Lecture 7 falling weight deflectometer for flexible pavement

Lecture about utilization of FWD in Pavement

1. Falling-Weight Deflec t ometer Operation and Data Analysis

2. Question Q1. Bagaimana cara mengevaluasi kapasitas struktural Perkerasan ? - Parameter untuk evaluasi kapasitas structural perkerasan Modulus adalah parameter paling penting Perkerasan Lentur Perkerasan Rigid/ Composit s Modulus resiliensi tanah dasar Modulus komposit SN efektif (AASHTO) Moduli lapisan Koefisien lapisan Faktor koreksi suhu Faktor koreksi musim Beban modulus elastis PCC efisiensi transfer Modulus terhadap reaksi tanah dasar terhadap rongga Slab bending / kompresi HMA Radius dengan kekakuan relatif Faktor koreksi suhu Faktor koreksi musim

3. Question Q2. Bagaimana menentukan modulus di lapangan ? - Perbandaingan destructive d an nondestructive testing NDT Sangat berguna untuk analisa perkerasan Destructive testing Nondestructive testing Kerusakan perkerasan Butuh waktu yang lama Gangguan lalu lintas Kondisi lapangan berbeda Cakupan terbatas Pengujian laboratorium Noninvasif Waktu operasi dan b erkerak cepat Lalu lintas tidak terlalu terganggu Kondisi in-situ Berbagai kondisi iklim Hemat biaya

4. Question Q3. Tipe NDT yang tersedia untuk memperoleh modulus Tebal Lapisan Perlu tahu parameter mana yang bisa digunakan !! Metode berbasis defleksi permukaan Methode Perambatan seismik ( gelombang ) Beban Static : Benkelman Beam Steady_State Beban : Dynaflect, Road Rater Impulse Load: Falling W eight Deflectometer Impact echo Spectral Analysis of Surface W aves Memperkirakan Defleksi Memperkirakan

5. Basic Idea •   Memperkirakan modulus lapisan δ = b h 3 I = δ 12 L P , L, I diketahui nilainya Defleksi adalah parameter yg penting untuk menghitung modul us !! E = f ( δ ) δ = f ( E , P , L , I ) E, I P L 3 4 8 EI

6. Tipe NDT Beban Statis Benkelman Beam (BB) California T raveling Deflectometer La Croix Deflectograph ww w .geosales.co.nz/ geoflecto r .html Beban getaran Dynaflect Road Rater Beban impuls Falling W eight Deflectometer (FWD) Propagasi Gelombang Permukaan Seismic Pavement Analyzer (S P A) Spectral Analysis of Surface W ave (SASW)

