2974
Can 1)
type machines, Fi
Definitions.
1966 covers the design requiremens for the foundations of these heavy impact
28.13 showns some typical sections of the foundations for these machines.
( Anvil: Anvil is a base-block for a hammer on which material is
forged into shape by repeated striking of the wp. (ii) Tup: Tup is a weighted block which
sirikes the material being forged on the anvil. (
concrete on which the anvil rests. (iv) Provective cushioning layer Goint Jy )
elastic cushioning of suitable material and hick-
ness provided between the anvil and the foun-
dation block in order to prevent bouncing
of anvil and creation of large impact stresses
and consequent damages (O the top surface
of the concrete in the foundation block. (4)
Foundation support (joint J ) : I is a support
for resting the foundation block. The block
may rest directly on ground or on a resilient
‘mounting such as timber sleepers, springs cork
layer es. The block may also be supported
on pile foundations.
Design Criteria (1) The stresses produced
at the time of impact in the foundation base
Gol, timber, sleeper, cork, spring elements
or piles) should be within 0.8 times allowable
static stresses,
(2) The design of the entre foundation
system should be such that the centres of
gravity of the anvil, and of the foundation
block. as well as the joints at whieh the
resultants of forces in the elastic joints
4 and Jy act, coincide with the line of
fall of the hammer mp. While determining
the centre of gravity of the foundation block,
the weight of the frame of the up could
also be considered.
©) The maximum vesical vibrational
amplinde of the foundation block should not
be more than 1.2 mm. In case of foundations
on sand below the ground water. he permissible
amplitude should not be more than 0.8 mm.
Foundation block : It is a mass of reinforced
Mois an
(© Fura rest o le
FIG. 28.13. DIFFERENT TYPES OF FOUNDATION
‘SUPPORTS FOR IMPACT TYPE MACHINES.
PART VII
PAVEMENT DESIGN
29. DESIGN OF FLEXIBLE PAVEMENT
30. DESIGN OF RIGID PAVEMENT
31. STABILISATION OF SOILS
PAVEMENT DESIGN
29. DESIGN OF FLEXIBLE PAVEMENT
30. DESIGN OF RIGID PAVEMENT
31. STABILISATION OF SOILS
2]
Design of Flexible Pavement
29.1. INTRODUCTION : TYPES OF PAVEMENTS
A natural earth track is incapable of supporting modern wheel loads, A constructed
pavement is required on the top of the soil in order to distribute the whee! load eficienly
and to provide the necessary wearing surface. A pavement is, therfore, defined as a relatively
stable crust constructed over the natural soil for the purpose of supporting and distributing
the wheel loads and providing an adequate wearing surface. Depending upon the mode
of supporting and distributing loads, pavements are classified as flexible, rigid and semi-flexble.
The flexible pavements consist of a relatively thin wearing surface built over a base
course and sub-base course, and they rest on compacted sub-grade. The flexible pavements
are able to resist only very small tensile stresses. In contrat to this, rigid pavements are
made up of Portland cement concrete and may or may not have a base course between
the pavement and the sub-grade. À rigid pavement can take appreciable tensile stresses
and is capable of bridging small weakness and depression in the sub-grade. A sentifleible
pavement is made of dry-lean concrete or soil cement, and possesses qualities intermediate
between the flexible and rigid pavements. A semiflexible pavement possesses appreciable
flexural strength but its modulus of elasticity is considerably lower than that of concrete,
‘The essential difference between rigid and flexible pavements is the manner in which
they distribute the load over the sub-grade. The design of a flexible pavement is based
on the principle that a surface load is dissipated by carrying it deep into the ground through
successive layer of granular materials, Hence the strength of a flexible layer is a result
of building up thick layers and thereby distributing the load over the sub-grade rather than
by the bending action. The thickness design of the flexible pavement is influenced primarily
by tie strength of the sub-grade.
Because of its rigidiy and high temsile srengh, a rigid pavement tends 10 distribute
ly wide arca of soil, and a major portion of the structural cap
supplied by the slab itself. For this reason, minor variations in sub-grade stength have
liule influence upon the structual capacity of the pavement
The rigid pavements are used for heavier loads and can be constructed over relatively
poor subgrade such as black cotton or plastic soils, peat etc. However, since the load
taken up by the bending action of the slab, uniform sub-grade support is the most
ws
Design of Flexible Pavement
29.1. INTRODUCTION : TYPES OF PAVEMENTS
A natural earth track is incapable of supporting modern wheel loads, A constructed
pavement is required on the top of the soil in order to distribute the whee! load eficienly
and to provide the necessary wearing surface. A pavement is, therfore, defined as a relatively
stable crust constructed over the natural soil for the purpose of supporting and distributing
the wheel loads and providing an adequate wearing surface. Depending upon the mode
of supporting and distributing loads, pavements are classified as flexible, rigid and semi-flexble.
The flexible pavements consist of a relatively thin wearing surface built over a base
course and sub-base course, and they rest on compacted sub-grade. The flexible pavements
are able to resist only very small tensile stresses. In contrat to this, rigid pavements are
made up of Portland cement concrete and may or may not have a base course between
the pavement and the sub-grade. À rigid pavement can take appreciable tensile stresses
and is capable of bridging small weakness and depression in the sub-grade. A sentifleible
pavement is made of dry-lean concrete or soil cement, and possesses qualities intermediate
between the flexible and rigid pavements. A semiflexible pavement possesses appreciable
flexural strength but its modulus of elasticity is considerably lower than that of concrete,
‘The essential difference between rigid and flexible pavements is the manner in which
they distribute the load over the sub-grade. The design of a flexible pavement is based
on the principle that a surface load is dissipated by carrying it deep into the ground through
successive layer of granular materials, Hence the strength of a flexible layer is a result
of building up thick layers and thereby distributing the load over the sub-grade rather than
by the bending action. The thickness design of the flexible pavement is influenced primarily
by tie strength of the sub-grade.
Because of its rigidiy and high temsile srengh, a rigid pavement tends 10 distribute
ly wide arca of soil, and a major portion of the structural cap
supplied by the slab itself. For this reason, minor variations in sub-grade stength have
liule influence upon the structual capacity of the pavement
The rigid pavements are used for heavier loads and can be constructed over relatively
poor subgrade such as black cotton or plastic soils, peat etc. However, since the load
taken up by the bending action of the slab, uniform sub-grade support is the most
ws
ms SOIL MECHANICS AND FOUNDATIONS.
essential condition for the satisfactory performance of rigid pavement, In the flexible pavements,
on the contrary, a high quality, well compacted sub-grade is essential.
29.2. STRUCTURAL ELEMENTS OF A FLEXIBLE PAVEMENT
A flexible pavement is usually built up in several layers as shown in Fig. 29.1,
each layer having a special function, Generally, tbe flexible pavement thickness consists
of three components : surfacing, base and sub-tase course. The wearing course or surfacing
is the component of. a pavement with which the wheels of vehicles are in actual comact.
‘The purpose of the wearing course, "made of bituminous material is to provide a smooth
riding surface that is resilient and will resist
pressure exerted by the tyres. It should be
flexible so that it will not fail if consolidation
of the subgrade or base course takes place
A base course is defined as a layer
of granular material which lies immediatly
below the wearing surface of a flexible pave-
ment. A sub-base is a layer of material
between the base and sub-grade. Base course
and sub-bases are used under flexible pave-
ments primarily to increase the load supporting
capacity of the pavement by distributing FIG. 29.1. BASIC STRUCTURAL ELEMENTS
the load through finite thickness of pavement. OF A FLEXIBLE PAVEMENT.
“The base course lies close to the pavement
surface, and hence it, must possess high resistance to deformation in order to withstand
the high pressures imposed upon it. However, a sub-base can be of a lower quality.
‘The sub-grade is the foundation layer, the structure which must eventually support
all the loads which come on to the pavement. The performance of the pavement is affected
by the characteristics of the subgrade. Desirable properties which the sub-grade should possess
are : strength, drainage, case of compaction, permanencey of compaction, and permanency
of strength. The strength of the sub-grade is increased by compaction, or in some cases
by stabilisation, Stability of the sub-grade is influenced by soil texture, water content, density,
frost action, shrinkage and swelling, and other climatic factors.
29.3. STRESSES IN FLEXIBLE PAVEMENT
1. Stresses In homogeneous mass : We have seen in chapter 13 that the vertical
stress distribution on any horizontal plane at a depth z below the ground surface, due
10 a concentrated load takes the form of a bell-shaped surface, The maximum stresses occur
‘on the vertical plane passing through the point of load application, According to Boussinesq's
analysis, the vertical stress 0 at any point (7,2) is given by
ar 1
29.)
essential condition for the satisfactory performance of rigid pavement, In the flexible pavements,
on the contrary, a high quality, well compacted sub-grade is essential.
29.2. STRUCTURAL ELEMENTS OF A FLEXIBLE PAVEMENT
A flexible pavement is usually built up in several layers as shown in Fig. 29.1,
each layer having a special function, Generally, tbe flexible pavement thickness consists
of three components : surfacing, base and sub-tase course. The wearing course or surfacing
is the component of. a pavement with which the wheels of vehicles are in actual comact.
‘The purpose of the wearing course, "made of bituminous material is to provide a smooth
riding surface that is resilient and will resist
pressure exerted by the tyres. It should be
flexible so that it will not fail if consolidation
of the subgrade or base course takes place
A base course is defined as a layer
of granular material which lies immediatly
below the wearing surface of a flexible pave-
ment. A sub-base is a layer of material
between the base and sub-grade. Base course
and sub-bases are used under flexible pave-
ments primarily to increase the load supporting
capacity of the pavement by distributing FIG. 29.1. BASIC STRUCTURAL ELEMENTS
the load through finite thickness of pavement. OF A FLEXIBLE PAVEMENT.
“The base course lies close to the pavement
surface, and hence it, must possess high resistance to deformation in order to withstand
the high pressures imposed upon it. However, a sub-base can be of a lower quality.
‘The sub-grade is the foundation layer, the structure which must eventually support
all the loads which come on to the pavement. The performance of the pavement is affected
by the characteristics of the subgrade. Desirable properties which the sub-grade should possess
are : strength, drainage, case of compaction, permanencey of compaction, and permanency
of strength. The strength of the sub-grade is increased by compaction, or in some cases
by stabilisation, Stability of the sub-grade is influenced by soil texture, water content, density,
frost action, shrinkage and swelling, and other climatic factors.
29.3. STRESSES IN FLEXIBLE PAVEMENT
1. Stresses In homogeneous mass : We have seen in chapter 13 that the vertical
stress distribution on any horizontal plane at a depth z below the ground surface, due
10 a concentrated load takes the form of a bell-shaped surface, The maximum stresses occur
‘on the vertical plane passing through the point of load application, According to Boussinesq's
analysis, the vertical stress 0 at any point (7,2) is given by
ar 1
29.)
DESIGN OF FLEXIBLE PAVEMENT =
Integrating the equation over a loaded circular area of radius a, the vertical stress
on a vertical line passing through the centre of the loaded area is given by
1
l a]
where p is the unit load on the circular loaded plate, 2 is the depth and a is the radius
of the’ plate, Similarly, the horizontal radial tres is given by
o (29.2)
ir PLE 09.
al Gea er en
where pe Placas. ri, »
2. Blas deformation under circular
load : The vertical strain €,, due to the triaxial PD da
load (On On 0, m9) mer the eme of | Fonte
pe ls given by Hockes law =
1 | |
“ug (0; - ua) (29.4) Sutgrdo
where Ee modulus of casi of the antes ton
bre, ETS
‘Subsinting Eq, 292 and 293 in Eq, FO. 292, ELASTIC Deronmanon
29.4, and integrating between z=z and UNDER CICULAR LOAD.
za, the clio stain A of the subgrade is given by
ala mean O2 cars
a AG rt De CE)
Taking 1=0.5, the above expresion reduces to
a HEN or e
mr 03.6) ar 27
wor’ = Bousineg selement factor. 09.8)
1+(2)
Eq, 29.6 or 29.7 give the elastic deformation of the sub-grade only. The elastic deformations
from surface to depth z are not considered since the only siginificant deflections are in the
ssub-grade, If the load is at the surface of the sub-grade (2=0), Eq. 29.6 reduces 0
amis E 29.9)
Fig. 29.3 gives the curves for deflection factor for various values of 3 and’. The
5 ratio corresponding to Eq. 29.6 is zero and the curve of Z=0 in Fig. 29.3 gives
the deflections according to Eq. 29.7 (Foster and Ahlvin, 1954).
