NCHRP LRFD DESIGN SPECIFICATIONS FOR SHALLOW FOUNDATIONS. Final Report September 2009 APPENDIX G BIAS CALCULATION EXAMPLES

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1 NCHRP 4-3 LRFD DESIGN SPECIFICATIONS FOR SHALLOW FOUNDATIONS Final Report September 009 APPENDIX G BIAS CALCULATION EXAMPLES Prepared for National Cooperative Highway Research Program Transportation Research Board National Research Council LIMITED USE DOCUMENT This Appendix is furnished only for review by members of the NCHRP project panel and is regarded as fully privileged. Dissemination of information included herein must be approved by the NCHRP and Geosciences Testing and Research, Inc. Shailendra Amatya Robert Muganga Geotechnical Engineering Research Laboratory University of Massachusetts Lowell University Ave., Lowell, MA 0854

2 TABLE OF CONTENTS G. BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING UNDER VERTICAL CENTRIC LOADING... G- G.. Given Data: Footings in Granular Soils: FOTID #35 in UML-GTR ShalFound07 G.. Interpreted Measured Failure Load G..3 Ultimate Bearing Capacity (Vesic, 975 and AASHTO, 007) G..4 Bias in the Bearing Capacity G. BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING UNDER VERTICAL ECCENTRIC LOADING... G-5 G.. Given Data: Footings in Granular Soils: FOTID #47 in UML-GTR ShalFound07 G.. Interpreted Measured Failure Load G..3 Ultimate Bearing Capacity (Vesic, 975 and AASHTO, 007) G..4 Bias in the Bearing Capacity G.3 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING UNDER INCLINED CENTRIC LOADING... G-7 G.3. Given Data: Footings in Granular Soils: FOTID #547 in UML-GTR ShalFound07 G.3. Interpreted Measured Failure Load G.3.3 Ultimate Bearing Capacity (Vesic, 975 and AASHTO, 007) G.3.4 Bias in the Bearing Capacity G.4 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING UNDER INCLINED ECCENTRIC LOADING... G-0 G.4. Given data: Footings in Granular Soils: FOTID #504 in UML-GTR ShalFound07 G.4. Interpreted Measured Failure Load G.4.3 Ultimate Bearing Capacity (Vesic, 975 and AASHTO, 007) G.4.4 Bias in the Bearing Capacity G.5 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING ON ROCK USING GOODMAN S (989) METHOD FOR PLATE LOAD TEST DATA... G-3 G.5. Given Data: UML-GTR RockFound07 Database Table: E-3 of Appendix E G.5. Interpreted Measured Failure Load G.5.3 Ultimate Bearing Capacity (Vesic, 975 and AASHTO, 007) G.5.4 Bias in the Bearing Capacity

3 G.6 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING ON ROCK USING GOODMAN S (989) METHOD FOR ROCK SOCKET LOAD TEST DATA... G-4 G.6. Given Data: UML-GTR RockFound07 Database Table: E-3 of Appendix E G.6. Interpreted Measured Failure Load G.6.3 Ultimate Bearing Capacity (Vesic, 975 and AASHTO, 007) G.6.4 Bias in the Bearing Capacity G.7 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING ON ROCK USING CARTER AND KULHAWY (988) METHOD FOR PLATE LOAD TEST DATA... G-5 G.7. Given Data: UML/GTR RockFound07 Database Table: E- of Appendix E G.7. Interpreted Measured Failure Load G.7.3 Ultimate Bearing Capacity (Vesic, 975 and AASHTO, 007) G.7.4 Bias in the Bearing Capacity G-ii

4 G. BIAS DETERMINATION FOR BEARING CAPACITYOF A FOOTING UNDER VERTICAL CENTRIC LOADING G.. Given Data: Footings in Granular Soils: FOTID #35 in UML-GTR ShalFound07 The tested footing data is from the source Briaud and Gibbens (994). The soil profile is given in Table G-, and the reported soil parameters are listed in Table G-. Figure G- shows the observed SPT-N counts for the subsurface. Further data about FotID #35 are: Footing dimension: L B = 39in 39in = 3.5ft 3.5ft Embedment depth: D f = 8in =.33ft Footing thickness: 46in Depth of groundwater table is 6.0ft > 7.ft (=.5B + D f ), hence there is no effect of GWT. The average relative density of the soil layer to a depth of B below the footing base is about 50%. Table G-. Soil profile Depth (ft) Soil Description.5 medium dense tan silty fine Sand 3.0 medium dense silty Sand w/ clay and gravel 36. medium dense silty Sand to sandy clay w/gravel 08.3 very hard dark Clay Table G-. Reported soil unit weight and soil friction angle of the subsoil (a) (b) Depth (ft) Unit wt (pcf) Depth (ft) φ f (deg) G-