7. b v . in . (mm ) lb s. (kN) in . ( mm ) senso r s de p e n de nt Deflec t o er ap h d e p e nd e nt AS T M D 11 9c Dyna fl ect Geo l og, I nc . diam ete r steel 4 O t o 4 8 (5) Vi br a t ory Roa d Ra t e r Mec h an i cs , 4 t o 7 O t o 4 8 5 (2 t o 1 30) O t o 60 V ibr a t o r E n g in ee r s d i am ete r pl a t e Dy n a t es t FWD (300 o r 4 50) 7 t o 9 O t o 90 E n g in ee ri ng ( 7 t o 1 20) D yn a test HWD (300 o r 4 50) 7 t o 9 O t o 90 (2 7 t o 2 4 0) E n g in ee ri ng TI LSFWD Mec h an i cs , (300 or 4 50) 7 O t o 96 ( 300 or 4 50) TI LSHWD Mec hani cs , 7 O t o 9 6 I mpul s e KUABFWD KUAB (300 or 4 50) 7 t o 9 O t o 90 ( 7 t o 1 50) K U ABHWD KUAB ( 300 o r 4 50) 7 O t o 90 (13 t o 2 9 4 ) C a rl Bro FWD C ar 1 B r o Group ( 300 o r 4 50) 9 to 1 2 Oto 1 00 ( 7 t o 1 50) C a rl Bro FWD C ar 1 B r o Gro u p ( 300 or 4 5 ) 9 to 1 2 O t o 1 00 ( 7 t o 250) 1 t o 3 C a rl B r o FWD C ar 1 Bro Gro u p (100 or 200 o r 30 ::; O t o 4 ( 1 t o 1 5) Ca t ego r y Eq u ip m ent Ma n ufacturer Load range, Loa d trans m itted N umb er of Se n sor spac i ng , Benk l e m an Be am Soj I te st, I n c. Ve hicl e Loa d ed tru ck or 1 N A depe nd e n t a ir c r a ft S t a ti c La C r oix Swi t ze rl and Ve h i cl e Loaded tru ck 1 NA P l a t e - b ear in g t es t Se v e r a l. Ve hicl e Loa d e d tru ck 1 N A 1 , 000 1 5 (2 , 4 00) Varia bl e, w h ee l s (0 t o 1 , 200) Fo und a ti o n 500 t o 8,000 1 8 ( 4 50) Varia bl e, Inc. (2 t o 35) d i am e t e r p l a t e (0 t o 1 , 200 ) WES Heavy U . S . C orps o f 500 t o 30,000 1 8 ( 4 50) Varia bl e, (0 t o 1 ,500) Dy n a t es t 1 , 500 t o 2 7 , 000 1 2 or 1 8 Varia bl e , d i am e t e r pl a t e (0 t o 2, 2 50) Dy n ates t 6 , 000 t o 5 4 , 000 1 2 or 1 8 Var i a bl e , d i am ete r p l a t e (0 t o 2,250) Fo und a ti o n 1 , 5 00 to 2 4 , 000 1 2 or 1 8 Varia b le, I n c. ( 7 t o 1 7 ) d i am e t e r plat e (O t o 2 , 4 00 ) Fo und a ti o n 6 , 000 t o 5 4 , 000 1 2 or 1 8 Va r iable, I n c . (2 7 to 2 4 0) d i am e t e r pl a t e (Oto 2, 4 00 ) 1 , 500 to 3 4 , 000 1 2 or 1 8 Varia b le , d i am e t e r pl a t e (0 t o 2,250) 3 , 000 to 66 , 000 1 2 o r 1 8 Va ri a b le , d i am e t e r pl a t e (0 to 2,250) 1 , 500 t o 3 4 , 000 1 2 o r 1 8 Varia b le, d i am e t e r pl a t e (0 to 2,500) 1 , 500 to 56 , 000 1 2 o r 1 8 Varia bl e, d i am ete r pl a t e (0 to 2 , 500) 225 t o 3 , 4 00 4 or 8 o r 1 2 Varia b le, d i am e t e r pl a t e (0 t o 1 ,000)

8. Benkelman Beam  Perangkat NDT sederhana untuk mengukur defleksi permukaan  Pemuatan statis ; Gandar belakang dengan dua ban di setiap sisi .    Ujung batang ditempatkan di depan dan di Antara kedua roda •   Awal , maks. selama mengemudi maju ke 3m di depan ujung, dan akhir defleksi pulih http://ww w .dot.ca.gov/hq/esc/ctms/CT_356_3-00.pdf

9. Seismic Pavement Analyzer    Mengukur kecepatan , amplitudo , dan panjang gelombang yang disebabkan pukulan atau getaran Sensors Hammer Amplitude

10. Dynaflect  Sistem elektromekanis untuk mengukur defleksi dinamis permukaan  Beban osilasi pada kecepatan 8cyc / detik  2000lbs statis dan positif / negatif 1000 lbs gaya dinamis tunak .  Geophone mengukur defleksi yang membentuk cekungan defleksi

11. Road Rater    Force Gaya sinusoid yang ditimbulkan oleh percepatan hidrolik beban baja  Pemuatan puncak ke puncak berkisar dari 500 lbs hingga 8.000 lbs  Geophone mengukur defleksi yang membentuk cekungan defleksi

12. Falling Weight Deflectometer  FWD mengukur defleksi permukaan oleh pemuatan dampak untuk mensimulasikan a beban bergerak kendaraan .  Sistem berlaku terkontrol memuat dan mengukur defleksi . http://ww w .dynatest.com/hardware/fwd_hwd.htm  Beberapa geofon mengukur kecepatan gerak , kemudian dikonversi menjadi defleksi dan disusun menjadi bak lendutan .  KUAB juga menggunakan seismometer yang mengukur defleksi langsung http://ww w .dot.ca.gov/hq/esc/ctms/CT_356_3-00.pdf ww w .erikuab.com