Integrating the equation over a loaded circular area of radius a, the vertical stress
on a vertical line passing through the centre of the loaded area is given by
1
l a]
where p is the unit load on the circular loaded plate, 2 is the depth and a is the radius
of the’ plate, Similarly, the horizontal radial tres is given by
o (29.2)
ir PLE 09.
al Gea er en
where pe Placas. ri, »
2. Blas deformation under circular
load : The vertical strain €,, due to the triaxial PD da
load (On On 0, m9) mer the eme of | Fonte
pe ls given by Hockes law =
1 | |
“ug (0; - ua) (29.4) Sutgrdo
where Ee modulus of casi of the antes ton
bre, ETS
‘Subsinting Eq, 292 and 293 in Eq, FO. 292, ELASTIC Deronmanon
29.4, and integrating between z=z and UNDER CICULAR LOAD.
za, the clio stain A of the subgrade is given by
ala mean O2 cars
a AG rt De CE)
Taking 1=0.5, the above expresion reduces to
a HEN or e
mr 03.6) ar 27
wor’ = Bousineg selement factor. 09.8)
1+(2)
Eq, 29.6 or 29.7 give the elastic deformation of the sub-grade only. The elastic deformations
from surface to depth z are not considered since the only siginificant deflections are in the
ssub-grade, If the load is at the surface of the sub-grade (2=0), Eq. 29.6 reduces 0
amis E 29.9)
Fig. 29.3 gives the curves for deflection factor for various values of 3 and’. The
5 ratio corresponding to Eq. 29.6 is zero and the curve of Z=0 in Fig. 29.3 gives
the deflections according to Eq. 29.7 (Foster and Ahlvin, 1954).
es SOIL MECHANICS AND FOUNDATIONS
Daten ctor Fe,
91 015 02 03 040508 08 10 15 20
CN ee
à IA
10
Vert oct (Polens ato=0.5)
FIG. 293. CHARTS FOR VERTICAL DEFLECTIONS (FOSTER AND ALVIN 1954)
. Burmister analysis : The flexible pavements consist of a mamber of layers the
‘moduli of elasticity of which decreases wih depth. In the previous analysis, the effect
of the pavement components was ignored while calculating the deflections. Burmister (1943,
45. 58), took into account the effect of various layers. In the simplest case, the whole
structure may be thought to be made up of two layers : the base course or pavement
layer, and the sub-grade layer. In the analysis of the two layer system, following assumptions
are made : ($ the layers are homogeneous, isotropic and elastic, (Hi) the surface layer
is infinite in extent in the
lateral direction, but of e
nite depth, (ii) the sub- Ez Ez
grade layer is infinite in
‘both horizontal and vertical
directions, (v) both the
layers are in continuous
contact, and (4) surface
layer is free from bearing
and normal stress outside
the loaded area. The ver-
stress at any depth
2, at the cente ofthe plate
na FIG, 294 BURMISTER TWO-LAYER STRESS
= Cup (29.10) INFLUENCE CURVES (BURSMISTER. 195).
Daten ctor Fe,
91 015 02 03 040508 08 10 15 20
CN ee
à IA
10
Vert oct (Polens ato=0.5)
FIG. 293. CHARTS FOR VERTICAL DEFLECTIONS (FOSTER AND ALVIN 1954)
. Burmister analysis : The flexible pavements consist of a mamber of layers the
‘moduli of elasticity of which decreases wih depth. In the previous analysis, the effect
of the pavement components was ignored while calculating the deflections. Burmister (1943,
45. 58), took into account the effect of various layers. In the simplest case, the whole
structure may be thought to be made up of two layers : the base course or pavement
layer, and the sub-grade layer. In the analysis of the two layer system, following assumptions
are made : ($ the layers are homogeneous, isotropic and elastic, (Hi) the surface layer
is infinite in extent in the
lateral direction, but of e
nite depth, (ii) the sub- Ez Ez
grade layer is infinite in
‘both horizontal and vertical
directions, (v) both the
layers are in continuous
contact, and (4) surface
layer is free from bearing
and normal stress outside
the loaded area. The ver-
stress at any depth
2, at the cente ofthe plate
na FIG, 294 BURMISTER TWO-LAYER STRESS
= Cup (29.10) INFLUENCE CURVES (BURSMISTER. 195).
so SOIL MECHANICS AND FOUNDATIONS,
the dual wheels are equal
10 those of a single whee!
depends upon the spacing
of the vhs. Fig. 29.6
sows the inflcnoo of mal
tiple wheel on stresses
At a depth approxi-
marc half the foceo-face
spacing (f), the wheels
cease 1 act independently,
and at a depth qual zo
twice the cenre to centre
icono mp, FIG. 294. INFLUENCE OF MULTIPLE WHEELS ON STRESSES.
ligible. An equivalen
whee load can be found either from the equal deflection criterion or equatstrest criterion.
Based on the equal deflcion criterion, the following expression for the equivalent wheel
toad P, results:
Fla = (Fi + FNP 1.29.13)
where Pe= equivalent wheels. load
Pa wheel load of each of the dual tyres
Fes settlement factor for equivalent wheel load
Fi=señlement factor contributed by one tyre of duals
Fam settlement factor contributed by the other tyre.
The solution of the problem is accomplished by determining values of P, and
Fe so that the Eq, 29.13 is satisfied. The load P is known and factors F, and F, can
be known from Fig. 29.5 for various values of 7 ratios. The maximum value of
Fit Es occurs at a small distance from the centre of the tyre. However, for practical
problems, the values of Fi + F, under the centre line, and under a tyre, need by calculated
and the greatest of the two may be taken to be used in Eq. 29.13. Thus the RLS.
of Eq. 29.13 is known. A number of values of P, are assumed and the values of
WE. E, are computed till Eq. 29.13 is satisfied
29.8. DESIGN METHODS
The flexible pavement design methods can be broadly classified into three distinct
groups :
(Empirical methods based on soil classification and otber factors such as climate
and moisure. They include the following:
(@) Group index method.
(6) Federal aviation agency (U.S.A.) method.
the dual wheels are equal
10 those of a single whee!
depends upon the spacing
of the vhs. Fig. 29.6
sows the inflcnoo of mal
tiple wheel on stresses
At a depth approxi-
marc half the foceo-face
spacing (f), the wheels
cease 1 act independently,
and at a depth qual zo
twice the cenre to centre
icono mp, FIG. 294. INFLUENCE OF MULTIPLE WHEELS ON STRESSES.
ligible. An equivalen
whee load can be found either from the equal deflection criterion or equatstrest criterion.
Based on the equal deflcion criterion, the following expression for the equivalent wheel
toad P, results:
Fla = (Fi + FNP 1.29.13)
where Pe= equivalent wheels. load
Pa wheel load of each of the dual tyres
Fes settlement factor for equivalent wheel load
Fi=señlement factor contributed by one tyre of duals
Fam settlement factor contributed by the other tyre.
The solution of the problem is accomplished by determining values of P, and
Fe so that the Eq, 29.13 is satisfied. The load P is known and factors F, and F, can
be known from Fig. 29.5 for various values of 7 ratios. The maximum value of
Fit Es occurs at a small distance from the centre of the tyre. However, for practical
problems, the values of Fi + F, under the centre line, and under a tyre, need by calculated
and the greatest of the two may be taken to be used in Eq. 29.13. Thus the RLS.
of Eq. 29.13 is known. A number of values of P, are assumed and the values of
WE. E, are computed till Eq. 29.13 is satisfied
29.8. DESIGN METHODS
The flexible pavement design methods can be broadly classified into three distinct
groups :
(Empirical methods based on soil classification and otber factors such as climate
and moisure. They include the following:
(@) Group index method.
(6) Federal aviation agency (U.S.A.) method.
DESIGN OF FLEXIBLE PAVEMENT ES
soaked as well as unsonked samples
are determined. Both during soaking
and penetration test, the specimen
is covered with equal surcharge as,
‘weights 10 simulate the effect of ae
overiying pavement or the particular
layer under construction. Each sur
charge slowed weight, 147 mm in
diameter with a central hole 53 mm
in diameter and weighing 25 ka
is considered approximately equiva-
lem to 6.5 em of construction. A
minimum of two surcharge weights
he 5 kg surcharge load) is placed
fon the specimen. Load is app
on the penetration piston so tht
the penetration i approximately 1.25
unio. The load readings are re-
zu
3
3
83
[correctos
‘mn
garcon
E
La on pion da
8
cometa 25 mm
penetration
corded e penados, 0.0.3, 10,
13.20.38 30, 40, 30: 7:
10 snd 125 mam, Te mati Gore oe
ead end penewacón Is rected if um
pp
fu 12.5 mm Un Dai pensais i
cur is ten pond a stows In a a
Pe 298. AE
The curve is mainly convex =
‘upwards along ell orton
cure uy be conca parts
LOAD PENETRATION CURVES IN CBR TEST.
ied by drawing a tangent to the curve at the point of greatest slope.
The corrected origin will be the point where the tangent meets the abscissa
The CBR values are usually calculated for penetrations of 2.5 mm and 5 mm. Generally
the CBR values at 2.5 mm penetration will be greater than that at S mm penetration
and in such a case the former is to be taken as the CBR value for design purposes.
If the CBR value corresponding to a penetration of $ mm exceeds that for 2.5 mm, the
test is repeated. If identical results follow, the beating ratio correponding to $ min penetration
is taken for design.
Fig. 29.9 gives the design curves for determining the appropriate thickness of construction
required above a material with a given CBR, for different wheel loads and traffic conditions.
These design curves for roads have been proposed by the Road Research Laboratory, England,
and are also followed in India
soaked as well as unsonked samples
are determined. Both during soaking
and penetration test, the specimen
is covered with equal surcharge as,
‘weights 10 simulate the effect of ae
overiying pavement or the particular
layer under construction. Each sur
charge slowed weight, 147 mm in
diameter with a central hole 53 mm
in diameter and weighing 25 ka
is considered approximately equiva-
lem to 6.5 em of construction. A
minimum of two surcharge weights
he 5 kg surcharge load) is placed
fon the specimen. Load is app
on the penetration piston so tht
the penetration i approximately 1.25
unio. The load readings are re-
zu
3
3
83
[correctos
‘mn
garcon
E
La on pion da
8
cometa 25 mm
penetration
corded e penados, 0.0.3, 10,
13.20.38 30, 40, 30: 7:
10 snd 125 mam, Te mati Gore oe
ead end penewacón Is rected if um
pp
fu 12.5 mm Un Dai pensais i
cur is ten pond a stows In a a
Pe 298. AE
The curve is mainly convex =
‘upwards along ell orton
cure uy be conca parts
LOAD PENETRATION CURVES IN CBR TEST.
ied by drawing a tangent to the curve at the point of greatest slope.
The corrected origin will be the point where the tangent meets the abscissa
The CBR values are usually calculated for penetrations of 2.5 mm and 5 mm. Generally
the CBR values at 2.5 mm penetration will be greater than that at S mm penetration
and in such a case the former is to be taken as the CBR value for design purposes.
If the CBR value corresponding to a penetration of $ mm exceeds that for 2.5 mm, the
test is repeated. If identical results follow, the beating ratio correponding to $ min penetration
is taken for design.
Fig. 29.9 gives the design curves for determining the appropriate thickness of construction
required above a material with a given CBR, for different wheel loads and traffic conditions.
These design curves for roads have been proposed by the Road Research Laboratory, England,
and are also followed in India
DESIGN OF FLEXIBLE PAVEMENT ws
he tip of the cone, A {Cone bearing at a)
corrections therefore, g 8 8 8 8 8 € 8
800
inch mima
added to or subtracted po A A
from all the readings
50 thatthe penetration à
Ps under 9 kg becomes. g
half of the penetration
Px under 36 kg. de
Correction. 3
C= pu- 2 it
„sn de
Knowing the
thickness of pavement 1
mer FIG. 2.10. NORT DAKOTA DESIGN CURVE (AFTER WISE, 159)
thickness of 24 cm is provided for bearing values of 28 kg/cm’ or more.
293. BURMISTER'S DESIGN METHOD
Burmise's design method is based on the concept of a two.yer system, consisting
of the road surfacing, base coune and the sub-basc as the top layer of thicknest A, and
the sub-arade as the atom layer of infinite exent. The displacement of such a system.
under a loaded. area of rads a with load intensity p is given by Eq. 29.11
sta
aser
where Ey= modulus of elasticity of the sub-grade
Fe defletion factor, determined from Fig. 29.5.
‘The method consists in selecting various values of the thickness A of the top layer
and finding the value of the deflection corresponding to each value of A, from Eq. 29.11,
the value of factor F being taken in each case from Fig. 29.5. The thickness h corresponding
lo an arbitrary deflection of A=02 inch (S mm) has been recommended by Burmister
required thickness of the pavement, Tentative design curves for flexibe runway pavements,
using 0.2 in. as limiting deformation have been drawn assuming approximate value of modulus
of elasticity für various types of sub-grades.
29.10. U.S. NAVY PLATE BEARING TEST METHOD
This method is also based on Burmister's two-layer theory. It consists of the following
three steps:
Step 1. The thickness h of the base course is calculated on the basis of the owo-layer
theory. For this the values of moudulus of elasticity E, and E, for the base course and
Aub-grade are determined from two plate bearing tests
he tip of the cone, A {Cone bearing at a)
corrections therefore, g 8 8 8 8 8 € 8
800
inch mima
added to or subtracted po A A
from all the readings
50 thatthe penetration à
Ps under 9 kg becomes. g
half of the penetration
Px under 36 kg. de
Correction. 3
C= pu- 2 it
„sn de
Knowing the
thickness of pavement 1
mer FIG. 2.10. NORT DAKOTA DESIGN CURVE (AFTER WISE, 159)
thickness of 24 cm is provided for bearing values of 28 kg/cm’ or more.
293. BURMISTER'S DESIGN METHOD
Burmise's design method is based on the concept of a two.yer system, consisting
of the road surfacing, base coune and the sub-basc as the top layer of thicknest A, and
the sub-arade as the atom layer of infinite exent. The displacement of such a system.
under a loaded. area of rads a with load intensity p is given by Eq. 29.11
sta
aser
where Ey= modulus of elasticity of the sub-grade
Fe defletion factor, determined from Fig. 29.5.
