ELASTIC SETTLEMENT OF SHALLOW FOUNDATIONS ON GRANULAR SOIL— A C A CRITICAL REVIEW BRAJA M. DAS Settlement, S • Elastic settlement, S Elastic settlement Se • Consolidation settlement Consolidation settlement • Primary, Sp • Secondary, Secondary Ss S = Se + Sp p + Ss In his landmark paper in 1927 entitled The Science of Foundations, Karl Terzaghi wrote: “Foundation problems, throughout, are of such character that a strictly theoretical mathematical treatment will always be a strictly theoretical mathematical treatment will always be impossible. The only way to handle them efficiently consists of finding out, first, what has happened on preceding jobs of a similar character; next, the kind of soil on which the operations were performed; and, finally, why the operations have led to certain results. By systematically accumulating have led to certain results. By systematically accumulating such knowledge, the empirical data being well defined by the results of adequate soil investigations, foundation engineering could be developed into a semi empirical science could be developed into a semi‐empirical science. . . . ” “The bulk of the work—the systematic accumulation of empirical data remains to be done. empirical data—remains to be done.” To evaluate the current state of the art for settlement predictions of shallow foundations in p sand, in an attempt to promote the use of shallow foundations. A FHWA initiative 1. 1 2. 3 3. 4. FFederal Highway Administration (FHWA) d l Hi h Ad i i t ti (FHWA) Texas A & M University Geotest Engineering American Society of Civil Engineers (ASCE) TTexas A&M University A&M U i it National Geotech Experiment Site Approximately 12m 28m 5 Square Footings: 1m 1m 1 1.5m 1.5 1 m 2.5m 2.5m 3m 3m (North) 3m 3m (South) PROBLEM: PROBLEM: Predict the load at 25 mm settlement In Situ Test Summary Bore hole shear test h l h 3 Cross hole test 4 Cone penetration test 7 Cone penetration test Dilatometer test 4 Pressuremeter test 4 Step blade test 1 Standard penetration test 6 Number of participants: 31 15 consultants 16 academics Israel – 1 Brazil – 1 Japan – Japan – 1 France – France – 1 Canada – 2 Italy – 1 Hong Kong – Hong Kong 1 Australia – Australia 2 USA – 21 Methods Used for Settlement Prediction 22 22 different methods different methods Schmertmann (1970, 1978), Burland and Burbidge (1985) and FEM being popular Alpan (3 times) Bowles (4) Bowles (4) Buisman, DeBeer (3) Burland & Burbidge (9) Canada Found. Manual (1) D’Appolonia (4) DeBeer ((1)) Decourt (1) FEM (1) Hanson (1) Hanson (1) Leonard & Frost (4) Menard/Briaud (5) Meyerhof (4) Meyerhof (4) NAVFAC (4) Oweis (4) Parry (1) Peck (2) Robertson & Campanella p ((1)) Schmertmann (18) Schulze & Sherif (3) Terzaghi & Peck (5) Terzaghi & Peck (5) Vesic (6) P di d Predicted vs. Measured Values of Q M dV l f Q25 Footing (m) Item 11 Prediction P di i range (kN) 591100 Measured 850 1.51.5 2.52.5 33 33 1162950 2954271 4075600 4156400 1500 3600 4500 5200 Elastic Settlement Se Elastic Settlement, S Existing methods for predicting settlement may be grouped into three categories: A — Methods in which observed settlement of structures are linked to in situ test results (t d d (standard penetration test, cone t ti t t penetration test, Pressuremeter tests) B Semi‐empirical method B — S i ii l th d C — Use of theory