13. Heavy W eight Deflectometer Portable FWD Rolling W eight Deflectometer Tipe FWD Falling W eight Deflectometer

14. Impulse Load Equipment Single Mass KUAB FWD T op Hoods Open ww w .erikuab.com

15. Impulse Load Equipment Dual Mass KUAB FWD Sensor Bar Backwards ww w .erikuab.com

16. Impulse Load Equipment Dual Mass KUAB FWD Sensor Bar Forwards ww w .erikuab.com

17. Impulse Load Equipment T ruck Mounted KUAB FWD ww w .erikuab.com

18. Impulse Load Equipment Interior V iew of T ruck Mounted KUAB ww w .erikuab.com FWD

19. Impulse Load Equipment V an Mounted KUAB FWD ww w .erikuab.com

20. Impulse Load Equipment Interior V iew of V an Mounted KUAB FWD ww w .erikuab.com

21. FWD 7-150kN Heavy Weight Deflectometer  Untuk mensimulasikan beban berat dari pesawat seperti Boeing 747  Digunakan di lapangan terbang dan jalan raya yang sangat tebal lapisannya  Rentang pemuatan :    HWD    30-240kN Dynatest Model 8082 HWD Dynatest Model 8000 FWD Dynatest Model 8082 Heavy W eight Deflectometer http://ww w .dynatest.com/hardware/fwd_hwd.htm

22. Rolling Weight Deflectometer D 1 C 1 B 1 A 1 Distance = 8 ft D 2 A 2 C 2 B 2 Deflection is di f ference between deflected and undeflected surfaces (i.e., D 2 – C 1 ) R WD FWD Bergerak & Sementara Ban ganda Defleksi Menerus tunggal Menyimpan puncak Tingkat Jaringan Stationing & impact Beban lingkarang Satu lendutan Lokasi yang dipilih Cekungan yang sebenarnya Tingkat proyek

23. Portable FWD  lendutan vertikal di tengah memuat piring  Relatif mudah dioperasikan dan biaya murah  Mudah diangkut dan digunakan  Analisis data sederhana http://ww w .mastrad.com/prima100.htm http://ww w .vti.se/nordic/3-03mapp/comparison.html

24. Fitur Penting FWD  Beban yang diterapkan  Satu Sistem Massa vs. Dua Sistem Massa  Muatan Plat  Kaku vs Tersegmentasi  Sensor Pengukuran Lendutan  Geofon vs. Seismometer loads

