CE 360-Introduction to Shallow Foundations2.pptx

Engineering

1.    CE 360: FOUNDATION ENGINEERING      

2. Foundations Definition A foundation is a member of an engineering structure whose function is to transmit the superstructure load to the soil for support. The depth in the soil at which a foundation may be placed gives rise to two categories of foundations, namely, Shallow Foundations Deep foundations

3. Shallow Foundations A shallow foundation is any type of foundation which is placed in the soil at a depth that does not exceed four times the width of the foundation. i.e., (1a) Or (1b) where, D f =depth in the soil at which the foundation is placed B =width of the foundation

4. A sketch of a shallow foundation showing depth ( D f ) and width (B). Note that the depth is measured from the ground surface to the underside of the foundation slab. B D f Foundation slab Column carrying foundation load

5. Types of Shallow Foundations Shallow foundations come in several types. They are: a) Strip footing (also Continuous footing) This is the type of foundation that supports load-bearing walls. b) Isolated footing (also Spread footing or Pad footing) A relatively small reinforced concrete slab which offers support to a single column of a structure.

6. c) Combined footing A single reinforced concrete slab which supports two or more columns of a structure. This type of foundation is used when two or more columns are so close to each other such that their individual footings would overlap or when a column is so close to a property line such that the use of an isolated footing would result in eccentric loading if the footing were to be kept entirely within the property line.

7. d) Raft or Mat foundation This is a large reinforced concrete slab which supports several columns or the structure as a whole and may cover the entire area of the building. This type of foundation is used when; the allowable soil pressure is low. there are several pockets of weak soil layers over the foundation area. the foundation columns are so close to each other such that the individual footings would overlap or nearly touch each other.

8. Types of Shallow Foundations When shallow foundations are characterised by their sizes (i.e. length and width) then they are distinguished as follows: , for strip footings and , for all other footings where, B =width (breadth) of foundation L =length of foundation

9. Sketch of Types of Foundations a) Isolated Footing b) Combined footing c) Mat Foundation Side view Side view Side view Plan view Plan View Plan view

10. Effect of Foundation Loads on Soils Foundation loads impose stress on the soil at the foundation depth in addition to what existed before the load application. The additional stress imposed may lead to instability in an otherwise stable soil or cause deformations in the soil large enough to be detrimental to the structure applying the stress. The soil will mobilise strength to contain the additional stress imposed on it to the maximum that it can before failure occurs.

11. Bearing Capacity The strength mobilised by soils to support the additional stress imposed on them by foundation loads is referred to as bearing capacity . The ultimate bearing capacity ( q u ) is the maximum foundation stress that the soil can sustain before undergoing a sudden catastrophic failure in shear. The allowable bearing capacity ( q all ) is the maximum safe stress that can be sustained by a foundation soil without failure by shear or excessive settlement.

12. Bearing Capacity The allowable bearing capacity is obtained by dividing the ultimate bearing capacity by an appropriate factor of safety ( FS ). i.e., (2) where, q all =allowable bearing capacity q u =ultimate bearing capacity FS =factor of safety

13. It is to be noted that the ultimate bearing capacity of a soil is not a fundamental property of the soil as its value depends on the following: the strength properties of the soil (i.e., c and φ ) ; the pressure applied on the soil by the overburden; the type and size of the foundation applying the superstructure load; the depth below the surface of the soil at which the foundation is placed the influence of the water table.

14. Foundation Design Requirements Two fundamental requirements must be satisfied in foundation design, namely, Adequate factor of safety ( FS ) against bearing capacity failure of the supporting soil. (Minimum values of FS =3 or 4 are normally specified.) The settlement of the foundation must be tolerable, and in particular, differential settlement should not cause any unacceptable damage nor interfere with the function of the structure. In the light of the above requirements, foundations are designed to cause stresses much lower than the ultimate bearing capacity.