‘The method consists in selecting various values of the thickness A of the top layer
and finding the value of the deflection corresponding to each value of A, from Eq. 29.11,
the value of factor F being taken in each case from Fig. 29.5. The thickness h corresponding
lo an arbitrary deflection of A=02 inch (S mm) has been recommended by Burmister
required thickness of the pavement, Tentative design curves for flexibe runway pavements,
using 0.2 in. as limiting deformation have been drawn assuming approximate value of modulus
of elasticity für various types of sub-grades.
29.10. U.S. NAVY PLATE BEARING TEST METHOD
This method is also based on Burmister's two-layer theory. It consists of the following
three steps:
Step 1. The thickness h of the base course is calculated on the basis of the owo-layer
theory. For this the values of moudulus of elasticity E, and E, for the base course and
Aub-grade are determined from two plate bearing tests
ws SON. MECHANICS AND FOUNDATIONS
Step 2. Ti sections are connected withthe pavement thickness equal 10
Ye ant da
Sap a aca ed a a sai a et à
mn the bees of e MN pol a efec of 02 in. 6 ta
Sup 1. In oder to we de wo layer theory of allen of equ paiement
thickness In Sp 1. t's nece ft of deine Ge ale of E by de ple being
tent co a sare. À 0 lc face plat cate Gr is te. pactos
the tot. cent vo we a sere of sed per © ine the Den te
pl it OF 2 wet
fom We tess andthe modus of sank Ei ceased rom 29.12 by ng
de plac wo be tal Tie decos cms Fr is ew iv emul D ey hor te
a Cal reas ts a coe toes pens Trae
18
02 i
29.18)
From this, & is determined. Afer the modulus of elasticity E, is known, a test
section consisting of the base course material is built and plate-bearing test is made on
this, The test section should be 5 m by 5 m square (or larger) amd 15 to 30 cm deep.
“The load intensity p corresponding to A = 02 in. is determined from the teus, Knowing
E, ftom the previous test, and &(=0.2 in) and p from the present test, the factor F
E
is calculated from Eq. 29.12 ati Ber
a8
or ri 129.19)
‘Thus, factor F is known. From Fig. 29.5, the value of E, / E, is found corresponding
10 the value of F and ha ratio,
After having known E, and £,/E, (and hence E, also). the value of F corresponding
10 a given wheel load intensity p is computed from Eq. 29.11 by taking A= 02 in,
[3
ser 29.20)
(Considering the whee! loxd to be a flexible plate)
In this equation à, Es, p and a (radius of the tyre comact area) are known. Knowing
F, and Ey/E, ratio, the thickness h of the base course is determined from Fig. 29.5.
Step 2. Inthe next step. trial sections are constructed of thickness h, 3% and } À
calculated in step 1. Each trial section of a given thickness is constructed for three different
soil conditions: one on a ıypical fil section, another on a typical cut section, and a
third at a position on grade. Thus, in all, nine trial sections are built. The sub-grade
and base courses are compacted lo the densities that will be expected during construction.
Step 3. Plote-bearing tests are performed on these trial sections. The data then are
used to determine the required pavement thickness which will result in the assumed deflection
12 à
Step 2. Ti sections are connected withthe pavement thickness equal 10
Ye ant da
Sap a aca ed a a sai a et à
mn the bees of e MN pol a efec of 02 in. 6 ta
Sup 1. In oder to we de wo layer theory of allen of equ paiement
thickness In Sp 1. t's nece ft of deine Ge ale of E by de ple being
tent co a sare. À 0 lc face plat cate Gr is te. pactos
the tot. cent vo we a sere of sed per © ine the Den te
pl it OF 2 wet
fom We tess andthe modus of sank Ei ceased rom 29.12 by ng
de plac wo be tal Tie decos cms Fr is ew iv emul D ey hor te
a Cal reas ts a coe toes pens Trae
18
02 i
29.18)
From this, & is determined. Afer the modulus of elasticity E, is known, a test
section consisting of the base course material is built and plate-bearing test is made on
this, The test section should be 5 m by 5 m square (or larger) amd 15 to 30 cm deep.
“The load intensity p corresponding to A = 02 in. is determined from the teus, Knowing
E, ftom the previous test, and &(=0.2 in) and p from the present test, the factor F
E
is calculated from Eq. 29.12 ati Ber
a8
or ri 129.19)
‘Thus, factor F is known. From Fig. 29.5, the value of E, / E, is found corresponding
10 the value of F and ha ratio,
After having known E, and £,/E, (and hence E, also). the value of F corresponding
10 a given wheel load intensity p is computed from Eq. 29.11 by taking A= 02 in,
[3
ser 29.20)
(Considering the whee! loxd to be a flexible plate)
In this equation à, Es, p and a (radius of the tyre comact area) are known. Knowing
F, and Ey/E, ratio, the thickness h of the base course is determined from Fig. 29.5.
Step 2. Inthe next step. trial sections are constructed of thickness h, 3% and } À
calculated in step 1. Each trial section of a given thickness is constructed for three different
soil conditions: one on a ıypical fil section, another on a typical cut section, and a
third at a position on grade. Thus, in all, nine trial sections are built. The sub-grade
and base courses are compacted lo the densities that will be expected during construction.
Step 3. Plote-bearing tests are performed on these trial sections. The data then are
used to determine the required pavement thickness which will result in the assumed deflection
12 à
DESIGN OF FLEXIBLE PAVEMENT =
of 0.2 in. In making these tests, a plate is employed which has à radius corresponding
10 the effective tye rias a
In the above method, the design thickness is the tal thickness of base muera
lo sustin given load at à given deflection, and no consideration of the type or depth
of wearing surface is given. However, the structural quales of wearing surface materia
aro always beter, and hence a cerain thickest of surface material can be substiuted for
the base course material, This wil, in effect, produce an added factor of safey.
29,11. LABORATORY EXPERIMENTS.
[EXPERIMENT 21 : DETERMINATION OF CALIFORNIA BEARING RATIO
Object and scope. The abject of the experiment Is to diemnine the California Beating Ratio (CR)
Of a compact soil sample in the laboratory, both in soaked as well as unsaked ste. The method
also covers the deteminaton of CBR of undiurbed toi sample obtained from the fed.
Material and equipment. () Cylindral mould (CB.R. mould) vid inside diameter 150 mm and
height 175 mm. provided with a detachable extension collar SO mon big and a deuchuble perforated
ase plate 10 mm thik, (1) Spacer die, 148 mm in diameter and 47.7 mm in height, along with a
handle for screwing in the die to falle hs removal (i) sel cating collar which can fü fash
with the mou both outside and inside, (1) Meul ranmers : (a) weight 26 kg with a drop of 310
mm or (b) weight 4.89 kg, with a drop of 450 mm, (9) Anmlar sn) weigh weighing 2.5 kg cach
147 mm ln diameter wih a cone tole $3 mm In dame, (0) Pesetraion piston, SO mm diameter
and minimum of 100 mm long. (4) Extension measuring aparatos consisting of : (a) perforated plate
148 mm amer, wi a thread sem in the cen, (Badhsabe cont head 10 be screwed over
the sem, (0) meu pod, (M) Loading device, with a capaci of at last 5000 kp an equipped with
à movable dead or base tht wavels at a uniform rate of 1.28 mmimin ; complete wilh loud indican.
device, (x) Two dal gauges reading w 001 mm, (0 Sieve : 475 mm and 20 mm IS Sees, um
Miscellaneous apparatus, such as à mixing boul, Sai edge scale, soaking unk or pus, drying ove
water coment determination tins, Mer paper et
‘Test Procedure
(0. PREPARATION OF TEST SPECIMEN
1. Remoulded Specimen : Remoubied specimen may be prepared at Procors maxkmam dry density
nd optimum water coment or at any ciber desired density and water content, The murat used should
pass à 20 mm IS Sieve. Allouance for large material should be made by replacing it by an eal amount
‘of material which passes à 20 mun IS Sieve but is retained on 4.75 mm IS Sieve. The specimen may
he prepared either by dynamic compaction or by static compaction.
(a) Dinamic compaction, Take about 45 10 5.5 kg of soll and mix it thoroughly with the
desired war. If the sample is to be compacted at opimun water coment and the corresponding dry
densty € termined by compaction test (ight compaction or heavy compaction) take exact weight of sol
required and necessary quanliy of water so that the water comet of the sil sample is equal o the
dcteminod optimum water content. Fix the extension colli to the top of the mould and the tase plate
to us boom. Inser the spacer dic over the base (withthe ceatal hole of the dic at the lower se).
Put a dsc of a come fier paper on tbe top of the displacer dic. Compact the mised soil in Ue
‘mould using ciber the light compaction or heavy compacton. For ligh compaction, compact the soil in
3 equal layers, each laer being given $6 blows, uniformly isis, by the 2.6 kg rammer. For hey
compacton, compact the soil in 5 layers, by giving 56 Blows lo cach layer by the 489 kg ranmer.
Remme the colar and arin off exces soll, Turn the mould upside down and remove the base plate
of 0.2 in. In making these tests, a plate is employed which has à radius corresponding
10 the effective tye rias a
In the above method, the design thickness is the tal thickness of base muera
lo sustin given load at à given deflection, and no consideration of the type or depth
of wearing surface is given. However, the structural quales of wearing surface materia
aro always beter, and hence a cerain thickest of surface material can be substiuted for
the base course material, This wil, in effect, produce an added factor of safey.
29,11. LABORATORY EXPERIMENTS.
[EXPERIMENT 21 : DETERMINATION OF CALIFORNIA BEARING RATIO
Object and scope. The abject of the experiment Is to diemnine the California Beating Ratio (CR)
Of a compact soil sample in the laboratory, both in soaked as well as unsaked ste. The method
also covers the deteminaton of CBR of undiurbed toi sample obtained from the fed.
Material and equipment. () Cylindral mould (CB.R. mould) vid inside diameter 150 mm and
height 175 mm. provided with a detachable extension collar SO mon big and a deuchuble perforated
ase plate 10 mm thik, (1) Spacer die, 148 mm in diameter and 47.7 mm in height, along with a
handle for screwing in the die to falle hs removal (i) sel cating collar which can fü fash
with the mou both outside and inside, (1) Meul ranmers : (a) weight 26 kg with a drop of 310
mm or (b) weight 4.89 kg, with a drop of 450 mm, (9) Anmlar sn) weigh weighing 2.5 kg cach
147 mm ln diameter wih a cone tole $3 mm In dame, (0) Pesetraion piston, SO mm diameter
and minimum of 100 mm long. (4) Extension measuring aparatos consisting of : (a) perforated plate
148 mm amer, wi a thread sem in the cen, (Badhsabe cont head 10 be screwed over
the sem, (0) meu pod, (M) Loading device, with a capaci of at last 5000 kp an equipped with
à movable dead or base tht wavels at a uniform rate of 1.28 mmimin ; complete wilh loud indican.
device, (x) Two dal gauges reading w 001 mm, (0 Sieve : 475 mm and 20 mm IS Sees, um
Miscellaneous apparatus, such as à mixing boul, Sai edge scale, soaking unk or pus, drying ove
water coment determination tins, Mer paper et
‘Test Procedure
(0. PREPARATION OF TEST SPECIMEN
1. Remoulded Specimen : Remoubied specimen may be prepared at Procors maxkmam dry density
nd optimum water coment or at any ciber desired density and water content, The murat used should
pass à 20 mm IS Sieve. Allouance for large material should be made by replacing it by an eal amount
‘of material which passes à 20 mun IS Sieve but is retained on 4.75 mm IS Sieve. The specimen may
he prepared either by dynamic compaction or by static compaction.
(a) Dinamic compaction, Take about 45 10 5.5 kg of soll and mix it thoroughly with the
desired war. If the sample is to be compacted at opimun water coment and the corresponding dry
densty € termined by compaction test (ight compaction or heavy compaction) take exact weight of sol
required and necessary quanliy of water so that the water comet of the sil sample is equal o the
dcteminod optimum water content. Fix the extension colli to the top of the mould and the tase plate
to us boom. Inser the spacer dic over the base (withthe ceatal hole of the dic at the lower se).
Put a dsc of a come fier paper on tbe top of the displacer dic. Compact the mised soil in Ue
‘mould using ciber the light compaction or heavy compacton. For ligh compaction, compact the soil in
3 equal layers, each laer being given $6 blows, uniformly isis, by the 2.6 kg rammer. For hey
compacton, compact the soil in 5 layers, by giving 56 Blows lo cach layer by the 489 kg ranmer.
Remme the colar and arin off exces soll, Turn the mould upside down and remove the base plate
ss SOIL MECHANICS AND FOUNDATIONS
and the diplcer dsc. Weigh the mould With the compacted soil, so tat ls Bulk density and dry Gest
may be dere, Pu filter paper on the tp of the compacted sll (olla side) and clap the perforated
tase plate où 10 it
(0) Sie compoction. Callate the weight of wet soll at the required water conten o give the
ested density when occupying the standard specimen volume in the mould by the following expression:
Warm Y
whee Weight of wet ail à wy desired dry density
we desired water coment; Va volume of specimen la the mould = 2250 em.