5 0 SPT-N count (blows/ft) Depth (ft) Figure G-. SPT-N counts of the subsurface G.. Interpreted Measured Failure Load Considering the average relative density of the soil below the footing, the failure of the footing in local shear failure mode can be expected. In the load-settlement curve for the footing presented in Figure G-, it can be observed that the minimum slope starts at a load of 3.94tsf (S e /B = 7.8%). Hence, using the Minimum Slope criterion (Vesić, 963), the interpreted failure (ultimate) load capacity of the footing is q u,meas = 3.94tsf (335kPa). G-

6 0 load intensity (tsf) settlement, Se (in) Figure G-. Load-settlement curve for FotID #35 footing G..3 Ultimate Bearing Capacity (Vesic, 975 and AASHTO, 007) The bearing capacity q u of the footing is given by equation (34) qu = cncsdi c cc + qnqsdi q qq+ γ BNsdi γ γ γ γ (34) where q= ( γ D) and B = B e, e being load eccentricity along width B. For this D f i i B B example, cohesion c = 0, hence only the terms with subscripts q and γ are considered. Also, e B = 0, hence, B = B and L = L. The soil parameters for the bearing capacity calculation are taken as the weighted average of the parameters of each layer, usually considered up to a depth of B below footing base, i.e., the influence depth = B + D f = 8.83ft below ground level. Here, the average (weighted) of soil friction angle to a depth B below footing base is (3.9.33) ( ) ( ) 9. + ( ) 9.4 φ f = = 3.7 ( ) Similarly, the average (weighted) of soil unit weight to a depth B below footing base is G-3

7 (3.0.33) ( ) ( ) ( ) 7.3 γ= ( ) = 8.pcf Bearing capacity factors (equations () and (9)): N = exp( πtan φ ) tan ( φ ) q f f = + = exp(3.46 tan3.7) tan ( ).43 N = ( N + ) tan φ = γ q f (.43 + ) tan(3.7) = 8.97 Shape factors: B sq = + tanφ f = + tan(3.7) =.68 L B sγ = 0.4 = 0.6 L Depth factors: Here, Df / B = 8/39= 0.78 <.0. Hence, d = + φ φ D B q tan f ( sin f )( f / ) = + = d γ =.0 tan(3.7) ( sin3.7) Bearing capacity: q= ( γ D) = (.33.0) = 77.5psf D f i i qu,calc = qnqsd q q + γbnsd γ γ γ = = (psf) = 5.40ksf = 7.70tsf G..4 Bias in the Bearing Capacity The bias, defined as the ratio of measured to calculated bearing capacities, for the current footing is: qu,meas 3.94 λ= = =.8 q 7.70 u,calc G-4

8 G. BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING UNDER VERTICAL ECCENTRIC LOADING G.. Given Data: Footings in Granular Soils: FOTID #47 in UML-GTR ShalFound07 The tested footing data is from the source Perau (995) (PeB.6). The soil profile and the reported soil parameters are given in Table G-. Further data about FotID #47 are as follows: Footing dimension: L B = 3.54in 3.54in (0.09m 0.09m) Embedment depth: D f = 0in Groundwater table is not present. Depth of test pit =.4in (0.9m) The average relative density of the soil layer is 84.5%. Load eccentricity along the footing width = e B = 0.9in (0.03m) Table G-. Soil profile Depth (ft) Soil Description Unit Wt (pcf) φ f (deg) 0.95 medium to coarse Sand, dense to very dense G.. Interpreted Measured Failure Load In the load-settlement curve for the footing presented in Figure G- for the load test carried out, it can be observed that the minimum slope starts at a load of about 50.0lbs (S e /B 8%). Hence, using the Minimum Slope criterion (Vesić, 963), the interpreted failure (ultimate) load capacity of the footing is Q u,meas = 50.0lbs Applied load (lbs) Settlement, Se (in) Figure G-. Load-settlement curve for FotID #47 footing G-5