15. Foundation Design Design Objective To find the minimum size of foundation that will cause the foundation load to impose a stress not exceeding the allowable bearing capacity of the foundation soil and also result in tolerable settlement. Basis for Size Selection Size selection is based on the concept of the definition of stress; Based on the above definition, foundation stress can be minimised only by increasing the foundation size (area) given that the load from the superstructure is fixed.

16. Types of Foundation Failures (a) Loaded foundation Fig. 2. Types of failures in a loaded foundation Foundations may fail by general shear or local shear . Based on the load-settlement curves in Fig. 2 above, general shear has a well-defined failure stress ( q u ) while local shear has no well-defined failure stress ( q u ). Failure in local shear may be defined by some level of maximum permissible settlement. Settlement q u (c) Local shear (b) General shear q u Stress Settlement

17. Bearing Capacity Theory In 1943, Terzaghi presented foundation failure condition in the Fig. 3 below for a strip footing. Fig. 3. Bearing capacity failure in foundation soil

18. Bearing Capacity Theory The failure zones under the foundation were separated into three distinct zones as follows: The triangular zone ACD immediately under the foundation; The radial shear zones ADF and CDE with curves DE and DF being log spirals; Two triangular passive Rankine zones AFH and CEG. In addition, it was assumed that; where, = soil friction angle.

19. Bearing Capacity Theory Also, the soil above the foundation level was replaced by an equivalent surcharge ( ). Analysis of the forces acting on the failure plane resulted in the following expression : (3) where, D f =foundation depth q u =ultimate bearing capacity c =cohesion of the foundation soil B =foundation width γ = unit weight of the soil N c , N q , N γ are bearing capacity factors dependent on friction angle .

20. Terzaghi Bearing Capacity Factors (4) (5) (6) K p =passive earth pressure coefficient

21. Table 1. Terzaghi’s Bearing Capacity Factors φ N c N q N γ φ N c N q N γ 5.70 1.00 0.00 13 11.41 3.63 1.04 1 6.00 1.10 0.01 14 12.11 4.02 1.26 2 6.30 1.22 0.04 15 12.86 4.45 1.52 3 6.62 1.35 0.06 16 13.68 4.92 1.82 4 6.97 1.49 0.10 17 14.60 5.45 2.18 5 7.34 1.64 0.14 18 15.12 6.04 2.59 6 7.73 1.81 0.20 19 16.56 6.70 3.07 7 8.15 2.00 0.27 20 17.69 7.44 3.64 8 8.60 2.21 0.35 21 18.92 8.26 4.31 9 9.09 2.44 0.44 22 20.27 9.19 5.09 10 9.61 2.69 0.56 23 21.75 10.23 6.00 11 10.16 2.98 0.69 24 23.36 11.40 7.08 12 10.76 3.29 0.85 25 25.13 12.72 8.34

22. Table 1 cont’d φ N c N q N γ φ N c N q N γ 26 27.09 14.21 9.84 39 85.97 70.61 95.03 27 29.24 15.90 11.60 40 95.66 81.27 115.31 28 31.61 17.81 13.70 41 106.81 93.85 140.51 29 34.24 19.98 16.18 42 119.67 108.75 171.99 30 37.16 22.46 19.13 43 134.58 126.50 211.56 31 40.41 25.28 22.65 44 151.95 147.74 261.60 32 44.04 28.52 26.87 45 172.28 173.28 325.34 33 48.09 32.23 31.94 46 196.22 204.19 407.11 34 52.64 36.50 38.04 47 224.55 241.80 512.84 35 57.75 41.44 45.41 48 258.28 287.85 650.67 36 63.53 47.16 54.36 49 298.71 344.63 831.99 37 70.01 53.80 65.27 50 347.50 415.14 1072.80 38 77.50 61.55 78.61        

23. Local Shear Strength Parameters In the case of failure of the foundation soils by local shear, Terzaghi proposed the following modifications to the strength parameters of the soil in determining the bearing capacity factors: (7) (8) where, c l =cohesion for local shear = friction angle for local shear

24. Square and Circular Foundations Equation (3) is the bearing capacity for strip foundations ( B/L =0). To deal with the bearing capacity of square and circular foundations, Terzaghi proposed the following equations: (square) (9) (circular) (10) For circular foundations, B =diameter of the footing .