Take about 43 10 5.5 kg of soll and rase its water coment to the desired value w. Take weight
W (calculated above) of the mix soll amd put ic ia mould filed wid me tase plate and fer paper
an ls todom. Tamp the soll by hand during pouring. Place à Mer paper and the dipicer dsc on
the top of the sol. Keep the mould assembly Im any compression machine and compact the sll by presing
the displace dis tll the level of the dise reaches the top of the mould. Keep the load for some time,
and then release, Remove the displaer be
2. Undisurbed specimen : To obtain undisturbed samples, attach the cating edge to de mould
and push it geally in the ground, When the mould is aufficiely fll of si, remove 1 by under tggog.
‘The ip and bonom surfaces are then tinmed fa so as o give the requked length of the specimen.
‘The density of the soil should be determined by weighing the sil with the mould or by any field method
(ooh as de sind replacement method) on the soll In te viinty of the spot at which sample s collected.
i) SOAKING OF SPECIMEN AND TEST FOR SWELLING.
1. Put after paper on the top of the soil amd place the adjusable stem and perforated plate
on the top of the filter paper.
2. Pas armaar weighs to produce a surcharge equal 1 the weight of the base material and parement
expected in acual construction. Each 2.5 kp weight Is equivalent 10 7 em of construction, À minimum
of two weighs shoold be put.
3. Immerse the mould assembly and weighs ct. in a unk of water allowing free aces of water
10 the top and bottom of the specimen.
4. Moun the tripod of the expansion measuring device on the edge of the mul and note owe
(he (nial reading of dal gasge.
5. Keep the setup undisturbed for 96 hours (£ days). Note down readings every day against the
tine of reading. Maina constant war level in tank.
6. Take the final reading at the end of period, remove the tripod and take out the mould. Allow
the specimen 10 din, for 15 minutes. Remove all de fee water collected in the mould taking. care
tte the surface of the specimen is oat disturbed dering the process.
7. Remove the weighs, perforated plate and top fier paper and weigh the mould with soaked
soil specimen.
Gin) PENETRATION TEST
1. Place the surcharge weighs back on the top of the scaked soil specimen, and place the moni
assembly on the penevation text machine loading. mache)
2. Seat the penetration piston at the centre of the specimen with the smiles possible load bat
mo case excess Of 4 Kg so that fll comet ls esahlihn) between the surface of the specimen and
the piston
3. Set the stress and sain dial gauge to seo. Apply the load on the penetration piston so dat
the penetration rte is approximately 1.25 mm/min. Record the losd reading at penetrations of 0, 0:5,
and the diplcer dsc. Weigh the mould With the compacted soil, so tat ls Bulk density and dry Gest
may be dere, Pu filter paper on the tp of the compacted sll (olla side) and clap the perforated
tase plate où 10 it
(0) Sie compoction. Callate the weight of wet soll at the required water conten o give the
ested density when occupying the standard specimen volume in the mould by the following expression:
Warm Y
whee Weight of wet ail à wy desired dry density
we desired water coment; Va volume of specimen la the mould = 2250 em.
Take about 43 10 5.5 kg of soll and rase its water coment to the desired value w. Take weight
W (calculated above) of the mix soll amd put ic ia mould filed wid me tase plate and fer paper
an ls todom. Tamp the soll by hand during pouring. Place à Mer paper and the dipicer dsc on
the top of the sol. Keep the mould assembly Im any compression machine and compact the sll by presing
the displace dis tll the level of the dise reaches the top of the mould. Keep the load for some time,
and then release, Remove the displaer be
2. Undisurbed specimen : To obtain undisturbed samples, attach the cating edge to de mould
and push it geally in the ground, When the mould is aufficiely fll of si, remove 1 by under tggog.
‘The ip and bonom surfaces are then tinmed fa so as o give the requked length of the specimen.
‘The density of the soil should be determined by weighing the sil with the mould or by any field method
(ooh as de sind replacement method) on the soll In te viinty of the spot at which sample s collected.
i) SOAKING OF SPECIMEN AND TEST FOR SWELLING.
1. Put after paper on the top of the soil amd place the adjusable stem and perforated plate
on the top of the filter paper.
2. Pas armaar weighs to produce a surcharge equal 1 the weight of the base material and parement
expected in acual construction. Each 2.5 kp weight Is equivalent 10 7 em of construction, À minimum
of two weighs shoold be put.
3. Immerse the mould assembly and weighs ct. in a unk of water allowing free aces of water
10 the top and bottom of the specimen.
4. Moun the tripod of the expansion measuring device on the edge of the mul and note owe
(he (nial reading of dal gasge.
5. Keep the setup undisturbed for 96 hours (£ days). Note down readings every day against the
tine of reading. Maina constant war level in tank.
6. Take the final reading at the end of period, remove the tripod and take out the mould. Allow
the specimen 10 din, for 15 minutes. Remove all de fee water collected in the mould taking. care
tte the surface of the specimen is oat disturbed dering the process.
7. Remove the weighs, perforated plate and top fier paper and weigh the mould with soaked
soil specimen.
Gin) PENETRATION TEST
1. Place the surcharge weighs back on the top of the scaked soil specimen, and place the moni
assembly on the penevation text machine loading. mache)
2. Seat the penetration piston at the centre of the specimen with the smiles possible load bat
mo case excess Of 4 Kg so that fll comet ls esahlihn) between the surface of the specimen and
the piston
3. Set the stress and sain dial gauge to seo. Apply the load on the penetration piston so dat
the penetration rte is approximately 1.25 mm/min. Record the losd reading at penetrations of 0, 0:5,
DESIGN OF FLEXIBLE PAVEMENT we
10, 15, 20, 25, 30, 40, 50, 73, 10 and 12.5 mm. Record the maximum load amd porcion
dí de occurs for a penevtion of less then 125 mm.
4. At the end of the perctraion te, detach the mould fe the loading equipment. Take about
20 10 $0 3 of soll from the top 3 em layer of the specimen, and keep it for wate content determination.
‘Tabulation of observations, The text data and observations are recorded as illustrated in Table
Da
TABLE 292. DATA AND OBSERVATION SHEET FOR CBR. DETERMINATION
1. Dry den a/a) 2. Moule water coment CE)
1 Dry easy before Eine 2, Belk deny before solo
3. Duk deny ater skins 4. Suctage welt wed during waking
10, 15, 20, 25, 30, 40, 50, 73, 10 and 12.5 mm. Record the maximum load amd porcion
dí de occurs for a penevtion of less then 125 mm.
4. At the end of the perctraion te, detach the mould fe the loading equipment. Take about
20 10 $0 3 of soll from the top 3 em layer of the specimen, and keep it for wate content determination.
‘Tabulation of observations, The text data and observations are recorded as illustrated in Table
Da
TABLE 292. DATA AND OBSERVATION SHEET FOR CBR. DETERMINATION
1. Dry den a/a) 2. Moule water coment CE)
1 Dry easy before Eine 2, Belk deny before solo
3. Duk deny ater skins 4. Suctage welt wed during waking
wo SOIL MECHANICS AND FOUNDATIONS
Cates dT Rest
1. Ban rl. Ts pme mio may be eed a foe
tapon re 00
where dye final dal prope reading. (mm) ; intial gauge reading (om)
him height of specimen (mm).
2. Load penetration. Plot the kad penetraon curve (Fig. 29.8). If the inal porion of the curve
is concave upwards, apply the correction by drawing a tangent to the curve at the pain of greatest
slope.
Te corrected origin wil be the point where the ion mets the abscissa, Find and record
the corrected load reading. comespoding to each peneiaon.
Corresponding 10 the penetration value at which the C.B.R. is desired, corected load valves are
found from the curve and CBR. is colculod as fellows
Br
care ho
Pr = corcted test load corresponing to the chosen penetration from the load
peneruion curve
Ps Samdard load for the same penetation as for Ar wen from Table 29.1.
The CBR. values are usually cal for penetration of 2.5 mm and $ mm. If CBR. for
3 cm exceeds hat for 2.5 mm, the test should be repented. If ental resus fallow, he C.B.R, corresponding
10 $ mm peseta should be taken for design,
Cates dT Rest
1. Ban rl. Ts pme mio may be eed a foe
tapon re 00
where dye final dal prope reading. (mm) ; intial gauge reading (om)
him height of specimen (mm).
2. Load penetration. Plot the kad penetraon curve (Fig. 29.8). If the inal porion of the curve
is concave upwards, apply the correction by drawing a tangent to the curve at the pain of greatest
slope.
Te corrected origin wil be the point where the ion mets the abscissa, Find and record
the corrected load reading. comespoding to each peneiaon.
Corresponding 10 the penetration value at which the C.B.R. is desired, corected load valves are
found from the curve and CBR. is colculod as fellows
Br
care ho
Pr = corcted test load corresponing to the chosen penetration from the load
peneruion curve
Ps Samdard load for the same penetation as for Ar wen from Table 29.1.
The CBR. values are usually cal for penetration of 2.5 mm and $ mm. If CBR. for
3 cm exceeds hat for 2.5 mm, the test should be repented. If ental resus fallow, he C.B.R, corresponding
10 $ mm peseta should be taken for design,
50]
Design of Rigid Pavement
30.1. INTRODUCTION
Rigid pavements are made up of Porlant cement concrete, and may or
have a base course between the pavement and the sub-grade. Because of its rigidity. and
high tensile strength, a rigid pavement tends to distribute the load over a relatively wide
arca of soil, and a major portion of the structural capacity is supplied by the slab itself.
For this reason, minor variations in sub-grade strength have litle influence upon the structural
capacity of the pavement. The rigid pavements are used for heavier loads and can be
constructed over relatively poor sub-grade such as black cotton or plastic soils, peat, etc.
A base under rigid pavements may be used for the following reasons :
1. Prevention of pumping of fine grained soil (Pumping is defined as the ejection
of water and sub-grade soils through joins, cracks and along the edges of pavements
caused by downward slab movement by the passage of heavy axle loads over the pavement
after the accumulation of free water on or in the sub-grade)
2. Protection against frost action
3. Provides drainage.
4. Controls the shrink and swell of sub-prade.
5. It forms a working surface on clays and silts, and thus enables the construction
10 proceed expeditiously during wet weather
6. Serves as a leveling course on irregular formations.
7. Lends some structural capacity 10 the pavement.
30.2. STRESSES IN RIGID PAVEMENT
‘The factors affecting stresses in rigid pavement can be placed in four broad categories:
1. Stress due to retains) emporte and moisture deformations.
2. Suresses due to the externally applied loads.
3. Stresses due to volume changes of the supporting material, including frost action.
4. Stresses due to continuity ofthe sub-grade support as affected by permanent deformations
of the sub-grade or loss of support through pumping
on
Design of Rigid Pavement
30.1. INTRODUCTION
Rigid pavements are made up of Porlant cement concrete, and may or
have a base course between the pavement and the sub-grade. Because of its rigidity. and
high tensile strength, a rigid pavement tends to distribute the load over a relatively wide
arca of soil, and a major portion of the structural capacity is supplied by the slab itself.
For this reason, minor variations in sub-grade strength have litle influence upon the structural
capacity of the pavement. The rigid pavements are used for heavier loads and can be
constructed over relatively poor sub-grade such as black cotton or plastic soils, peat, etc.
A base under rigid pavements may be used for the following reasons :
1. Prevention of pumping of fine grained soil (Pumping is defined as the ejection
of water and sub-grade soils through joins, cracks and along the edges of pavements
caused by downward slab movement by the passage of heavy axle loads over the pavement
after the accumulation of free water on or in the sub-grade)
2. Protection against frost action
3. Provides drainage.
4. Controls the shrink and swell of sub-prade.
5. It forms a working surface on clays and silts, and thus enables the construction
10 proceed expeditiously during wet weather
6. Serves as a leveling course on irregular formations.
7. Lends some structural capacity 10 the pavement.
30.2. STRESSES IN RIGID PAVEMENT
‘The factors affecting stresses in rigid pavement can be placed in four broad categories:
1. Stress due to retains) emporte and moisture deformations.
2. Suresses due to the externally applied loads.
3. Stresses due to volume changes of the supporting material, including frost action.
4. Stresses due to continuity ofthe sub-grade support as affected by permanent deformations
of the sub-grade or loss of support through pumping
on
se SOIL MECHANICS AND FOUNDATIONS
Relative Stiffness of Slabs : When a load is applied on a slab, it deforms in a
saucer shape, and the resistance to deformation depends upon the stiffbess of the supporting
medium as well as flexural stiffoess of the slab, The relative stiffness of the sub-grade
and the slab is indicated in terms of radius of relative stifiness, defined by Westergaard
(1927) by the following characteristic equation :
Ee
12a |
where L= radius of relative stiffness (cm) (a linear dimension)
E= modulus of elasticity of the pavement (kg/cm)
= thickness of pavement (cm)
= Poisson's ratio of the pavement
ky= modulus of sub-grade reaction (kg/cm)
The modulus of sub-grade reaction is defined as the intensity of pressure on the
horizontal surface of a soil mass required to cause a unit settlement of surface ;
bok 602)
where p= sub-grade reaction. p = vertical deflection
30.3. STRESSES DUE TO WHEEL LOAD
Westergaard (1926) considered three cases of loading : (1) corner load, (2) load
at the edge of the pavement, and (3) interior load. His original equation for interior loading
was later modified by him (Westergaard, 1933). The equations for edge and corner loading
were modified by Sutherland (1943). The modified equations converted into metric units,
are given below :
Somme 202750140) À [159 E) tiene tiza ade se 0 LJ] con
cow = 052 +054 E ego) 1080 (557)] es
| 005)
where
(Guam = maximum tensile stress at the bottom of slab due to loading at the
interior (g/em’)
(dee = maximum tensile stress at the bottom of slab due to loading at the edge
(kg/cm)
(Gone = maximum tensile stress
(kg/cm)
P= wheel load 63)
the top of the slab due to loading at comer
Relative Stiffness of Slabs : When a load is applied on a slab, it deforms in a
saucer shape, and the resistance to deformation depends upon the stiffbess of the supporting
medium as well as flexural stiffoess of the slab, The relative stiffness of the sub-grade
and the slab is indicated in terms of radius of relative stifiness, defined by Westergaard
(1927) by the following characteristic equation :
Ee
12a |
where L= radius of relative stiffness (cm) (a linear dimension)
E= modulus of elasticity of the pavement (kg/cm)
= thickness of pavement (cm)
= Poisson's ratio of the pavement
ky= modulus of sub-grade reaction (kg/cm)
The modulus of sub-grade reaction is defined as the intensity of pressure on the
horizontal surface of a soil mass required to cause a unit settlement of surface ;
bok 602)
where p= sub-grade reaction. p = vertical deflection
30.3. STRESSES DUE TO WHEEL LOAD
Westergaard (1926) considered three cases of loading : (1) corner load, (2) load
at the edge of the pavement, and (3) interior load. His original equation for interior loading
was later modified by him (Westergaard, 1933). The equations for edge and corner loading
were modified by Sutherland (1943). The modified equations converted into metric units,
are given below :
Somme 202750140) À [159 E) tiene tiza ade se 0 LJ] con
cow = 052 +054 E ego) 1080 (557)] es
| 005)
where
(Guam = maximum tensile stress at the bottom of slab due to loading at the
interior (g/em’)
(dee = maximum tensile stress at the bottom of slab due to loading at the edge
(kg/cm)
(Gone = maximum tensile stress
(kg/cm)
P= wheel load 63)
the top of the slab due to loading at comer
DESIGN OF RIGID PAVEMENT se
= slab thickness (em)
w= Poisson’s ratio for concrete
radios of relative stiffness. (cm)
E= modulus of elasticity (kg/cm)
‘ke= modulus of sub-grade reaction (kg/cm’)
= radius of equivalent distribution of pressure (cm), given by the following
uations _:
Arr - 06156 ‚when a < 1.724 h . (30.6)
bea vien a2 1.724h 307)
am radius of area of contact between the slab (em), the area being assumed
circular in case of corner and interior loads, and semi circular for edge loads
ci. €2 correlation factors 10 allow for a redistribution of sub-grade reactions ;
eye
Picker (1951) gave the following semi-empirical formulae for corner loading for protected
and unprotected corners
For slab corners protected by loadairansfer devices such as bars ete.
an |
DB oil ee
Yi)
55027071) 009)
The above two formulae are in FPS units in which P in lbs, 0 is in lb/i ,
La and are in inches and A, is in Ibfin.
The formulae for the stresses in pavements are complicated for direct calculations,
Use may be made of the influence diagrams and chars prepared by Docker (1948) and
Pickett (1951).
30.4. STRESSES DUE TO WARPING
The surface of the slab is subjected 10 wide range of temperature during the daily
cycle, Whereas the temperature of the bottom of the slab in contact with the sub-grade
of the base remains relatively more constant. This temperature gradient through the slab
causes differemial expansion or contraction between the top and baktam of the slab,
Im the day, top surface expands more than the bottom and the slab assumes a shape
convex upwards. The weight of the slab and toad transfer devices or fiction at joint will
restrain free warping. and wil tend to bend it back imo its original shape, and hence
compressive siesses st top and tensile at the bottem are created
In the night, te sides and corners warp upwards, and might actualy leave the sub grade,
In this poston, the weight of the raised portions of the slab tend to bend them down.
= slab thickness (em)
w= Poisson’s ratio for concrete
radios of relative stiffness. (cm)
E= modulus of elasticity (kg/cm)
‘ke= modulus of sub-grade reaction (kg/cm’)
= radius of equivalent distribution of pressure (cm), given by the following
uations _:
Arr - 06156 ‚when a < 1.724 h . (30.6)
bea vien a2 1.724h 307)
am radius of area of contact between the slab (em), the area being assumed
circular in case of corner and interior loads, and semi circular for edge loads
ci. €2 correlation factors 10 allow for a redistribution of sub-grade reactions ;
eye
Picker (1951) gave the following semi-empirical formulae for corner loading for protected
and unprotected corners
For slab corners protected by loadairansfer devices such as bars ete.
an |
DB oil ee
Yi)
55027071) 009)
The above two formulae are in FPS units in which P in lbs, 0 is in lb/i ,
La and are in inches and A, is in Ibfin.
The formulae for the stresses in pavements are complicated for direct calculations,
Use may be made of the influence diagrams and chars prepared by Docker (1948) and
Pickett (1951).
30.4. STRESSES DUE TO WARPING
The surface of the slab is subjected 10 wide range of temperature during the daily
cycle, Whereas the temperature of the bottom of the slab in contact with the sub-grade
of the base remains relatively more constant. This temperature gradient through the slab
causes differemial expansion or contraction between the top and baktam of the slab,
Im the day, top surface expands more than the bottom and the slab assumes a shape
convex upwards. The weight of the slab and toad transfer devices or fiction at joint will
restrain free warping. and wil tend to bend it back imo its original shape, and hence
compressive siesses st top and tensile at the bottem are created
In the night, te sides and corners warp upwards, and might actualy leave the sub grade,
In this poston, the weight of the raised portions of the slab tend to bend them down.
su SOIL MECHANICS AND FOUNDATIONS.
Hence tension at top and 1
compression in the bottom is de-
veloped. Bradbury (1938) gave
the following equations for edge
stress and interior stress due to
warping: ge
(he = SE Sod
0 2 [|
nme EAN Gt NG, 7
er) ded
(80.11)
where — @u= co-efficient of expan-
sion of concrete ( 5x 10%
fact ¿ HET
4 te oral difference intem- L
perature (may be taken to be equal rot
to about 1° F per 1 cm thickness FIG. 301. WARPING STRESS CO-EFFICIENTS
o RADEURY, 138)
E modulus of clasiciy of conerete
= Poisson's ratio
C= coefficient given by Fig. 30.1, corresponding to LA ratio
Ca = co-efficient in he desired. directon(say, x direction)
Gi= co-efficient in the perpendicular direction (say, y direction)
Le length of the edge
J free length in x direction (Le the direction in which Sur is sought)
Lie fee width in y direcion.
30.5. STRESSES DUE TO SUB-GRADE FRICTION
Suesses can also be set up in rigid pavemens due to uniform temperature change,
which cause the slab to contract or expand. If the slab is free to move and there is
o friction between the slab and the sub-grade, no stresses will result. However, if ition
exists between the slab and sub-grade, restraint results from the fiction forces and the
slab is sessed. During expansion, the underside of the slab is subjected 1» compressive
stress, while during contraction tensile stress are induced due w the sub-grade frcin.
Fig. 30.2 @) shows the distribution of frictional stresses, as suggested by Kelley (1939)
Test results have shown that fully mobilised frictional resistance fq is realised for a distance
Lx us om ee De cen of es, e avs dilo par In pe,
The equations for the average co-efficient of sub-grade resistance J are as follows
Hence tension at top and 1
compression in the bottom is de-
veloped. Bradbury (1938) gave
the following equations for edge
stress and interior stress due to
warping: ge
(he = SE Sod
0 2 [|
nme EAN Gt NG, 7
er) ded
(80.11)
where — @u= co-efficient of expan-
sion of concrete ( 5x 10%
fact ¿ HET
4 te oral difference intem- L
perature (may be taken to be equal rot
to about 1° F per 1 cm thickness FIG. 301. WARPING STRESS CO-EFFICIENTS
o RADEURY, 138)
E modulus of clasiciy of conerete
= Poisson's ratio
C= coefficient given by Fig. 30.1, corresponding to LA ratio
Ca = co-efficient in he desired. directon(say, x direction)
Gi= co-efficient in the perpendicular direction (say, y direction)
Le length of the edge
J free length in x direction (Le the direction in which Sur is sought)
Lie fee width in y direcion.
30.5. STRESSES DUE TO SUB-GRADE FRICTION
Suesses can also be set up in rigid pavemens due to uniform temperature change,
which cause the slab to contract or expand. If the slab is free to move and there is
o friction between the slab and the sub-grade, no stresses will result. However, if ition
exists between the slab and sub-grade, restraint results from the fiction forces and the
slab is sessed. During expansion, the underside of the slab is subjected 1» compressive
stress, while during contraction tensile stress are induced due w the sub-grade frcin.
Fig. 30.2 @) shows the distribution of frictional stresses, as suggested by Kelley (1939)
Test results have shown that fully mobilised frictional resistance fq is realised for a distance
Lx us om ee De cen of es, e avs dilo par In pe,
The equations for the average co-efficient of sub-grade resistance J are as follows
DESIGN OF RIGID PAVEMENT ss
x
For re} hiso(1-28) Go
CENTRE NE 430.13) e
It has been shown chat the minimum amount (a) Fricton forces acting
of displacement required for friction to be fully
developed is 0.06 inch (1.5 mm). poe era
For equilibrium conditions, the summation "| |
of the fiction forces from the centres of the gp.
slab to the free end must be equal 10 the total A
tension in the concrete. The frictional resistance =
is assumed 10 be a finie value, dependent upon
the weight of the slab and coefficient of sliding
Bieten. FIG. 302. STRESSES RESULTING
Let We weight ofthe slab per sq. metre FROM CONTRACTION.
(gm)
L=lengih of the slab, in metres
= thickness of the slab in cm
oo stress in concrete, kg/cm*
‘f= average co-efficient of sub-grade resistance (f=2.3 to 1.15 ; average 1.5)
‘Then frictional resistance up 10 the centre of the slab
t= Temperatura crop CP)
(©) Varason off wath langen
swab tas Qs) er mere width of te san)
Total tension in the concrete = (1 x 100 (per metre width of the slab)
Equating (1) and @ we gt L100 hon
= WL eg
md U iron 6014)
Taking unit weight of concrete as 2400 kg/m’,
a
Wee dn A "2100-244 kg (90.15)
Substicuing in equation 30.14, we get
EA e019
More exact calculations could be made by taking into account the variation in friction
bee te eta de ene of ti a
Combi armes due 1 oa and temperature : Te rl ates contin in
te sb oreo VA ann ‘oe mp an areas ti 1 Lu ar
‘ue, Ts cis can eal rea de sub Cc we aye vn at el à
ia app ae ior of es Sin tg a car. cn ig towed
x
For re} hiso(1-28) Go
CENTRE NE 430.13) e
It has been shown chat the minimum amount (a) Fricton forces acting
of displacement required for friction to be fully
developed is 0.06 inch (1.5 mm). poe era
For equilibrium conditions, the summation "| |
of the fiction forces from the centres of the gp.
slab to the free end must be equal 10 the total A
tension in the concrete. The frictional resistance =
is assumed 10 be a finie value, dependent upon
the weight of the slab and coefficient of sliding
Bieten. FIG. 302. STRESSES RESULTING
Let We weight ofthe slab per sq. metre FROM CONTRACTION.
(gm)
L=lengih of the slab, in metres
= thickness of the slab in cm
oo stress in concrete, kg/cm*
‘f= average co-efficient of sub-grade resistance (f=2.3 to 1.15 ; average 1.5)
‘Then frictional resistance up 10 the centre of the slab
t= Temperatura crop CP)
(©) Varason off wath langen
swab tas Qs) er mere width of te san)
Total tension in the concrete = (1 x 100 (per metre width of the slab)
Equating (1) and @ we gt L100 hon
= WL eg
md U iron 6014)
Taking unit weight of concrete as 2400 kg/m’,
a
Wee dn A "2100-244 kg (90.15)
Substicuing in equation 30.14, we get
EA e019
More exact calculations could be made by taking into account the variation in friction
bee te eta de ene of ti a
Combi armes due 1 oa and temperature : Te rl ates contin in
te sb oreo VA ann ‘oe mp an areas ti 1 Lu ar
‘ue, Ts cis can eal rea de sub Cc we aye vn at el à
ia app ae ior of es Sin tg a car. cn ig towed
ww
SOIL MECHANICS AND FOUNDATIONS,
by a hot, sunny day, the edges and corners of the slab will warp upward and the comers
‘may then be only partially supported or even unsupported. This condition will gi
‘maximum stresses due 10 loading.