25. Aplikasi dari Gaya Impulsi M a s s D r o p h e i g S p r i n g c o n s t a n t L o a d p l a t e h t

26. Aplikasi Gaya Impulsi

27. Pelat Beban KUAB FWD Four Segmented Load Plate

28. Distribu si Tekanan P e lat Beban

29. Gephone Pengukur Defleksi KUAB FWD Geophone in T ripod Stand

30. Defleksi Pengukur Seismometers KUAB FWD Seismometers

31. Fo und a t i o n S p ec ifi ca t io n s D yn a t es t KUAB Ca rl Bro Gro u p Mec h an i cs , I nc. ( 7 t o 2 4 0) ( 7 t o 2 4 0) ( 7 t o 29 4 ) ( 7 t o 250) T ype o f loa d p l at e rubb e r i z e d p ad o r Ri g id p l a te w i th r u bb e r i z e d p a d w i th ru b b e r i ze d pa d s T ype o f d e flec ti o n d e v i c e o r Geo p h o n es calibration device c a li bra ti o n de v ice d y namic c alibrati o n M i l s ( m m ) Seis m o m e t ers: 200 (2 o r 2 . 5 m m ) d e fl ec ti o n sensors l (fo ur l oa d s) E qu ip m e nt E qu ip m e nt m a nu fa c tur e r Loa d range , lb s (kN) 1 , 5 t o 5 4 , 000 1 , 500 to 5 4 , 000 1 ,500 t o 66 , 000 1 , 500 t o 56 , 000 Loa d d ur a ti o n 25 t o 30 m i ll i seco nd Se l ec tabl e Se l ec t a bl e 25 t o 30 m ill iseco nd Load r i se tim e Va r i ab l e Se l e ctabl e Se l ec t a bl e 1 2 t o 1 5 m ill iseco nd Lo a d ge n era t o r O n e - m ass O n e -m ass Two- m ass O n e Mass R i g i d w it h R i gi d wi t h F o ur se gm e nt e d or F o ur se gm e n t e d p l a t e s plit p l a te ru b b e ri z e d pad s Diameter of l o ad plate , 1 2 and 1 8 12 a nd 1 8 1 2 and 1 8 12 a n d 1 8 in . ( mm) ( 3 and 450 ) ( 3 a n d 45 ) ( 3 a n d 4 5 ) ( 300 a n d 4 5 0) S e i s m o mete r s wit h Geopho n e s with or s t a t ic fi e l d c a li brat i o n Ge o phone s w i t h or s e n s or s w ith o ut d y na m ic Ge o phon e s w i t h or withou t w i th o u t d y nam i c d e v i c e Defle c t i o n s ens or O to 9 O to 9 6 O t o 9 O t o 1 p o si t i o n s , in. ( mm ) ( Oto 2 2 5 ) ( O t o 2 4 ) ( Oto 2 2 5 ) (O t o 2 5 00 ) N umb e r o f se n sor s 7 t o 9 7 7 t o 9 9 t o 1 2 G e o p h o n e s : 8 o r 1 D e fl ec ti o n s e n s o r ran ge 80 o r 100 80 (2) (2 or 2.5 mm ) 90 (2.2) (5 . mm ) De fl ec ti on reso l uti o n 1 um (0.0 4 mi l s) 1 um (0.0 4 mil s) 1 um (0 . 04 mi l s) 1 um (0.0 4 m il s) Re l at i ve acc ur ac y o f 2 um ± 2 % 2µm ± 2% 2 µm ± 2% 2µm ± 2% Tes t t im e r e q u i re d 25 seco n ds 30 seco nd s 35 seco nds 20 seco n d s T ype o f co m p u te r P e r s o n a l c o m p u te r P e r so n a l c o m p ut e r Pe r s o n a l c o m p u t e r Per s o n a l co mpu t e r

32. FWD Testing  Interval 30 hingga 150m  Hanya jalur luar saja  Kedua arah - terhuyung  Fleksibel - jalur roda luar  JPCP / JRCP – mid slab , sambungan , sudut  CRCP - jalur roda luar , antara celah , dan pada retak · Jointed plain concrete pavement (JPCP) · Jointed reinforced concrete pavement (JRCP) · Continuously reinforced concrete pavement (CRCP )

33. FWD Testing Procedures ( 1 )  Pada lokasi yang dipilih , memuat pelat beban dan geophones pada posisinya  Pemuatan kecil diterapkan  Tes utama dilakukan ww w .ce.umn.edu/~guzina/

34. FWD Testing Procedures (2) A-B: Lift B-C: Drop W eight Geophones Loading plate B. B. Guzina and R. H. Osburn (2002) Deflection Distance T ypical deflection basins

35. Data Defleksi

36. Cekungan Def leksi Smart Road FWD T esting – Section A

37. Factor yang Mempengaruhi Pengukuran FWD    Beban yang bekerja    Jenis / kondisi Perkerasan    Kondisi cuaca / iklim

38. Faktor Beban - Sensitivitas Tegangan 0.40 0.35 0.30 0.251 0.20 Proyeksi defleksi untuk 40kN dengan beban 4.4kN . 2 5 1 = 0. 2 8 × 40 4 . 4 0.10 0.028 10 20 30 40 50 Load (kN) Deflection (mm) Measured 40-kN deflection

39. Faktor Jenis dan Kondisi Perkerasan  Kerusakan  Menguji lokasi melintang  Diskontinuitas permukaan  Variasi di bawah permukaan  Rongga di bawah lapisan  Keragaman acak

40. Faktor Lingkungan  Kelembaban  Suhu  Penetrasi beku

41. Tipikal Variasi Musim Period of Strength Loss Period of Rapid Strength Recovery Period of Deep Frost Period of Slow Strength Recovery DEC JAN FEB MAR APR M A Y JUN JUL AUG SEP OCT TIME NOV DEFLECTION

42. Analsisa Perkerasan    T i pi k al lapis perkerasan Layer Characteristics NDT Load r Base E 2 , ν 2 , H 2 Subgrade E 3 , ν 3 , H 3 (=∞) Surface E 1 , ν 1 , H 1