25. Example Problem 1.1 A square foundation which carries a load of 400kN is to be placed at a depth of 1.2m in a soil with the following strength parameters: If the unit weight of the soil is 18.5kN/m 3 , determine the size of foundation required for a factor of safety of 3 against bearing capacity failure by; general shear local shear

26. Solution For a square foundation For general shear, N c = 29.24, N q =15.9, N γ =11.6 Hence, (a) Stress caused by foundation load= (b) Equate (a) to (b) and obtain; (c)

27. Simplify Eq. (c) to obtain; Solve the above to obtain, B =1.068m. ii) For local shear; Obtain the bearing capacity factors by interpolation as follows:

28. Hence, (d) Hence, (e) Solve Eq. (e) to obtain B=1.715m

29. Effect of Water Table on Bearing Capacity When the water table is close to the base of the foundation or even above it, adjustments to the bearing capacity equation are required to account for the effect of the water. Case I When the water table is located above the foundation such that 0≤ D 1 ≤ D f (see Fig. 4): Fig. 4. Water table above foundation level Adjustments T he parameter in the last term of the ultimate bearing capacity equation should be replaced by the buoyant unit weight . D 2 D 1 B D f Water Table

30. b) The overburden pressure parameter q in the bearing capacity equation should be expressed in terms of effective stress as Case II When the water table is located below the foundation at a distance d less than or equal to the foundation width, i.e., such that 0≤ d < B (see Fig. 5). Fig. 5. Water table below foundation level D f d B Water Table

31. Case II Adjustments The parameter remains unchanged but in the last term of the bearing capacity expression must be replaced by . Note that . Case III When the water table is located at a distance d below the foundation such that d ≥ B , it will have no effect on the bearing capacity .  

32. Modifications to General Bearing Capacity Equation The bearing capacity equations developed by Terzaghi for strip footings, square, and circular foundations were modified by Meyerhof to deal with rectangular foundations, foundation carrying inclined loads, eccentric loads, etc. as follows: (11) where, F cs , F qs , F γs = shape factors F cd , F qd , F γd =depth factors F ci , F qi , F γi =inclination factors

33. Shape, Depth and Inclination Factors Factor Expression Shape , , where L=length of foundation and B=width Depth Case (a) : Case (b): > 1 Inclination =inclination of the load on the foundation with respect to the vertical.

34. Modified Bearing Capacity Factors ( Vesic ) In Fig. 3, Terzaghi assumed that but Vesic established from laboratory studies that is closer to than to . This led to the modification of the bearing capacity factors as follows: (12) (13) (14) The corresponding bearing capacity factors are given in Table 2. The values lead to a more conservative design as they are lower than corresponding Terzaghi’s values for a given value of .

35. Vesic’s Bearing Capacity Factors Φ N c N q N γ φ N c N q N γ 5.14 1.00 0.00 26 22.25 11.85 12.54 1 5.38 1.00 0.07 27 23.94 13.20 14.47 2 5.63 1.20 0.15 28 25.80 14.72 16.72 3 5.90 1.31 0.24 29 27.86 16.44 19.34 4 6.19 1.43 0.34 30 30.14 18.40 22.40 5 6.49 1.57 0.45 31 32.67 20.63 25.99 6 6.81 1.72 0.57 32 35.49 23.18 30.22 7 7.16 1.88 0.71 33 38.64 26.09 35.19 8 7.53 2.06 0.86 34 42.16 29.44 41.06 9 7.92 2.25 1.03 35 46.12 33.30 48.03 10 8.35 2.47 1.22 36 50.59 37.75 56.31 11 8.80 2.71 1.44 37 55.63 42.92 66.19 12 9.28 2.97 1.69 38 61.35 48.93 78.03 13 9.81 3.26 1.97 39 67.87 55.96 92.25 14 10.37 3.59 2.29 40 75.31 64.20 109.41 15 10.98 3.94 2.65 41 83.86 73.90 130.22 16 11.63 4.34 3.06 42 93.71 85.38 155.55 17 12.34 4.77 3.53 43 105.11 99.02 186.54 18 13.10 5.26 4.07 44 118.37 115.31 224.64 19 13.93 5.80 4.68 45 133.88 134.88 271.76 20 14.83 6.40 5.39 46 152.10 158.51 330.35 21 15.82 7.07 6.20 47 173.64 187.21 403.67 22 16.88 7.82 7.13 48 199.26 222.31 496.01 23 18.05 8.66 8.20 49 229.93 265.51 613.16 24 19.32 9.60 9.44 50 266.89 319.07 762.89 25 20.72 10.66 10.88        