30.6. DESIGN METHOD
the
Portland Cement Association (1951) has developed a design procedure for rigid highway
pavements based upon formulae developed by Pickett (Eqs. 30.8 and 30.9). Fig. 303 and
30.4 show the design charıs for protected and unprotected corners, based on the formulae
by Pickett for the design of highway pavements. The values of A, are in Ibfin’,
‘The arrows shown on
the diagrams indicate the
procedure for finding the
pavement thickness h for a
givén value of allowable
stress in concrete, magnitude
of wheel load and given
value of k, and also for
finding the stress in he pave-
ment of a given thickness
corresponding to a given
Wheel load and a given value
of £. The working stress
in the concrete that is used.
in the analysis is obtained
by dividing the modulus of
rupture of the concrete by
a safety factor of 2.0. Loads
‘which are applied to the
pavement are increased 20
Per cent to account for im-
Conerete pavements
designed with the help of
these charts are considered
to have excess strength 10
Offset working. stresses.
30.5, 30.6 and
30.7 give the PCA (Portland
Concrete Association) de-
sign chants for Rigid airport
os FAT Hh
12
u
an
se
ho
im
L
RE
‘
20!
FIG, 303. FCA DESIGN CHARTS FOR RIGID HIGHWAY
PAVEMENTS PROTECTED CORNERS, FOR LOADS
'ON DUAL “TYRES.
pavements, with various wheel loads and gre pressure (indicated dotted lines).
‘Thokroms hin inches
SOIL MECHANICS AND FOUNDATIONS,
by a hot, sunny day, the edges and corners of the slab will warp upward and the comers
‘may then be only partially supported or even unsupported. This condition will gi
‘maximum stresses due 10 loading.
30.6. DESIGN METHOD
the
Portland Cement Association (1951) has developed a design procedure for rigid highway
pavements based upon formulae developed by Pickett (Eqs. 30.8 and 30.9). Fig. 303 and
30.4 show the design charıs for protected and unprotected corners, based on the formulae
by Pickett for the design of highway pavements. The values of A, are in Ibfin’,
‘The arrows shown on
the diagrams indicate the
procedure for finding the
pavement thickness h for a
givén value of allowable
stress in concrete, magnitude
of wheel load and given
value of k, and also for
finding the stress in he pave-
ment of a given thickness
corresponding to a given
Wheel load and a given value
of £. The working stress
in the concrete that is used.
in the analysis is obtained
by dividing the modulus of
rupture of the concrete by
a safety factor of 2.0. Loads
‘which are applied to the
pavement are increased 20
Per cent to account for im-
Conerete pavements
designed with the help of
these charts are considered
to have excess strength 10
Offset working. stresses.
30.5, 30.6 and
30.7 give the PCA (Portland
Concrete Association) de-
sign chants for Rigid airport
os FAT Hh
12
u
an
se
ho
im
L
RE
‘
20!
FIG, 303. FCA DESIGN CHARTS FOR RIGID HIGHWAY
PAVEMENTS PROTECTED CORNERS, FOR LOADS
'ON DUAL “TYRES.
pavements, with various wheel loads and gre pressure (indicated dotted lines).
‘Thokroms hin inches
SOIL MECHANICS AND FOUNDATIONS
amu escent,
ag HE
GES ‘a
=: wo
i E
H
A
a a
HEA i à
fe ’
e ae m
H it w HB vos
amu escent,
ag HE
GES ‘a
=: wo
i E
H
A
a a
HEA i à
fe ’
e ae m
H it w HB vos
Stabilisation of Soils
31.1. INTRODUCTION
‘Stabilisation, in a broad sense, incorporates the various methods employed for modifying
the properties of a soil to improve its engineering performance. Stabilisation is being used
for a variety of engineering works, the most common application being in the construction
of road and airfield pavements, where the main objective is to increase the strength or
stability of soil and to reduce the construction cost by making best use of the locally
available materials. Methods of stabilisation may be grouped under two main types : (a)
modification or Improvement of a soll propery of the existing soil without any admixture,
and (b) modification of the properties with the help of admixtures. Compaction and drainage
are the examples of the fist type, which improve the inherent shear strength of soil. Examples
of the second type are : mechanical stabilisation, stabilisation with cement, lime, bitumen
and chemicals etc. Some of the more commonly used methods will be discussed in this
chapter.
31.2. MECHANICAL STABILISATION
Mechanical stabilisation involves two operations : (9) changing the composition of soil
by addition or removal of certain constituents, and (li) densification or compaction. The
parie size distribution and composition are the important factors governing the engineering
behaviour of a soil. Significant changes in the properties can be made by addition or removal
of suitable soil fractions. For mechanical stabilisation, where the primary purpose is to
have a soil resistant to deformation and displacement under loads, soil materials can be
divided into two fractions : the granular fraction retained on a 75 micron IS sieve and
the fine sell fraction passing a 75-micron sieve. The granular fraction impart strength and
hardness, The fine fraction provides cohesion or binding property, water-reention capacity
aod also acts as a filler for the voids of the coarse fraction.
Mechanical stabilisation has been largely used in the construction of cheap roads
Guide of specifications have been drawn for gradation requirements of the bases and surfacing.
‘Typical examples are given in Table 31.1. Instead of striily observing the specifications,
‘emphasis should be laid on making the maximum use of the locally available materials
33 many materials are found to be quite satisfactory under load conditons.
Co
31.1. INTRODUCTION
‘Stabilisation, in a broad sense, incorporates the various methods employed for modifying
the properties of a soil to improve its engineering performance. Stabilisation is being used
for a variety of engineering works, the most common application being in the construction
of road and airfield pavements, where the main objective is to increase the strength or
stability of soil and to reduce the construction cost by making best use of the locally
available materials. Methods of stabilisation may be grouped under two main types : (a)
modification or Improvement of a soll propery of the existing soil without any admixture,
and (b) modification of the properties with the help of admixtures. Compaction and drainage
are the examples of the fist type, which improve the inherent shear strength of soil. Examples
of the second type are : mechanical stabilisation, stabilisation with cement, lime, bitumen
and chemicals etc. Some of the more commonly used methods will be discussed in this
chapter.
31.2. MECHANICAL STABILISATION
Mechanical stabilisation involves two operations : (9) changing the composition of soil
by addition or removal of certain constituents, and (li) densification or compaction. The
parie size distribution and composition are the important factors governing the engineering
behaviour of a soil. Significant changes in the properties can be made by addition or removal
of suitable soil fractions. For mechanical stabilisation, where the primary purpose is to
have a soil resistant to deformation and displacement under loads, soil materials can be
divided into two fractions : the granular fraction retained on a 75 micron IS sieve and
the fine sell fraction passing a 75-micron sieve. The granular fraction impart strength and
hardness, The fine fraction provides cohesion or binding property, water-reention capacity
aod also acts as a filler for the voids of the coarse fraction.
Mechanical stabilisation has been largely used in the construction of cheap roads
Guide of specifications have been drawn for gradation requirements of the bases and surfacing.
‘Typical examples are given in Table 31.1. Instead of striily observing the specifications,
‘emphasis should be laid on making the maximum use of the locally available materials
33 many materials are found to be quite satisfactory under load conditons.
Co
so SOI MECHANICS AND FOUNDATIONS
TABLE 31. ‘TYPICAL GRADATION SPECIFICATIONS OF MECHANICALLY STABILISED
BASES_AND_SURFACINGS
| Prune pasto
Sine Base 1 Surfacing | Base or surfacing
es Pr mr |
Ge [ae | as ims
oo » | - - -
2m m- 00 | wo | 100 =
= u. a
435 mm as »-m
— un 2-0
ite a .-e
wu = E
20 non 2-. a
75 mim s- [sos 1-2 10-28
Note. (1) For bases ; Liquid limit not exceeding 25% and plasticity index not exceeding
6
(ib) For surfacing : Liquid limit not exceeding 35% and plasticity index between
4 and 9.
If the soil from one source does not meet the gradation and plasticity requirements
of a job, it becomes necessary to mix materials from two more sources for obtaining
the desired mixture. The blending of materials can be carried out by making trial combinations.
Proper compaction plays a very important role in stabilisation. Compaction has a
great effect on soil properties, such as strength and stress-strain characteristics, permeability,
‘compression, swelling and water absorption. The properties of a soil under compaction depend
upon the water content, amount of compaction and the type of compaction. compared 10
coarse grained soils, the properties of fine grained soils are affected to a greater extent
by the placement conditions. Compaction has been discussed in Chapter 17
31.3. CEMENT STABILISATION
1. Soil cement and its influencing factors. The soil stabilised with cement (Portland)
is known as soil cement. The cementing action is belived to be the result of chemical
reaction of cemeat with the silicious soil during hydration. The binding action of individual
particles through cement may be possible only in coarse-grained soils. In fine , cabesive
TABLE 31. ‘TYPICAL GRADATION SPECIFICATIONS OF MECHANICALLY STABILISED
BASES_AND_SURFACINGS
| Prune pasto
Sine Base 1 Surfacing | Base or surfacing
es Pr mr |
Ge [ae | as ims
oo » | - - -
2m m- 00 | wo | 100 =
= u. a
435 mm as »-m
— un 2-0
ite a .-e
wu = E
20 non 2-. a
75 mim s- [sos 1-2 10-28
Note. (1) For bases ; Liquid limit not exceeding 25% and plasticity index not exceeding
6
(ib) For surfacing : Liquid limit not exceeding 35% and plasticity index between
4 and 9.
If the soil from one source does not meet the gradation and plasticity requirements
of a job, it becomes necessary to mix materials from two more sources for obtaining
the desired mixture. The blending of materials can be carried out by making trial combinations.
Proper compaction plays a very important role in stabilisation. Compaction has a
great effect on soil properties, such as strength and stress-strain characteristics, permeability,
‘compression, swelling and water absorption. The properties of a soil under compaction depend
upon the water content, amount of compaction and the type of compaction. compared 10
coarse grained soils, the properties of fine grained soils are affected to a greater extent
by the placement conditions. Compaction has been discussed in Chapter 17
31.3. CEMENT STABILISATION
1. Soil cement and its influencing factors. The soil stabilised with cement (Portland)
is known as soil cement. The cementing action is belived to be the result of chemical
reaction of cemeat with the silicious soil during hydration. The binding action of individual
particles through cement may be possible only in coarse-grained soils. In fine , cabesive
STABILISATION OF SONS ss
In the mixaplace method, the sub-grade is fist shaped 10 the required grade and
is cleared of undesirable materials. Ie is then scariied to the required depth of treatment
and the soils is pulverised, until at least 80% of the material (excluding stones) passes
2 475 mm sieve. If another soil is to be blended, it is mixed with the loose, pulveriscd
soil. The pulverised sol is spread and shaped co proper grade. Calculated amount of cement
is then evenly distributed over the surface and intimately mixed. Water is added as required
for compaction and the soil cement-water is turned into an intimate mixture. The wet mixture
‘operation should not last more than 3 hours, after which the compaction should be completed
within the mext 2 hours. It is fairly easy 10 process coarse grained soil, Pulverisation and
mixing of plastic clays can be facilid by adding lime in proportions of 1 to 4%. The
compacted soil cement is moistured for at least 7 days. A bituminous wearing surface is
mormally provided to protect the foilcement base from abrasion and shsorption of water
in shrinkage cracks.
‘The mixinplace method is considered cheaper and more adaptible to different field
conditions, but the processing of soil is not so thorough and accurate as with other methods.
In the sravelling plant method, the pulveriscd soil is heaped into a window and the
cement is spread on the top. The soil and cement are lied by an elevator to a mixer
carried on a traveling platform where water is added and mixing is done. The mixture
is then discharged on to the subgrade. It is spread with a grader and compacted. Unifrom
mixing and accurate control on added water can be ensured in the method. A uniform
subgrade surface with controlled depth of treatment is possible. The plant is however, cost
In the stationary plant method, the excavated soil is brought to a stationary mixing plant
AX the plant, cement and water are added and mixed with the soil. The mixture is then
transported back to the desired location, dumped, spread and compacted. Similar to the
travelling method, the method affords an. accurate proportioning of materials and thorough
mixing. The depth of treatment can be easily controled. The method is slower and may
prove expensive due 1 additional haulage of soil.
314. LIME STABILISATION
Hydeated (or slaked) lime is very effective in treating heavy, plastic clayey soi.
Lime may be used alone, or in combination with cement, bitumen or fly ash. Sandy soils
can also be stabilised with these combinations. Lime has been mainly used for stabilising
the road bases and sub-grades.
On addition of lime to soil, wo main types of chemical reactions occur : () alteration
in the nature of the absorbed layer through base exchange phenomenon, and (i) cementing
or puzzolanic action, Lime reduces the plasticity index of highly plastic soils making them
more friable and easy to be handled and pulverised. The plasticity index of soils of low
plasticity generally increases. There is generally an increase in the optimum water content
and a decrease in the maximum compacted density. but the strength and durability increases,
The amount of lime required may be used on the unconfined compressive strength
or the CBR test criteria, Normally 2 or 8% of lime may be required for course grained
sols, and 5 10 10% for phase soils. The amount of fly ash as admixture may vary
from 8 to 20% of the soil weight (Lambe, 1962)
In the mixaplace method, the sub-grade is fist shaped 10 the required grade and
is cleared of undesirable materials. Ie is then scariied to the required depth of treatment
and the soils is pulverised, until at least 80% of the material (excluding stones) passes
2 475 mm sieve. If another soil is to be blended, it is mixed with the loose, pulveriscd
soil. The pulverised sol is spread and shaped co proper grade. Calculated amount of cement
is then evenly distributed over the surface and intimately mixed. Water is added as required
for compaction and the soil cement-water is turned into an intimate mixture. The wet mixture
‘operation should not last more than 3 hours, after which the compaction should be completed
within the mext 2 hours. It is fairly easy 10 process coarse grained soil, Pulverisation and
mixing of plastic clays can be facilid by adding lime in proportions of 1 to 4%. The
compacted soil cement is moistured for at least 7 days. A bituminous wearing surface is
mormally provided to protect the foilcement base from abrasion and shsorption of water
in shrinkage cracks.