of elasticity and modulus of elasticity, E l i i Es CATEGORY A Terzaghi and Peck (1948, 1967) Meyerhof (1956, 1965) DeBeer and Martens (1957) Hough (1969) Peck and Bazaraa (1969) ( ) Burland and Burbidge (1985) Terzaghi and Peck (1948 1967) Terzaghi and Peck (1948, 1967) Se 4 Se(1) B1 2 1 B Se = settlement of prototype foundation measuring = settlement of prototype foundation measuring BB Se(1) = settlement of a test plate measuring B l f l i 1B1 B1 is usually of the order of 0.3m to 1m y Terzaghi and Peck (1948, 1967) 2 3q B Se CW CD N60 B 0.3 where q is in kN/m²; B is in m; S is in mm CW = ground water table correction 1 if depth of water table is greater than 2B = 1 if depth of water table is greater than 2B below foundation = 2 if depth of water table is less than or equal p q to B CD = correction for depth of embedment p = 1 – (Df /4B ) Sivakugan, Eckersley and Li (1998) Si ak gan Eckersle and Li (1998) analyzed 79 settlement records of foundations provided by Jeypalan and Boehm (1986) yp ( ) and Papadopoulos (1992). 2 Se B 4 Se(1) B 0.3 B 1 Se B 0.3 4 Se(1) 2 2 3q B Se N60 B 0.3 3q Se N60 q Se(1) 1 Se 4 Se(1) N60 0.75 Meyerhof y 2q(kN/m2 ) (B 1.22m) Se (mm) N60 1956 2 2 3 q (kN/m ) B (B 1.22m) S (mm) e N60 B 0.3 1.25q(kN/m / 2) (B 1.22m) Se (mm) N60 1965 2 2 2 (kN/m ) q B (B 1.22m) S (mm) e 0 . 3 N60 B Note: q increased by about 50% and 1.25q (B 1.22m) Se (mm) CW CD N60 2 2q((kN/m / Se (mm) ( ) CW CD N60 ) B (B 1.22m)) B 0.3 CW 1.0 and 2 Df CD 1.0 4B Meyerhof’s Analysis (1965) Meyerhof’s Analysis (1965) Structure T. Edison, Sao Paulo Banco do Brasil, Sao Paulo Iparanga, Sao Paulo p g , C.B.I. Esplanada, Sao Paulo Riscala, Sao Paulo Thyssen Dusseldorf Thyssen, Dusseldorf Ministry, Dusseldorf Chimney, Cologne B (m) Average N60 q (kN/m2) Se(predicted) 18.3 22.9 9.15 14.6 3.96 22 6 22.6 15.9 20.4 15 18 9 22 20 25 20 10 229.8 239.4 220.2 383.0 229.8 239 4 239.4 220.4 172.4 1.95 0.99 1.29 1.20 1.56 0 77 0.77 0.98 3.30 Se (observed) Average ≈ 1.50 DeBeer and Martens (1957) o 2.3 Se log10 H C o ‘o = effective overburden pressure at a depth = increase in pressure due to foundation loading H = thickness of layer considered qc C 1.5 o Sepredicted 1.9 Field Test Results: Seobserved DeBeer (1965) Method applied to normally consolidated sand Method applied to normally consolidated sand Reduction factor needed for over−consolidated Reduction factor needed for over consolidated sand Hough (1969) o Cc Se H log10 1 eo o C c a(eo b) Value of constant t t Type of soil a b Uniform cohesionless material Uniform cohesionless material (uniformity coefficient Cu ≤ 2) Clean gravel Coarse sand Medium sand Fine sand Inorganic silt 0.05 0.06 0.07 0.08 1.00 0.50 0.50 0.50 0.50 0.50 Well‐graded cohesionless soil Silty sand and gravel Clean, coarse to fine sand Coarse to fine siltyy sand Sandy silt (inorganic) 0.09 0.12 0.15 0.18 0.20 0.35 0.25 0.25 Peck and Bazaraa (1969) 2 2q(kN/m Se (mm) CW CD (N1 )60 2 ) B B 0.3 where B is in m (N1)60 = corrected standard penetration number CW = ‘o o //o o at 0.5B below the bottom of foundation o = total overburden pressure ‘o = effective overburden pressure p CD = 1.0 – 0.4(D/q) 0.5 = unit weight of soil unit weight of soil Peck and Bazaraa (1969) 4N60 (N1 )60 (o 75 kN/m2 ) 3.25 0.01o 4N60 (N1 )60 (o 75 kN/m2 ) 1 0.04o Peck and Bazaraa’s Method ( f D’A (after D’Appolonia et al. 1970) l i l 1970) GRANULAR SOIL Burland and Burbidge (1985) For gravel or sandyy ggravel N60(a) 1.25N60 For fine sand or silty sand below the ground water N60(a) 15 0.6(N60 15) and d N60 15 where N60(a) = adjusted N60 value Depth of Stress Influence, z' Depth of Stress Influence, z If N60(a) [or N60(a)] is approximately constant (or increasing) with depth, B z 1.4 BR BR 0.75 where BR = reference width = 0.3m width of the actual foundation (m) B = width of the actual foundation (m) Depth of Stress Influence, z' If N60(a) [or N60(a)] is decreasing with depth, calculate z‘ = 2B and z‘ = distance from the bottom of the foundation to the bottom of the soft soil layer (z“ ). Use z‘ = 2B Use z 2B or z or z‘ = zz“,, whichever is smaller. whichever is smaller. Depth of Influence H H Correction factor, 2 1 z z H = thickness of compressible layer For Normally Consolidated Soil For Normally Consolidated Soil Se 1 .71 0 .14 1 .4 BR [N 60 or N 60 (a ) ] 2 1 .25 L 0 .7 B B q L BR pa 0 .25 B where L = length of the foundation pa = atmospheric pressure (= 100 kN/m / 2) For Overconsolidated Soil (q c ; c overconsolidation pressure) Se 0.57 0.447 1.4 BR [N 60 or N 60(a) ] 1.25 L B L 0.25 B 2 0.7 B q BR pa For Overconsolidated Soil For Overconsolidated Soil (q c ) : Se 0.57 0.14 1.4 BR [N 60 or N 60(a) ] 1.25 L B L 0.25 B 2 0.7 B q 0.67c pa BR Probability of Exceeding 25‐mm Settlement in the Field (After Sivakugan and Johnson 2004) (After Sivakugan and Johnson 2004) Predicted methods Predicted settlement (mm) 1 5 10 15 20 25 30 35 40 Terzaghi & Peck (1948) 0.00 0.00 0.00 0.09 0 20 0.20 0.26 0.31 0 35 0.35 0.387 Schmertmann (1970) 0.00 0.00 0.02 0.13 0 20 0.20 0.27 0.32 0 37 0.37 0.42 Burland & Burbidge (1985) 0.00 0.03 0.15 0.25 0 34 0.34 0.42 0.49 0 44 0.44 0.51 CATEGORY B Schmertmann (1970), Schmertmann et al. (1978) et al (1978) Briaud (2007) Terzaghi, Peck and Mesri (1996) Akbas and Kulhawy (2009) Schmertmann (1970) q(1 s ) z [(1 2 s )A B] Es zE s (1 s )[(1 2 s )A B] Iz q Iz Se C1C2 q z Es q = net stress at the level of the foundation C 1 = correction factor for the depth of the foundation correction factor for the depth of the foundation = 1 – 0.5(qo /q) qo = effective overburden pressure at the level of the = effective overburden pressure at the level of the foundation C 2 = correction factor to account for creep in soil = correction factor to account for creep in soil = 1+0.2 log(t/0.1) Es = 2qc The same 79 foundations records given by Jeypalan and Boehm (1986) and Papadopoulos (1992) were analyzed by y y Sivakugan et al. (1998). Schmertmann et al. (1978) q Iz(peak) 0.5 0.1 o 0.5 Item Iz at z = 0 zp /B L/B = 1 0.1 0.5 L/B 10 0.2 1.0 zo /B Es 2.0 2 0 2.5qc 4.0 4 0 3.5qc Salgado (2008) L Iz (at z 0) 0.1 0.0111 2 B zp L 0.5 0.0555 1 1 B B L zo 2 0.222 1 4 B B Lee et al. (2008) FEM Analysis Iz (peak) 0.5 zp L 0.5 0.11 1 1 B B L with a maximum of 1 at 6 B zo L 0.95 cos 1 3 4 B 5 B L with i h a maximum i of f 4 at 6 B Terzaghi et al. (1996) L zo 21 log 4 B I z Se q z z 0 E s z zo E s (L / B ) L 1 0 .4 log 1 .4 E s ( L / B 1 ) B E s ( L / B 1 ) 3 . 