36. Eccentrically-loaded Foundations A foundation is said to be eccentrically loaded when the load is applied at a location other than the centre of the foundation area. This means, the foundation load is not concentric with the foundation area. The amount by which the centre of the load is shifted from the centre of the foundation area is called eccentricity ( e ) (see Fig. 6). Eccentric loading can also result if a concentrically- loaded foundation also carries a moment, M (see Fig.7). Such a loading is equivalent to an eccentrically loaded foundation with eccentricity given as

37. Eccentrically-loaded Foundations Fig. 6. Fig. 7. Eccentrically-loaded foundation Concentrically-loaded foundation with eccentricity, e . with moment, M . Q F e B Q F B/2 B/2 L M

38. Pressure distribution under eccentrically-loaded foundations. (a) when e<B /6 (b) when e>B /6 For condition (a) (i.e., e<B/ 6), the minimum and a maximum pressures imposed on the soil are given by the following expressions; (15) (16) B x L q min q max Q F e Q F B x L e q max

39. When e=B /6, q min will be zero. For condition (b), (i.e. e>B /6) q min will be negative, implying the development of tension or detachment of the foundation slab from the foundation soil which must be avoided. The maximum pressure ( q max ) under such condition will be given as; (17) where, B =foundation with L =foundation length Q F =foundation load Eccentrically loaded foundations must, therefore, be designed such that B>6e (same as e<B/6 ).

40. Analysis of Eccentrically-Loaded Foundations Effective Area Method The effective area of an eccentrically-loaded foundation is a fictitious area whose centroid coincides with that of the load to transform the foundation from eccentrically-loaded to concentrically loaded (see Fig. 8 below). Fig. 8. Original foundation area modified to effective area (shaded region) B/2-e B/2-e 2e L

41. Analysis cont’d The Effective Area method was proposed by Meyerhoff to determine the width B of an eccentrically loaded foundation. In the analysis the general bearing capacity equation is applied in a modified form as follows: Step 1 Determine the effective width ( ) and effective length ( ) of the foundation as follows:

42. Step 2 Evaluate the ultimate bearing capacity using the expression; For the shape factors F cs , F qs and F γs use and in the appropriate equations. However, the depth factors F cd , F qd and F γd are evaluated with B.

43. Analysis cont’d Step 3 Evaluate the effective area as follows; The stress imposed by the foundation load based on the effective area is evaluated as; where, Q F =foundation load q F =foundation stress .

44. Analysis cont’d Step 4 Equate the foundation stress to the allowable bearing capacity and solve for B , i.e., Step 5 With the value of B determined, evaluate q F and then determine the values of q u and q max as follows:

45. Step 6 Check the factor of safety against maximum foundation pressure as follows: There is adequate stability against maximum foundation pressure if; FS≥3

46. Foundations on Saturated Clays For saturated clays under un-drained conditions, φ u = 0 and the general bearing capacity equation for a foundation carrying a vertical load under such conditions reduces to ; (18) where, c u =un-drained cohesion. For φ u = 0, N c =5.14, N q =1 and N γ =0 (using Vesic’s bearing capacity factors for a more conservative design). The relevant shape factors then become;

47. Foundations on Saturated Clays Substitution of the shape factors into Equation (18) gives the following expression; (19a) Or (19b) where, q u (net) =( q u -q ) is the net ultimate bearing capacity Because conditions are un-drained, the overburden stress q must be evaluated in terms of total stress and NOT effective stress.