‘The mixinplace method is considered cheaper and more adaptible to different field
conditions, but the processing of soil is not so thorough and accurate as with other methods.
In the sravelling plant method, the pulveriscd soil is heaped into a window and the
cement is spread on the top. The soil and cement are lied by an elevator to a mixer
carried on a traveling platform where water is added and mixing is done. The mixture
is then discharged on to the subgrade. It is spread with a grader and compacted. Unifrom
mixing and accurate control on added water can be ensured in the method. A uniform
subgrade surface with controlled depth of treatment is possible. The plant is however, cost
In the stationary plant method, the excavated soil is brought to a stationary mixing plant
AX the plant, cement and water are added and mixed with the soil. The mixture is then
transported back to the desired location, dumped, spread and compacted. Similar to the
travelling method, the method affords an. accurate proportioning of materials and thorough
mixing. The depth of treatment can be easily controled. The method is slower and may
prove expensive due 1 additional haulage of soil.
314. LIME STABILISATION
Hydeated (or slaked) lime is very effective in treating heavy, plastic clayey soi.
Lime may be used alone, or in combination with cement, bitumen or fly ash. Sandy soils
can also be stabilised with these combinations. Lime has been mainly used for stabilising
the road bases and sub-grades.
On addition of lime to soil, wo main types of chemical reactions occur : () alteration
in the nature of the absorbed layer through base exchange phenomenon, and (i) cementing
or puzzolanic action, Lime reduces the plasticity index of highly plastic soils making them
more friable and easy to be handled and pulverised. The plasticity index of soils of low
plasticity generally increases. There is generally an increase in the optimum water content
and a decrease in the maximum compacted density. but the strength and durability increases,
The amount of lime required may be used on the unconfined compressive strength
or the CBR test criteria, Normally 2 or 8% of lime may be required for course grained
sols, and 5 10 10% for phase soils. The amount of fly ash as admixture may vary
from 8 to 20% of the soil weight (Lambe, 1962)
ast SOIL MECHANICS AND FOUNDATIONS
The construction procedures of lime stabilised bases are similar (0 those sil-ceme
No strict time limitations for completion of the job are however necessary, since the soiklime
cementation reactions are respectively slow.
31.5. BITUMEN STABILISATION
Asplalls and tars are the bituminous materials which are used for stabilisation of
soil, generally for pavement construction. These materials are normally 100 viscous 10 be
incorporated directly with soil. The fluidity of asphals is increased by either heating, emulsifying
or by cutback process, Tars are heated or cut back. The bituminous materials when added
10 a soil impart cohesion or binding action and reduced water absorption. Thus either the
binding action or the water proofing action or both the actions, may be utilised for stabilisation.
Depending upon these actions and the nature of soil, bitumen stabilisation is classified
under the following four types : (A) sand- bitumen, (ji) seikbitumen, (Hi) water-proofed
mechanical stabilisation and (+) led earth.
1. Sand bitumen.
This term refers 10 binumenstblised cohesionless soil, such as loose beach, dane,
pit or river sand, The primary function of bitumen is to bind the soil particles. Sand
should be substantially free from clay and organic mater. The gradation may vary within
a wide range, but the fraction passing a 75 micron sieve should normally not exceed 12%
3 in case of fine done sand the fraction may be upto 25%. Crushed stone, rock dust,
gravel, eie., may be added 10 poorly graded sand.
‘The climatic conditions such as rainfall and temperature decide the type of bituminous
material to be used and the method of mixing and consiniction to be cemployed. Hot
mix sand asphalt is suitable in area of heavy rainfall, and emulsions are preferable in
arid zones. Rapid curing cut-backs are recommended for low temperatures and slow curing
for high temperatures. The quantity of.bitaminous material required is determined by laboratory
tests, The approximate proportions on dry weight basis of sand are as follows (Uppal and
Bhalla, 1965); hot mix asphat, 5 10 11% ; cutback, 4 to 10% ; emulsions, 5 to 10%.
Hydrated lime, 1 to 2% is sometimes used as an admixture 10 assist coating of sand
gras.
2. Soil bitumen.
It refers to a cobesive soil in which the main function of bitumen is lo preserve
the natural cohesive stengúh by water-proofing the soil or reducing the water absorption.
A large variety of soils can be thos stabilised. For best results the following requirements
are recommended (HRB, 1946) :
(0 Maximum size : not greater than approximately one-third the compacted thickness,
(i) Passing 4.75 mm sieve : more than 50% ,
(i) Passing 425 micron sieve : 35—100%,
6») Passing 75 micron sieve 10-50%,
€ Liquid limit : Less than 40%,
(i) Plasticity index : Less than 18.
The construction procedures of lime stabilised bases are similar (0 those sil-ceme
No strict time limitations for completion of the job are however necessary, since the soiklime
cementation reactions are respectively slow.
31.5. BITUMEN STABILISATION
Asplalls and tars are the bituminous materials which are used for stabilisation of
soil, generally for pavement construction. These materials are normally 100 viscous 10 be
incorporated directly with soil. The fluidity of asphals is increased by either heating, emulsifying
or by cutback process, Tars are heated or cut back. The bituminous materials when added
10 a soil impart cohesion or binding action and reduced water absorption. Thus either the
binding action or the water proofing action or both the actions, may be utilised for stabilisation.
Depending upon these actions and the nature of soil, bitumen stabilisation is classified
under the following four types : (A) sand- bitumen, (ji) seikbitumen, (Hi) water-proofed
mechanical stabilisation and (+) led earth.
1. Sand bitumen.
This term refers 10 binumenstblised cohesionless soil, such as loose beach, dane,
pit or river sand, The primary function of bitumen is to bind the soil particles. Sand
should be substantially free from clay and organic mater. The gradation may vary within
a wide range, but the fraction passing a 75 micron sieve should normally not exceed 12%
3 in case of fine done sand the fraction may be upto 25%. Crushed stone, rock dust,
gravel, eie., may be added 10 poorly graded sand.
‘The climatic conditions such as rainfall and temperature decide the type of bituminous
material to be used and the method of mixing and consiniction to be cemployed. Hot
mix sand asphalt is suitable in area of heavy rainfall, and emulsions are preferable in
arid zones. Rapid curing cut-backs are recommended for low temperatures and slow curing
for high temperatures. The quantity of.bitaminous material required is determined by laboratory
tests, The approximate proportions on dry weight basis of sand are as follows (Uppal and
Bhalla, 1965); hot mix asphat, 5 10 11% ; cutback, 4 to 10% ; emulsions, 5 to 10%.
Hydrated lime, 1 to 2% is sometimes used as an admixture 10 assist coating of sand
gras.
2. Soil bitumen.
It refers to a cobesive soil in which the main function of bitumen is lo preserve
the natural cohesive stengúh by water-proofing the soil or reducing the water absorption.
A large variety of soils can be thos stabilised. For best results the following requirements
are recommended (HRB, 1946) :
(0 Maximum size : not greater than approximately one-third the compacted thickness,
(i) Passing 4.75 mm sieve : more than 50% ,
(i) Passing 425 micron sieve : 35—100%,
6») Passing 75 micron sieve 10-50%,
€ Liquid limit : Less than 40%,
(i) Plasticity index : Less than 18.
Li SOIL. MECHANICS AND FOUNDATIONS
they can be printed by the numerical printer elongwith time and channel no. at programmed
time intervals and sequences. The system can be programmed to shift the decimal poins
according to requirement. The datalogger has provision of peak hold facility which stores
he peak values of any parameter, attained during the test.
33.3. ELECTRONIC TRIAXIAL SHEAR TEST EQUIPMENT
Plate XII shows HEICO electronic triaxial test apparatus. This instrument eliminates
‘the constant recording and computation of the data by the observer. All the above funct
are carried out by continuous sensing of pore pressure, axial strain and axial load with
the help of pore pressure transducer, displacement transducer and load cell respectively and
their display directly in respective engincering unis on the digital read out unit coupled
to it through selectable switch. The unit is designed to be connected to micro-processor
based dat-logger [Pate XI (0)] which continuously scan the data received from the transducer
and in addition to their display, prints them in their respective engineering units at programmed
time intervals and sequences. A battery is provided to store the data programmed into
‘the daa-logger during power failure,
33.4, HYDRAULIC EARTH PRESSURE CELL
Earth pressure cells are used to measure the actual earth pressure on retaining walls,
building basements, bridge abutments sheet piling surface of tumel lining as well as for
measurement of total pressure at foundations of earth dams and embankments. Such measurements
help in evaluating their post construction behaviour and taking timely remedial measures
for the structures showing. distress.
Earth pressure cells, also called stress cells, are generally of two categories :
@ Flexible diaphragm type, and
GD Sfr cylinder type.
The flexible diaphragm ype earth pressure cell consists of a flexible circular or rectangular
dinphragm attached to a rigid stiff case. The pressure is measured due to continuous displaced
shape of the flexible diaphragm, the greatest deflection occuring at the centre, In the su
‘finder ype cell, the axial compression of the stiff, prismatic element, usually enclosed
within a case to isolate it from the lateral stresses of the surrounding soil mass, is used
to sense the total pressure.
Various systems available to measure earth pressure use the following :
(Electra resistance strain. gauges
i) Semiconductor strain gauges,
(ii) Vibrating wire system,
G) Closed uid system (usually called Gloetz or hydraulie pressure cell, and
(9) Pncumatic system, where air pressure is used to balance the siffness of the cell.
Out of the above systems, the strain gauge type, the vibrating wire type and the
closed fluid system type (Le hydraulic pressure cell) are commonly used since they are
most accurate, Resistance strain gauge type cells are casy 10 use and have linear rapid
response, but they are susceptible to damage and are affected by the moisture of the earth
material in long use. Vibrating wire type cells are more durable but have non-linear
response ; these are described in $ 23.5.
they can be printed by the numerical printer elongwith time and channel no. at programmed
time intervals and sequences. The system can be programmed to shift the decimal poins
according to requirement. The datalogger has provision of peak hold facility which stores
he peak values of any parameter, attained during the test.
33.3. ELECTRONIC TRIAXIAL SHEAR TEST EQUIPMENT
Plate XII shows HEICO electronic triaxial test apparatus. This instrument eliminates
‘the constant recording and computation of the data by the observer. All the above funct
are carried out by continuous sensing of pore pressure, axial strain and axial load with
the help of pore pressure transducer, displacement transducer and load cell respectively and
their display directly in respective engincering unis on the digital read out unit coupled
to it through selectable switch. The unit is designed to be connected to micro-processor
based dat-logger [Pate XI (0)] which continuously scan the data received from the transducer
and in addition to their display, prints them in their respective engineering units at programmed
time intervals and sequences. A battery is provided to store the data programmed into
‘the daa-logger during power failure,
33.4, HYDRAULIC EARTH PRESSURE CELL
Earth pressure cells are used to measure the actual earth pressure on retaining walls,
building basements, bridge abutments sheet piling surface of tumel lining as well as for
measurement of total pressure at foundations of earth dams and embankments. Such measurements
help in evaluating their post construction behaviour and taking timely remedial measures
for the structures showing. distress.
Earth pressure cells, also called stress cells, are generally of two categories :
@ Flexible diaphragm type, and
GD Sfr cylinder type.
The flexible diaphragm ype earth pressure cell consists of a flexible circular or rectangular
dinphragm attached to a rigid stiff case. The pressure is measured due to continuous displaced
shape of the flexible diaphragm, the greatest deflection occuring at the centre, In the su
‘finder ype cell, the axial compression of the stiff, prismatic element, usually enclosed
within a case to isolate it from the lateral stresses of the surrounding soil mass, is used
to sense the total pressure.
Various systems available to measure earth pressure use the following :
(Electra resistance strain. gauges
i) Semiconductor strain gauges,
(ii) Vibrating wire system,
G) Closed uid system (usually called Gloetz or hydraulie pressure cell, and
(9) Pncumatic system, where air pressure is used to balance the siffness of the cell.
Out of the above systems, the strain gauge type, the vibrating wire type and the
closed fluid system type (Le hydraulic pressure cell) are commonly used since they are
most accurate, Resistance strain gauge type cells are casy 10 use and have linear rapid
response, but they are susceptible to damage and are affected by the moisture of the earth
material in long use. Vibrating wire type cells are more durable but have non-linear
response ; these are described in $ 23.5.
ADVANCED MEASURING INSTRUMENTS ws
‘The hydraulic earth pressure cell, also known as Gloetz cell, has recently come into
vogue as means of measuring total pressure changes in soil, earth or rockfil, or at the
interface berwcen any of these materials. It may also be used (0 measure pressure changes
in rock, when installed in a machined stot,
Plate XIV shows the photograph of a hydraulic pressure cell manufactured by HEICO.
‘The pressure cell essentially consists of a sensor Mat jack or id filled pressure pad connected
to a hydraulic or pneumatic diaphragm transducer. which in curn, is connected by a flexible
tubing to a read out unit. Pressure transferred from the surrounding soil to the Mat jack
is measured by balancing the fluid pressure in the cell by a pressure applied 10 the reverse
side of the transducer diaphragm.