5q c S e (creep) 0 .1 t days z o log 1 day qc q c weighted mean value q c (in MN/m 2 ) 81 Foundation and 92 Plate Load Tests Load‐Settlement Curve Based on Pressuremeter Test Briaud (2007) Pressuremeter Test q [ f(L / B) , fe , f , fd ]pp(mean) R Se 0.24 B R gamma function SHAPE FACTOR B f(L / B) 0.8 0.2 L ECCENTRICITY FACTOR e fe 1 0.33 Center B 0 0.5 e fe 1 Edge B LOAD INCLINATION FACTOR (deg) f 1 Center 90 2 (deg) f 1 Edge 360 0.5 SLOPE FACTOR SLOPE FACTOR 0.1 f, d f, d d 0.8 1 3 : 1 slope B d 0.7 1 B 0.15 2 : 1 slope L Long‐term settlement, including creep = l i l di t Se t1 0.03 t = design life (in hours) t 1 = 1 hour t 1 hour Akbas and Kulhawy and Kulhawy (2009) L1 ‐ L2 Method 37 Sites 37 Sites 167 Axial compression field load tests Mean Se(L1) = (0.23%)B Mean S = (0 23%)B Mean Se(L2) Mean S (5.39%)B e(L2) = (5.39%)B Se Q B QL2 0.69 Se 1.68 B B > 1 m >1m QL2 = ultimate bearing capacity Q ultimate bearing capacity Qu (Vesic 1973, 1975) 1973, 1975) B 1 B ≤ 1 m Qu QL2 Quq B Qu N portion of Vesic' s theory Quq Nq portion of Vesic' s theory Note: Vesic’s theory includes compressibility factor. So Qu f ( , E s , , , B) Proper assumption of Es and Proper assumption of E and is needed. is needed CATEGORY C Use of Theory of Elasticity and Modulus of Elasticityy 1 2s Se qo (B) Is If Es Es = average modulus of elasticity (z = 0 to z = 4B) B‘ = B/2 s = Poisson’s ratio Steinbrenner (1934) Is = shape factor = f (m, n) For Se at the center : = 4 L m B H n B 2 Fox (1948) ( ) Df L I f depth factor f , and s B B Se(rigid) 0.93Se(flexible, center) Variation of If L /B Df /B 1.0 2.0 5.0 Poisson’s ratio s = 0.30 Poisson’s ratio 0 30 0.20 0.40 0 60 0.60 0.80 1.00 2 00 2.00 0.902 0.808 0 738 0.738 0.687 0.650 0 562 0.562 0.930 0.857 0 796 0.796 0.747 0.709 0 603 0.603 0.951 0.899 0 852 0.852 0.813 0.780 0 675 0.675 Poisson’s ratio s = 0.40 0.20 0.40 0.60 0.80 1 00 1.00 2.00 0.932 0.848 0.779 0.727 0 689 0.689 0.596 0.955 0.893 0.836 0.788 0 749 0.749 0.640 0.970 0.927 0.886 0.849 0 818 0.818 0.714 Bowles (1987) Bowles (1987) Weighted average, E s E s ( i ) z z = H = H or 4B, whichever is smaller or 4B whichever is smaller Es = 500(N 500(N60 + 15) kN/m + 15) kN/m2 z Mayne and Poulos (1999) E s Eo kz q Be IG IR IE (1 2s ) Se Eo Eo H IG influence i fl f t f factor , k Be Be IR foundation rigidity correction factor IE foundation embedment correction factor 4BL Be 0.5 IR 4 IE 1 1 Ef 2t 3 4.6 10 Eo Be k Be 2 1 Be 3.5 exp1.22 s 0.4 1.6 Df Berardi and Lancellotta (1991) qB Se Is Es Is = influence factor for a rigid foundation (μs = 0.15) (Tsytovich, 1951) H 1 /B LL /B /B 1 2 3 5 10 0.5 0 5 0.35 0 39 0.39 0.40 0.41 0.42 1.0 1 0 0.56 0 65 0.65 0.67 0.68 0.71 1.5 1 5 0.63 0 75 0.75 0.81 0.84 0.89 2.0 2 0 0.69 0 88 0.88 0.96 0.99 1.06 Berardi and Lancellotta (1991) re‐analyzed field p performance of 130 structures on predominantly p y silica sand as reported by Burland and Burbidge 0.5 o 0.5 Es KE pa (Janbu, 1963) pa pa = atmospheric pressure atmospheric pressure o and at a depth B/2 below the foundation K E f N1 60 N1 60 average corrected standard penetration number b in i the th influence i fl zone Influence zone for square foundation: Influence zone for square foundation: H15 = (1.2 to 2.8)B H25 = (0.8 to 1.3)B (0 8 to 1 3)B Influence zone for L/B / ≥ 10: H15 (1.8 to 2.4)B H25 (1.2 to 2.0)B 25 (1.2 to 2.0)B Skempton (1986) 2 N1 60 N60 1 0.01o o is i in i kN/m kN/ 2 N1 60 Dr2 60 Procedure for Calculating S g E Berardi and Lancellotta (1991) 1. Obtain the variation of N60 within the influence zone ((i.e., H , 25)). 