48. Foundations on Saturated Clays For a square foundation (B/L=1), the net allowable bearing capacity based on Equation (19b) is given as; (20) For FS =3, this may be approximated to; (21)

49. Bearing Capacity from Field Load Tests Field load tests are tests carried out in-situ to determine the bearing capacity of soils. Such tests become necessary under any of the following circumstances: When the soil is cohesion-less (sandy), thus making it difficult to take samples to the laboratory for strength evaluation. When the soil is sensitive such that sampling disturbance will alter its strength dramatically.

50. Plate Loading Test The test may be used to determine the ultimate bearing capacity as well as the allowable bearing capacity of a foundation based on tolerable settlement. It involves a steel plate 25mm thick with a diameter ranging from 150mm to 762mm. A square plate can also be used. The test is conducted in a hole excavated to a size of at least four times the diameter of the plate and to the proposed foundation depth. The plate is placed at the centre of the hole and load is applied in steps of about 20% to 25% of the estimated ultimate load by means of a jack (see Fig. 10) and the corresponding settlement noted.

51. Plate Loading Test Fig. 10. Set up of plate loading test The test is conducted until failure or at least until the plate has undergone a settlement of 25mm.

52. Plate Loading Test The stress at any stage of loading is obtained as the load applied divided by the area of the plate. At the end of the test, a stress-settlement curve (see Fig. 11) is plotted from the test data. Fig. 11. Load-settlement curve from a plate loading test Stress ( kN /m 2 ) Settlement (mm) q u (P)

53. Analysis of Plate Loading Test Data Procedure A The ultimate bearing capacity of the foundation is obtained as follows; for clayey soils (22) for sandy soils (23) where, q u (F) = ultimate bearing capacity (failure stress) of the foundation q u (P) = ultimate bearing capacity (failure stress) in the plate loading test (see Fig. 11) B F =width of foundation B P =width (diameter) of the test plate.

54. Equation (22) suggests that the ultimate bearing capacity of clayey soils is not affected by plate size. Consider any general foundation with dimension L x B such that (24) Hence, and where , α =a constant whose value is to be decided by the designer (1 for a square, >1 for a rectangle) L =foundation length B =foundation width A F =foundation area

55. Analysis of Plate Loading Test Data If FS is the factor of safety against bearing capacity failure, then based on Equation (23) and foundation load Q F (25a) (25b)

56. Analysis of Plate Loading Test Data Re-arrange Equation (25b) to obtain (26a) For a square foundation, α =1 Hence, (26b)

57. Procedure B The allowable bearing capacity of the foundation is analysed based on settlement considerations. The settlement of the plate under a given intensity of stress q and the settlement of the foundation under the same intensity of stress are related as follows: for clayey soils (27) for sandy soils (28) where, S F =foundation settlement S P =settlement of the plate B F =width of foundation B P =width (diameter) of the test plate.

58. Analysis of Plate Loading Test Data To use Eq. (27) or (28) to estimate the allowable bearing capacity, the following steps are followed: Step 1 Plot a graph of stress against settlement using the data from the plate loading test. Step 2 For a square foundation, assume a value for the foundation width ( B F ) and based on the foundation load ( Q F ), calculate the foundation stress ( q F ) .

59. Step 3 Enter the stress-settlement curve obtained in Step 1 with the value of q F and find the settlement of the plate corresponding to q F ; call this settlement S P . Compute the corresponding settlement S F for the foundation soil using Eq. (27) or (28) as appropriate. Step 4 Repeat Steps 2 and 3 for different assumed values of B F .