43. T i pi k al Nilai Modulus (MPa) Material Range (MPa) T ypical value PCC HMA A TB CTB Lean Concrete Granular Base Granular Soil Fine-grained Soil 20,000-55,000 1,500-4,500 400-3,000 3,500-7,000 7,000-20,000 100-350 50-150 20-50 30,000 4,000 1,000 5,000 10,000 250 100 30

44. T i pi k al Nilai Rasio Poisso n value Material Range T ypical PCC HMA/ A TB Cement Stabilization Base Granular Base/ Subbase Subgrade 0.10-0.20 0.15-0.45 0.15-0.30 0.30-0.40 0.30-0.50 0.15 0.35 0.20 0.35 0.40

45. Perhitungan maju (Forward Analysis) dan perhitungan mundur ( Backcalculation ) Pavement Inputs Forward Analysis Prediksi displacement, stress, dan strain Backcalculation Memperkirakan Modulus Dan Ketebalan Pavement Responses Loading

46. Metode Analisa Perhitungan Maju  Analisa Elastisitas Berlapis  Solusi numerik untuk persamaan diferensial orde keempat  Metode Ketebalan Setara  Dikonversi menjadi satu lapisan ; sangat cepat  Metode Elemen Hingga  Analisis struktur yang rumit ; dan memakan waktu  Metode Elemen Diskrit

47. Analisa Elastisitas Berlapis (1)  Asumsi dasar  Beban vertikal terdistribusi secara merata di area melingkar  Kontinuitas pada permukaan lapisan  Elastis homogen , isotropik , dan linier  Tak terbatas dalam arah horizontal  Setengah terbatas , setengah tak terbatas di lapisan bawah  Deformasi kecil 2a q s z z t zr t rz s r s t0 E 1 , v 1 , TH 1 E 2 , v 2 , TH 2 E 3 , v 3 , TH 3 E 4 , v 4 r

48. Analisa Elastisitas Berlapis (2) ∇ 4 φ    Stress function, - Single layer , φ = P r  ⎡   ⎤ 2   )  2    = z i th layer  z  z ⎣ ⎦ H i th - layer in multiple layers Using the Hankel transform J ( m  ) J ( m  ) ⎪  [ A i  m  ) ] e i  C i ( 1  2  i ⎪ dm (  ) =  q   ⎨ ⎩  m (     1 ) ⎬ ⎭ z 1 i i i r z a , , ρ = λ = α = A, B, C, D = integration constants m = a parameter H H H 1 ( z / 2 ) ( t − 1 / t ) − n − 1 J , J 1 = Bessel J n ( z ) = ∫ e t dt function 2 π i of the first kind  ⎧  m (  i   ) ⎫ ⎪ + [ B  D ( 1  2  + m  ) ] e i ⎪ 2 z ⎢  ( 2 ⎥

49. Analisa Elastisitas Berlapis (3)    Boundary and continuity conditions    At the upper layer, ( τ ) ( σ ) 1 = − m J ( m ρ ) * rz * = z 1    At each interface under fully bonded case, ( w ) = ( w ) ( u ) = ( u ) ( σ ) = ( σ ) ( τ ) = ( τ ) * * * * * * * rz * rz z z i i + 1 i i + 1 i i + 1 i i + 1    At each interface under nonbonded or frictionless case, ( w ) i = ( w ) i ( σ z ) i = ( σ z ) i + 1 ( τ r z ) i = ( τ r z ) i + 1 * * * * * * = 1 +    At infinite depth, ( w * ) ( u * ) = ( σ * ) ( τ * ) = = = z rz n n n n

50. = 371x10 -6 ε Contoh – Perasan 4 lapis r = 5.64 in FWD sensors q = 90 psi t σ v E 4 = 6,000psi, ν 4 = 0.4 Subgrade 4" HMA σ E 1 = 450,000psi, ν 1 = 0.35 t 6" Base E 2 = 25,000psi, ν 2 = 0.3 6" Subbase E 3 = 12,000psi, ν 3 = 0.3 ε z