9 G..3 Ultimate Bearing Capacity (Vesić, 975 and AASHTO, 007) The bearing capacity q u of the footing is given by qu = cncsdi c cc + qnqsdi q qq+ γ BNsdi γ γ γ γ (34) where q= ( γ D) and B = B e B. For this example, cohesion c = 0, hence only the terms D f i i with subscripts q and γ are considered. Here, e B = 0.9in, hence, B =.73in (= = 0.044m) and L = L. Since the subsoil is homogeneous dense sand, the soil parameters are taken as reported in Table G-. Bearing capacity factors: N = exp( πtan φ ) tan ( φ ) q f f exp(3.46 tan44.93) tan ( ) = + = N = ( N + ) tan φ = γ q f ( ) tan(44.93) = 68.3 Shape factors: B.73 sq = + tanφ f = + tan(44.93) =.50 L 3.54 B.73 sγ = 0.4 = 0.4 = 0.80 L 3.54 Depth factors: Here, Df / B = 0. Hence, the term with subscript q in the BC equation is zero and d γ =.0. Bearing capacity: qu,calc = qnqsd q q + γbnsd γ γ γ = (.73/) i.e., = (psf) =.74ksf Q ucalc, = 74.0 ( )/44= 73.0lbs G..4 Bias in the Bearing Capacity The bias, defined as the ratio of measured to calculated bearing capacities, for the current footing is: Qu,meas 50.0 λ= = =.06 Q 73.0 u,calc G-6

10 G.3 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING UNDER INCLINED CENTRIC LOADING G.3. Given Data: Footings in Granular Soils: FOTID #547 in UML-GTR ShalFound07 The tested footing data is from the source Gottardi (99) (GoD6.3). The soil profile and the reported soil parameters are given in Table G3-. Further data about FotID #547 are as follows: Footing dimension: L B = 9.70in 3.94in (0.50m 0.0m) Embedment depth: D f = 0in Groundwater table is not present. Depth of test pit =.0ft (0.3m) The average relative density of the soil layer is 86.0%. Load inclination to the vertical = δ = 6.5 ; load applied in radial load path at 90 to the longitudinal side, i.e., θ = 90. Table G3-. Soil profile Depth (ft) Soil Description Unit Wt (pcf) φ f (deg).0 Dense Adige Sand G.3. Interpreted Measured Failure Load The load-displacement curves obtained from the load test of the footing is presented in Figure G3-. In the vertical load vs. settlement curve, it can be observed that the slope of the curve changes from positive to negative when the applied vertical component of the inclined load is.6kips, meaning failure takes place at this point. Since the load has been applied in the radial load path, the corresponding horizontal component at this failure point is given by: F3, ult = F, ult tanδ=.6 tan(6.5) = 0.4kips Upon examination of the horizontal load vs. horizontal displacement curve, it can be seen that the abrupt change in slope occurred when the horizontal component of the inclined load is about 0.4kips. This suggests that the footing bearing capacity failure observed in both horizontal and vertical load-displacements curves coincide. Hence, as concluded in Chapter 3, interpretation of the failure load form only the vertical load vs. settlement curve suffices. Thus, using the Minimum Slope criterion (Vesić, 963), the interpreted failure (ultimate) load capacity of the footing is established as Q u,meas =.6kips. G-7

11 0.00 Applied vertical load (kips) Applied horizontal load (kips) Settlement, Se (in) Horizontal displacement (in) Figure G3-. Load-displacement curves for loads and displacements in vertical and horizontal directions for FotID #547 footing, respectively..40 G.3.3 Ultimate Bearing Capacity (Vesić, 975 and AASHTO, 007) The bearing capacity q u of the footing is given by qu = cncsdi c cc + qnqsdi q qq+ γ BNsdi γ γ γ γ (34) where q= ( γ D). For this example, D f = 0 and cohesion c = 0, hence only the term with D f i i subscript γ is considered. B = B e B = Bsince e B = 0. Since the subsoil is homogeneous dense sand, the soil parameters are taken as reported in Table G3-. Bearing capacity factors: N = exp( πtan φ ) tan ( φ ) q f f = + = exp(3.46 tan44.84) tan ( ) 3.49 N = ( N + ) tan φ = γ q f ( ) tan(44.84) = 63.5 Shape factors: B 3.94 sγ = 0.4 = 0.4 = 0.9 L 9.7 Depth factors: d γ =.0 G-8

12 Load inclination factors: Since θ = 90, + B / L n=.0= B / L i γ n+ F 3 + (.833+ ) tan tan(6.5) 0.70 n = = ( δ ) = ( ) = F Bearing capacity: qu,calc = qnqsd q q + γbnsdi γ γ γ γ = (3.94/) = (psf) = 96.4psf i.e., 3 Q ucalc, = 96.4 ( )/44 0 (kips) =.58kips G.3.4 Bias in the Bearing Capacity The bias, defined as the ratio of measured to calculated bearing capacities, for the current footing is: Qu,meas.6 λ= = =.36 Q.58 u,calc G-9