“The Mat jack (pressure sensor or cel) is formed from two sheets of stainless steel
welded around the periphery. The narrow gap of 1.5 mm between the plates is filled with
fluid of comparable deformity to that of the ground. Mercury is used in rocks and où
is used in soils. The cells can be either circular or rectangular in plan with dimensions
ranging from 6 10 40 cm.
‘The cell is connected to a hydraulic transducer by a short length of stainless steel
tubing forming a closed hydraulic circuit. Both the cell and the transducer are embedded
in the structure to be monitored, Hydraulic transducer is a hydraulic valve consisting of
à flexible steel, plastic or rubber diaphragm, incorporated in metal housing. The diaphragm
must completely separate the cell fluid from the measuring Avid. One side of the diaphragın
is connected to the cell Mid and the other to the measuring fluid delivery and retum
tubes. The transducer design is such that the pressure in cell Mut is slightly greater
than that in the measuring fluid in order to prevent return of the measuring fluid. When
the applied measuring pressure equals the cell fluid pressure, the diaphragm will displace,
allowing flow along the measuring Auid return line.
Read out equipment consists of a fluid reservoir, a pump with pressure gauge 10
measure the applied pressure, and Pressure cos
a detector to indicate the Maid coman one reg
return from the cell. Smaller ap- ©“ a
plied pressures are measured by
using a manometer instead. of
pressure gauge.
Hydraulic transducer is
connected to the terminal panel
or directly to the read out uni
bby two nylon high pressure pipes
carrying quick couplings at each
end. To take reading, hydraulic
pressure is supplied from the read
out unit to one side ofthe flexible
diaphragm valve incorporated in
the transducer. When the supply FIG, 331 INSTALLATION OF CELLS IN TUNNEL LINING
Termidor
‘The hydraulic earth pressure cell, also known as Gloetz cell, has recently come into
vogue as means of measuring total pressure changes in soil, earth or rockfil, or at the
interface berwcen any of these materials. It may also be used (0 measure pressure changes
in rock, when installed in a machined stot,
Plate XIV shows the photograph of a hydraulic pressure cell manufactured by HEICO.
‘The pressure cell essentially consists of a sensor Mat jack or id filled pressure pad connected
to a hydraulic or pneumatic diaphragm transducer. which in curn, is connected by a flexible
tubing to a read out unit. Pressure transferred from the surrounding soil to the Mat jack
is measured by balancing the fluid pressure in the cell by a pressure applied 10 the reverse
side of the transducer diaphragm.
“The Mat jack (pressure sensor or cel) is formed from two sheets of stainless steel
welded around the periphery. The narrow gap of 1.5 mm between the plates is filled with
fluid of comparable deformity to that of the ground. Mercury is used in rocks and où
is used in soils. The cells can be either circular or rectangular in plan with dimensions
ranging from 6 10 40 cm.
‘The cell is connected to a hydraulic transducer by a short length of stainless steel
tubing forming a closed hydraulic circuit. Both the cell and the transducer are embedded
in the structure to be monitored, Hydraulic transducer is a hydraulic valve consisting of
à flexible steel, plastic or rubber diaphragm, incorporated in metal housing. The diaphragm
must completely separate the cell fluid from the measuring Avid. One side of the diaphragın
is connected to the cell Mid and the other to the measuring fluid delivery and retum
tubes. The transducer design is such that the pressure in cell Mut is slightly greater
than that in the measuring fluid in order to prevent return of the measuring fluid. When
the applied measuring pressure equals the cell fluid pressure, the diaphragm will displace,
allowing flow along the measuring Auid return line.
Read out equipment consists of a fluid reservoir, a pump with pressure gauge 10
measure the applied pressure, and Pressure cos
a detector to indicate the Maid coman one reg
return from the cell. Smaller ap- ©“ a
plied pressures are measured by
using a manometer instead. of
pressure gauge.
Hydraulic transducer is
connected to the terminal panel
or directly to the read out uni
bby two nylon high pressure pipes
carrying quick couplings at each
end. To take reading, hydraulic
pressure is supplied from the read
out unit to one side ofthe flexible
diaphragm valve incorporated in
the transducer. When the supply FIG, 331 INSTALLATION OF CELLS IN TUNNEL LINING
Termidor
ADVANCED MEASURING INSTRUMENTS. m
known, the magnitude of the physical quantity which is measured, such as pressure, st
or force, can be calculated using formula and constants in calibration schemes supplied
with each transducer
A seco os viana m
conan an ete plop and acer ce
shown in Fig, 33.3. The electrical Voratng wre
pora, whch te peda sey, Re
are mounted inside the body of the
transducer.
AIMIL manufactures (wo ypes of =
cel : P-100 cel and P-105 cell. The FIG. 333. SCHEMATIC DIAGRAM OF
membrane diameter of P-100 cells (75 mm) VIBRATING-WIRE STRAIN GAUGE. (AIMIL)
limits the grain size of the soil to 1.5 mm. For larger grain size (0-2 mm). in earth/rock
fill dams and offshore applications, the P-10S cell with its active membrane diameter of
100 mm is recommended. Because of their thickness/diameter ratio (0.28 for P-100 and
0.22 for P-105), the transducers are installed in special steel frames when used in earth
fills for earth pressure measurements.
‘The P-100 transducer is often used
to measure total pressure or pore pressure
acting on different kinds of walls. For
Tow pressures, atmospheric pressure may
be maintained inside the transducer
through the PE tube encasing the lead
wires. The signal cable P-S40 is used
alongwith this cell >
‘The P-540 cable is made of standard FIG. 334. PSO CABLE,
PPOP one-pair shielded cable with OD
10 mm PE tubing outside as an extra protection and to maintain atmospheric pressure inside
the transducer.
The P-105 transducer is widely used in earthrockfill dams (0 measure total earth
pressure. Plate XV (c) shows vertical positioned P-105 cell in dam embankment. Gauge
redundancy has been provided for by installing two independent vibrating-wire systems (wire
and magnet sytsem) inside the transducer
‘The P-105 transducer is not vented 10
atmosphere ; hence variations in atmos- cvconaucer
Pheric pressure should not be ignored paa
at low total pressures. The signal cable fea el
P-430 is used with this cel
The P-430 cable is specially de-
signed to withstand strong vertical forces.
It is steel armoured and has a thick PE
outside insulation (Fig. 33.9). The space FIG. 335. P50 CABLE
ange el re
Peso oy
Outer haath PE
known, the magnitude of the physical quantity which is measured, such as pressure, st
or force, can be calculated using formula and constants in calibration schemes supplied
with each transducer
A seco os viana m
conan an ete plop and acer ce
shown in Fig, 33.3. The electrical Voratng wre
pora, whch te peda sey, Re
are mounted inside the body of the
transducer.
AIMIL manufactures (wo ypes of =
cel : P-100 cel and P-105 cell. The FIG. 333. SCHEMATIC DIAGRAM OF
membrane diameter of P-100 cells (75 mm) VIBRATING-WIRE STRAIN GAUGE. (AIMIL)
limits the grain size of the soil to 1.5 mm. For larger grain size (0-2 mm). in earth/rock
fill dams and offshore applications, the P-10S cell with its active membrane diameter of
100 mm is recommended. Because of their thickness/diameter ratio (0.28 for P-100 and
0.22 for P-105), the transducers are installed in special steel frames when used in earth
fills for earth pressure measurements.
‘The P-100 transducer is often used
to measure total pressure or pore pressure
acting on different kinds of walls. For
Tow pressures, atmospheric pressure may
be maintained inside the transducer
through the PE tube encasing the lead
wires. The signal cable P-S40 is used
alongwith this cell >
‘The P-540 cable is made of standard FIG. 334. PSO CABLE,
PPOP one-pair shielded cable with OD
10 mm PE tubing outside as an extra protection and to maintain atmospheric pressure inside
the transducer.
The P-105 transducer is widely used in earthrockfill dams (0 measure total earth
pressure. Plate XV (c) shows vertical positioned P-105 cell in dam embankment. Gauge
redundancy has been provided for by installing two independent vibrating-wire systems (wire
and magnet sytsem) inside the transducer
‘The P-105 transducer is not vented 10
atmosphere ; hence variations in atmos- cvconaucer
Pheric pressure should not be ignored paa
at low total pressures. The signal cable fea el
P-430 is used with this cel
The P-430 cable is specially de-
signed to withstand strong vertical forces.
It is steel armoured and has a thick PE
outside insulation (Fig. 33.9). The space FIG. 335. P50 CABLE
ange el re
Peso oy
Outer haath PE
oe SOIL MECHANICS AND FOUNDATIONS
between the cable cores and also between steel armour wire are filed with petroleum jelly
10 prevent longitudinal leakages caused by light surface damage to the cable, An extra
protecting PE tubing for the P-430 cable (OD 25 x 3 mm) is sometimes used in adverse
environments and where large sculements are expected.
Reading of P-100 and P-105 wansdusers may be performed either manually or the
automatic recording equipment, Plates XV (a) amd XVI show the P-520 F frequency indicator.
lt may be connected directly 10 the transducer cable or to a switch box. Automatic read out
‘ean be obtained by means of a micro-logger with digital prin our of al d it
33.6. VIBRATING-WIRE EXTENSOMETER
‘A vibrating-wire extensometer is used to monitor displacements or stains ih earth
structures. IC is particularly useful for monitoring internal deformation and cracking of dam
‘embankment near the abutments.
‘The extensometers are normally
linked together with steel pipe
and anchor plates 10 form a con-
tinuous chain over the distance
10 be monitored. Fig. 33.6 shows
P-265 extensometer manufac-
tured by AIMIL.
‘The complete measuring
system consist of three main parts
(aia
(iy Extensomster A
ti Cable HO, 3846. VIERATING WIRE EXTENSOMETER
(i) Read ow .
The basic principle (Fig. 33.7) of the vibrting-wire soin gauge is that the change
in natural frequency of a sieched wire depends on the change of the tension in the wire,
In this insrument one end ofthe wire is atache to the movable head of the extensometer
by a steel spring. A displacement of the extensometer is this transformed lo variation
ofthe spring and ao emery
ibrating-wire. Thus, the nd
frequency of the vire isa me E
ur of de displacement between 508m]
extensometer and anchor. The =
square difference of frequencies
is proportional to the displace
ment. The signal cable of P-430
‘ype (Fig. 33.5) ls used, The
430 cab is mpecaly designed
cetro
ONE
to wind son ener
forces in hostile environment, FG 37. SCHEMATIC DIAGRAM. OF VIBRATINGWIRE
EXTENSOMETER,
Peruana
erating wre
between the cable cores and also between steel armour wire are filed with petroleum jelly
10 prevent longitudinal leakages caused by light surface damage to the cable, An extra
protecting PE tubing for the P-430 cable (OD 25 x 3 mm) is sometimes used in adverse
environments and where large sculements are expected.
Reading of P-100 and P-105 wansdusers may be performed either manually or the
automatic recording equipment, Plates XV (a) amd XVI show the P-520 F frequency indicator.
lt may be connected directly 10 the transducer cable or to a switch box. Automatic read out
‘ean be obtained by means of a micro-logger with digital prin our of al d it
33.6. VIBRATING-WIRE EXTENSOMETER
‘A vibrating-wire extensometer is used to monitor displacements or stains ih earth
structures. IC is particularly useful for monitoring internal deformation and cracking of dam
‘embankment near the abutments.
‘The extensometers are normally
linked together with steel pipe
and anchor plates 10 form a con-
tinuous chain over the distance
10 be monitored. Fig. 33.6 shows
P-265 extensometer manufac-
tured by AIMIL.
‘The complete measuring
system consist of three main parts
(aia
(iy Extensomster A
ti Cable HO, 3846. VIERATING WIRE EXTENSOMETER
(i) Read ow .
The basic principle (Fig. 33.7) of the vibrting-wire soin gauge is that the change
in natural frequency of a sieched wire depends on the change of the tension in the wire,
In this insrument one end ofthe wire is atache to the movable head of the extensometer
by a steel spring. A displacement of the extensometer is this transformed lo variation
ofthe spring and ao emery
ibrating-wire. Thus, the nd
frequency of the vire isa me E
ur of de displacement between 508m]
extensometer and anchor. The =
square difference of frequencies
is proportional to the displace
ment. The signal cable of P-430
‘ype (Fig. 33.5) ls used, The
430 cab is mpecaly designed
cetro
ONE
to wind son ener
forces in hostile environment, FG 37. SCHEMATIC DIAGRAM. OF VIBRATINGWIRE
EXTENSOMETER,
Peruana
erating wre
ELECTRONIC CONSOLIDATION APPARATUS WITH READ-OUT UNIT (HEICO)
PLATEXI
To Face Page 880
PLATEXI
To Face Page 880
(088 2654 2904 01)
Axauvıa
CEE
INEIVANVENE HIV NITED S014 (0) INN ANOVA ONY SEV HLLA TEA) DUNST HLIVA SHIM ONILYASLA (©)
Axauvıa
CEE
INEIVANVENE HIV NITED S014 (0) INN ANOVA ONY SEV HLLA TEA) DUNST HLIVA SHIM ONILYASLA (©)
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