51. Analisa Perhitungan Maju (1)

52. Three options Loading position Analisa Perhitungan Maju ( 2 )

53. Infinite thickness Analisa Perhitungan Maju ( 3 )

54. Critical locations FWD sensor s ’ locations Analisa Perhitungan Maju ( 4 )

55. Analisa Perhitungan Maju ( 5 )

56. Analisa Perhitungan Maju ( 6 )

57. Analisa Perhitungan Maju ( 7 )

58. Metode Ketebalan Seragam    Ketebalan Seragam ( Ullidtz 1998): 1 layer 2 layers h , E , ν h e , E 2 , ν 2 1 1 1 E , ν E , ν 2 2 2 2    f = 1 untuk lapisan permukaan bila lapisannya banyak ; = 0.9 untuk lapisan permukaan bila hanya 2 lapis ; = 0.8 untuk lapisan lainnya .    Hanya berlaku untuk menghitung tegangan dan regangan di bawah lapisan yang telah ditransformasikan .

59. Perhitungan maju (Forward Analysis) dan perhitungan mundur ( Backcalculation ) Pavement Inputs Forward Analysis Prediksi displacement, stress, dan strain Backcalculation Memperkirakan Modulus Dan Ketebalan Pavement Responses Loading

60. Backcalculation (1)    Tujuan : Menentukan moduli lapisan trotoar . Kedalaman batuan dasar , non- linearitas , ketergantungan terhadap beban , dll Menentukan ketebalan lapisan    Kegunaan : Integritas dan daya dukung beban Analisis struktur perkerasan Monitoring Pemantauan variasi musiman

61. Backcalculation (2)    Metode Close-form Gunakan persamaan bentuk tertutup secara langsung untuk menghitung moduli dari defleksi yang diukur Berdasarkan Panduan Desain AASHTO 1993 dan the Metodologi berbasis AREA    Metode Iterasi Sesuaikan defleksi yang dihitung dengan defleksi yang terukur dengan iterasi Berdasarkan teori elastisitas berlapis Proses panjang untuk menghitung nilai modulus

62. Closed-form Backcalculation (1)    Berdasarkan Panduan Desain AASHTO 1993    Berdasarkan modulus resilient , Mr, lapisan sub grade

63. Closed-form Backcalculation (2)    M et ode berbasis AREA    Untuk PCC atau HMA overlay di atas PCC    Tergantung pada modulus subgrade dan rea ksi , k    AREA dalam inchi pada cambung defleksi

64. Closed-form Backcalculation (3)    Metode berbasis AREA    Untuk berbagai konfigurasi sensor

65. Closed-form Backcalculation (4)    Metode berbasis AREA    R adius pondasi kekakuan relative Winker λ k , A, B, C = constants for λ k    Modulus reaksi tanah dasar , k , psi/in. d r = Nondimensional coe f ficient for radial distance r , in. * d r * x, y , z = Coe f ficients for    M odulus elastis efektif , E, psi d r = Measured deflection at radial distance, r , in. h = Thickness of all bound layers above the subgrade, in. P = Applied NDT load, lbs

66. Closed-form Backcalculation (5)    Metode berbasis AREA    Konstanta λ k    Konstanta dr*

67. Closed-form Backcalculation (6)    Metode berbasis AREA    M odulus elastisitas untuk lapisan atas , psi (Bonded case) β = E 2 / E 1    M odulus elastisitas untuk lapisan bawah , psi ( unbonded case) Layer 1, h 1 , E 1 Layer 2, h 2 , E 2    A xis netral , x, in. Subgrade

68. Closed-form Backcalculation (7)  Metode berbasis AREA    Nilai tipikal β T ype T ypical value HMA overlaid PCC 10 PCC overlaid PCC 1.4 PCC with lean concrete base 0.40 PCC with cement treated base 0.25 PCC with asphalt treated base 0.10

69. Iterasi Backcalculation (1)

70. Iterasi Backcalculation (2)    Defleksi vs Modulus Semakin tinggi defleksi , semakin lemah perkerasan Setiap sensor memiliki kedalaman yang khas untuk mempengaruhi permukaan defleksi . Semua lapisan memengaruhi defleksi pada A. Hanya lapisan di bawah pengaruh kedalaman yang mempengaruhi defleksi pada B . Distance Distance A B Deflection basins Influence depth curve Deflection Depth Strong pavement W eak pavement