2. Obtain (N1)60 within the influence zone. 3 Obtain 3. Obtain N 1 60 . 4. Obtain KE at Se /B = 0.1%. 0.5 o 0.5 . 5. Calculate E s KE pa pa Procedure for Calculating SE (continued) 6. Determine Is. 7 Use an equation from theory of elasticity to 7. Use an equation from theory of elasticity to calculate Se. 8 Calculate S 8. Calculate Se /B. Is it equal to assumed S /B Is it equal to assumed Se /B ? /B ? 9. If so, the calculated Se in Step 7 is the answer. 10 If not, use S 10. If not use Se /B from Step 8 to obtain the new K /B from Step 8 to obtain the new KE. 11. Repeat Steps 5, 7 and 8 until the assumed and calculated Se /B are equal. calculated S /B are equal Settlement Prediction in Granular Soils ― A Probabilistic Approach A P b bili ti A h Sivakugan and Johnson (2004), Geotechnique, Vol. 54, No. 7, 449‐502. No. 7, 449 502. Predicted Settlement – 25 mm Method Terzaghi & Peck (1948) Schmertmann (1970) Burland & Burbidge (1985) B Berardi di & Lancellotta &L ll tt (1991) Probability of exceeding 25 mm g in the field 0.26 (26%) 0.27 (27%) 0.42 (42%) 0 52 (52%) 0.52 (52%) COMMENTS AND CONCLUSIONS COMMENTS AND CONCLUSIONS 1. Meyerhof’s relations (1965) simple to use. On the average, will give Se(predicted)/Se(observed) 1.5 to 2.0. 2. Peck & Bazaraa method (1969) is not superior to that of Meyerhof (1965). 3. Burland & Burbidge (1965) is an improved method over that of Meyerhof (1965) and Peck & Bazaraa (1969). Difficult to estimate overconsolidation pressure from field exploration. 4 Modified 4. Modified strain influence factor methods of strain influence factor methods of Schmertmann et al. (1978), Terzaghi et al. (1996), Salgado (2008) and Lee et al. (2008) will give g ( ) ( ) g reasonable results with proper values of Es . gg 5. Suggested E s relations: s E s(L / B) L 1 0.4 log 1.4 E s(L / B1) B E s(L / B1) 3.5qc 6. The Es (L/B = 1) relationship can be related to N60 via D50 . 7. Pressuremeter method of developing load method of developing load‐ settlement relationship is very effective, but may not be cost effective. 8. L1 – L2 (Akbas and Kulhawy) is a good method. However proper assumption of E and needed to estimate QL2. 9. Relationships for settlement developed using p p g theory of elasticity will give equally good results provided a realistic Es is used. Use of iteration method is suggested. If not, used Terzaghi et al.’s relationship (1996). What we have seen is a systematic accumulation of knowledge over 60 years. acc m lation of kno ledge o er 60 ears The parameters for comparing settlement prediction methods are accuracy and prediction methods are accuracy and reliability. Reliability is the probability that the actual settlement would be less than that computed by a specific method. In choosing a method for design, it all comes h h df d ll down to keeping a critical balance between reliability and accuracy, accuracy which can be difficult which can be difficult at times, knowing the non‐homogeneous nature of soil in general. We cannot be over‐ g conservative but, at the same time, not be accurate. We need to keep in mind what Karl Terzaghi said in the 45 id i th 45th James Forrest Lecture at the J F tL t t th Institute of Civil Engineers in London: “Foundation Foundation failures that occur are no longer failures that occur are no longer ‘an act of God’.”