60. Step 5 Plot a graph of q F against S F and read from the plot the q F value corresponding to the tolerable foundation settlement S e as the allowable bearing capacity, q a . The width of the foundation ( B ) is determined from the relationship Alternatively, Plot foundation settlement ( S F ) against assumed foundation widths ( B F ). The value of B F corresponding to the tolerable settlement of the foundation is read from the graph as the minimum foundation width.

61. Analysis of Plate Loading Test Data Procedure C This procedure will determine the dimensions of the foundation that will carry the foundation load Q F with an allowable settlement S e . The procedure requires two plate load tests to be carried out using plates of different dimensions. For each plate, a load-settlement curve is plotted from the test data and the load Q 1 (or Q 2 ) on the plate corresponding to the settlement S e is determined .

62. The loads on the plates can be expressed as; (29) (30) where , A 1 , A 2 =areas of Plates no. 1 and 2, respectively P 1 , P 2 =perimeters of Plates no. 1 and 2, respectively m, n =constants corresponding to bearing pressure and perimeter shear, respectively .

63. Equations (29) and (30) are solved simultaneously for the values of m , and n . For the foundation carrying a load Q F to be designed to have the same allowable settlement S e , we can write; (31) where, A=area of the foundation P=perimeter of the foundation Equation (31) can be written for a square foundation of width B F as (32) Equation (32) is a quadratic equation which is then solved for B F .

64. Standard Penetration Test (SPT) This is an in-situ test conducted on cohesion-less soils (sandy soils) to estimate the allowable bearing capacity and hence foundation size. The test determines the N -value which is the number of blows required to drive a 50mm diameter bar a distance of 300m into the base of a borehole. The test is usually carried out at intervals of 0.75m and 1.5m over the depth of influence below the footing, which is approximately 1.5 times the width of the foundation.

65. Standard Penetration Test (SPT) For design, the N values at the various depths are corrected for the effect of overburden pressure using the following expression proposed by Skempton : (33) where , N = SPT value at a given depth N cor =corrected N value = effective overburden pressure in kN /m 2 The average of the corrected values for the depth range considered in the test becomes the design value ( N des ).

66. The net allowable bearing capacity ( q a (net) ) for a given tolerable settlement is given by the following expressions proposed by Meyerhoff ; for B ≤1.22m (34) for B >1.22m (35) where, S e =tolerable settlement

67. Analysis of SPT Data The following steps are followed in the analysis of SPT data. Step 1 Correct each of the N -values for the effect of overburden using Equation (33). Step 2 Find the average of the corrected N -values in Step 1 and designate the value as the design value, N des . Step 3 Assume a value for foundation width (B) and together with the tolerable settlement, compute the net allowable bearing capacity ( q a (net) ) using either Equation (34) or (35) as appropriate.

68. Analysis of SPT Data Step 4 Calculate the net allowable foundation load Q a (net) from q a (net) . Step 5 Repeat Steps 3 and 4 for different assumed values of foundation width ( B). Step 6 Plot the calculated Q a (net) values against the assumed B values. From the plot, the B value corresponding to the foundation load Q F is read as the design width.

69. Mat (Raft) Foundations A mat foundation also sometimes referred to as raft foundation is a large combined footing with several columns and covering the entire area under a structure. Mat foundations may be used under any of the following circumstances: When foundation soils have low bearing capacity but have to support high column and/or wall loads. When the total area of the spread footings or combined footings exceeds about 50% of the gross area of the building.

70. When there are several pockets of soft and loose soil distributed over the gross area of the building area. When large differential settlements must be avoided When individual isolated footings are so close to each other or overlap.

71. Mat Foundations Mat foundations on granular soils When mats are to be placed in granular soils, the large foundation widths allow the following approximation to be made in Equation (35); This modifies the net allowable bearing capacity expression to; (36)

72. Compensated Mat Foundation Excavation to place a foundation relieves the foundation soil of overburden stress due to material removed. If stress relief due to material removed is equal to the expected stress increase from the foundation, there will be zero net pressure increase so the soil will suffer no settlement. A mat foundation constructed under such conditions is described as fully-compensated foundation.