71. Iterasi Backcalculation (3)    Prosedur optimasi Moduli Lendutan luar mewakili moduli lapisan yang lebih dalam . Pada langkah perhitungan mundur pertama , moduli tanah dasar ditentukan dengan memasang defleksi pada jarak terjauh .    Δ n = f( E subgrade ) E subgrade = f(Δ n ) r σ = contact pressure under loading plate a = radius of loading plate Δ = deflection at distance r 1 2 3 n σ a 2 ( 1 − ν 2 ) E = r × Δ r Δ n Δ 3 r Δ 2 Δ 1

72. Iterasi Backcalculation (4)    P ro s edur optimalisasi modulus    Defleksi pada hasil menengah dari kombinasi lapisan subgrade, subbase , dan base Modulus Subbase dan base di tentukan dengan mencocokkan defleksi pada jarak menengah . Δ intermediate = f( E subbase , E base , E subgrade ) E subbase or base = f(Δ intermediate )

73. Iterasi Backcalculation (5)    P ro s edur optimalisasi modulus    Defle ksi pada jarak terdekat adalah kombinasi dari semua lapisan Modulus permukaan ditentukan dengan mencocokkan defleksi pada jarak te rdekat E surface = f( Δ 1 ) Δ 1 = f( E surface , E subbase , E base ) 2 ) 2 σ a (1- ν Δ E 1 = Δ 1 = deflection at the center of the load 1

74. Iterasi Backcalculation (6)    Minim alisasi Error    Melakukan iterasi sampai perbedaan antara data lendutan yang dihitung dan diukur berada dalam toleransi dengan mengubah modulus lapisan    Absolute mean square error, MSE m c W i , W i = Measured and calculated deflections at sensor i W e i = weight factor at sensor i n = Number of sensors    Percent mean square error, MSE(%) L. J. Bendana et al. (1994)

75. Iterasi Backcalculation (7)    Optim alisasi untuk hasil terbaik    Modified Newton algorithm (MICHBACK)    Modified augmented Gauss-Newton algorithm (Evercalc)    Hooke-Jeeves pattern-search (MODULUS)

76. Linear Analysis Backcalculation Programs

77. Non-Linear Analysis Backcalculation Programs

78. Evercalc    Backcalculation program to estimate the modulus of pavement layers from FWD data.    It is based on Waterways Experiment Station Layered Elastic Analysis (WESLEA) method.    Modified augmented Gauss-Newton algorithm is adapted to optimize backcalculation algorithm.    Maximum 5 layers, 10 sensors, and 12 drops per station

79. Influential Factors    Number of layers    Layer thickness    Layer interface condition    HMA layer temperature    Layer “Seed” values    Pavement cracks    Sensor errors    Loading plate    Pulse duration    Frequency duration    Seasonal E f fects    Material property variability    Adjacent layer modulus    Underlying stiff layer ratios

80. Effect of Loading Magnitude and Plate Size 5 4 5 r 4 3 5 3 2 5 2 1 5 1 50 - 2 4 6 8 1 00 1 2 00 B u lk S t r es s (k Pa ) Lab R e s i l i e nt M o d u lus ( M P a ) M = 7 . 3 4 ⋅ θ . 60 y = 1. 3 6 1 x . 80 R 2 = 0. 9 7 S m a ll P l a te La b M o du l u s La r g e P l a te R e g r e ssi o n

81. 35 40 45 re ( o C) 120 R 2 = 0.91 R 2 = 0.91 16, 00 Wearting S urface Te m peratu 14, 00 E T = 7125 e T em pe r ature ( ° C) -25°C Center Defle c tion (mm) Backcalcul a ted H MA Mod u li (MP a ) 100 80 60 40 20 A: y = 35.4 e 0.0301x R 2 = 0.92 Temperature Corrections D: y = 25.7 e 0.033x 2 R = 0.96 C: y = 39.9 e 0.0254x SECT I ON A SECT I ON B SECT I ON C SECT I ON D E x pon. (SECT I ON A) E x pon. (SECT I ON B ) E x pon. (SECT I ON C) E x pon. (SECT I ON D) B: y = 28.4 e 0.0333x 5 10 15 20 25 30 12, 00 10, 00 8, 00 6, 00 4, 00 2, 00 -0.03(T-25) R 2 = 0.7664 - 3 - 2 5 - 2 - 1 5 - 1 -5 5 10 15 20 25

82. Location of Loss of Suppor t    Examine difference between deflections on approach and leave slab A L Approach Slab Leave Slab Approach NDT Load Potential void Leave

83. Load Transfe r Joint/Crack = 0.66 mm (loaded) = 0 mm (unloaded) 0% Load transfer = 0.33 mm (loaded) = 0.33 mm (unloaded) 100% Load transfer L T E ( % ) = Δ U × 1 Δ L

84. Uniformity of Projec t

85. Deflection Basin Parameter s    Available deflection basin parameters from FWD Deflection parameters Formula Area AREA=6(D +2D 12 +2D 24 +D 36 )/D Area Indexes AI 1 =(D +D 12 )/2D Area Under Pavement Profile AUPP=(5D -2D 12 -2D 24 -D 36 )/2 Base Damage Index BDI=D 12 -D 24 Deflection Ratio DR=D r /D Load Spreadability Index LSI=(D 48 /D 24 ) x F Shape Factors F 1 =(D -D 24 )/D 12 Structural Strength Index SSI=A x /(X min x E min ) Structural Integrity Index SII=A x /(X s x E m ) Surface Curvature Index SCI=D -D 12 T angent Slope TS=(D -d x )/x

86. Parametric Study    Full-depth pavement    HMA layer condition R 2 =0.994 R 2 =0.987 Log(E HMA )=-1.0831xlog(SCI)-2.6210xlog(H HMA )+0.0482xH HMA +5.2961 Log( ε HMA )=0.9977xlog(BDI)+1.7142    Subgrade strength Log( ε sg )=0.9823xlog(BDI)+2.1460 E smin -0.0186F HMA -5.4088F HMA +1.0637 R 2 =0.978 2 E sg = R 2 =0.981 H sg <160in 2 -0.1944F /D 3 +1.033 0.108F +39.5426F HMA HMA HMA sg

87. ε = 371x10 -6 Example - 3 Layered Flexible Pavement    Analysis conditions r = 6 in. q = 80 psi Distance (in.) 12 24 36 48 60 72 Deflection (mils) 19.53 13.65 8.68 5.95 4.39 3.44 2.82 5 in. HMA E 1 = 500,000psi, ν 1 = 0.35 10 in. B a t se E 2 = 28,000psi, ν 2 = 0.35 Subgrade E 3 = 12,000psi, ν 4 = 0.4

88. Example - 3 Layered Flexible Pavement    Backcalculation with Evercalc 5.0 program Open and create general and deflection data

89. Example - 3 Layered Flexible Pavement    Input data for pavement and seed values Uniform Inverse RMS Sensor location User Seed moduli and range

90. Example - 3 Layered Flexible Pavement    Input data for pavement, load, and deflections Thickness Deflections

91. Example - 3 Layered Flexible Pavement    Backcalculation with batch mode    Results in *.txt for iteration, *.out for details, summary and *.sum for - Iteration process Starting Drop No 1 of 1 drops at Station 210.00 at 1 1: 30: 32 Seed Moduli: Percent RMS R of Backanalysis = 130.89 Current Moduli: Percent RMS Relative Error at the End of Iteration 1 = 63.72 Decrease RMS Current Moduli: Percent RMS Relative Error at the End of Iteration 2 = 1 1.14 Current Moduli: Percent RMS Relative Error at the End of Iteration 3 = .60 Final Moduli: Finished Drop No 1 of 1 drops at Station 210.00 at 1 1: 30: 32 300. 20. 5. elative Error at the Start 405. 29. 7. elative Error at the End 451. 32. 1 1. elative Error at the End 497. 29. 12. elative Error at the End 497. 29. 12.

92. Example - 3 Layered Flexible Pavement - Detailed result Final calculated modulus Modulus (ksi) Seed 300.00 20.00 5.00 Calculated 496.52 28.55 1 1.91 Real 500.00 28.00 12.00

93. FWD Specifications    Geophone spacing patterns    e.g., 0, 203, 305, 457, 610, 914, 1219, 1520mm Applied loads    Standard Load: 40kN (9000lb)    Other loads may be used to investigate load-dependent behavior (e.g., 22, 30, 40, 49 and 58kN) Plate sizes    Standard: Φ = 203mm          Unbounded Materials: Φ = 300mm (up to 457mm).    Temperature Measurements    Surface/ pavement