13 G.4 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING UNDER INCLINED ECCENTRIC LOADING G.4. Given data: Footings in Granular Soils: FOTID #504 in UML-GTR ShalFound07 The tested footing data is from the source Perau (995) (PeE.). The soil profile and the reported soil parameters are given in Table G4-. Further data about FotID #504 are as follows: Footing dimension: L B = 3.54in 3.54in (0.09m 0.09m) Embedment depth: D f = 0in Groundwater table is not present. Depth of test pit =.4in (0.9m) The average relative density of the soil layer is 89.7%. Inclined load applied in a step-like load path at 90 to the longitudinal side, i.e., θ = 90. -way load eccentricity along the footing width, e B = 0.59in (0.05m) generating positive moment (refer to Chapter 3 for sign conventions). Table G4-. Soil profile Depth (ft) Soil Description Unit Wt (pcf) φ f (deg) 0.95 medium to coarse Sand, dense to very dense G.4. Interpreted Measured Failure Load The load-displacement curves obtained from the load test of the footing is presented in Figure G4-. In the vertical load vs. settlement curve (left), it can be observed that the curve changes abruptly when the applied vertical component of the inclined load is 7.4lbs, meaning failure takes place at this point. Hence, the vertical component of the ultimate load F,ult (= Q u,meas ) is 7.4lbs. Similar failure load can be identified in the horizontal load vs. horizontal displacement curve (right). The horizontal component of the applied inclined load thus identified is F 3,ult = 0.8lbs. Since the load has been applied in a step-like load path, the angle of load inclination at failure is given by: F 0.8 F, ult 7.4 3, ult δ= arctan = arctan = 3.6 G-0

14 0.00 Applied vertical load (lbs) Applied horizontal load (lbs) Settlement, Se (in) Horizontal displacement (in) Figure G4-. Load-displacement curves for loads and displacements in vertical and horizontal directions for FotID #504 footing, respectively. G.4.3 Ultimate Bearing Capacity (Vesic, 975 and AASHTO, 007) The bearing capacity q u of the footing is given by qu = cncsdi c cc + qnqsdi q qq+ γ BNsdi γ γ γ γ (34) where q= ( γ D). For this example, D f = 0 and cohesion c = 0, hence only the term with D f i i subscript γ is considered. Effective width, B = B e B =.36in (= = 0.06m) Since the subsoil is homogeneous dense sand, the soil parameters are taken as reported in Table G4-. Bearing capacity factors: N = exp( πtan φ ) tan ( φ ) Shape factors: q f f = + = exp(3.46 tan44.75) tan ( ) 9.64 N = ( N + ) tan φ = γ q f ( ) tan(44.75) = G-

15 s γ B.36 = 0.4 = 0.4 = L 3.54 Depth factors: d γ =.0 Load inclination factors: Since θ = 90, + B / L n=.0=.60 + B / L i γ n+ ( n+ ) (.60+ ) F F 3 3, ult F F, ult 7.4 = = = = Bearing capacity: qu,calc = qnqsd q q + γbnsdi γ γ γ γ = (.36/) i.e., = (psf) = 74.7psf Q ucalc, = 74.7 ( )/44= 0.05lbs G.4.4 Bias in the Bearing Capacity The bias, defined as the ratio of measured to calculated bearing capacities, for the current footing is: Qu,meas 7.4 λ= = =.7 Q 0.05 u,calc G-

16 G.5 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING ON ROCK USING GOODMAN S (989) METHOD FOR PLATE LOAD TEST DATA G.5. Given Data: UML-GTR RockFound07 Database Table: E-3 of Appendix E Database Case No.: Type of Load Test: Plate Load Test Rock Description: Sandstone Interpreted Foundation Capacity (q L ): ksf Rock Properties: Friction angle (φ) = 30 o Uniaxial compressive strength (q u ) = ksf Discontinuity Spacing: Fractured Using Equation (77): N φ tan 45 φ ( ) = + (77) where φ = internal friction angle Substituting φ into equation (77): Using equation (79): ( ) N tan φ = + = 3 qult qu N φ ( ) = + (79) where q u = uniaxial compressive strength of the intact rock Substituting q u and N φ values into equation (77): qult ( ) = = 334.7ksf The bias of Goodman s (989) method in case no. : λ = measured capacity ql calculated capacity = q = = ult G-3

17 G.6 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING ON ROCK USING GOODMAN S (989) METHOD FOR ROCK SOCKET LOAD TEST DATA G.6. Given Data: UML-GTR RockFound07 Database Table: E-3 of Appendix E Database Case No.: 9 Type of Load Test: Rock Socket Rock Description: Fractured clay-shale Interpreted Foundation Capacity (q L ): 4.87 ksf Rock Properties: Friction angle (φ) = 3.5 Uniaxial compressive strength (q u ) = 9.66 ksf Discontinuity Spacing: Fractured Using equation (77): N φ tan 45 φ ( ) = + (77) where φ = internal friction angle Substituting φ into equation (77): Using equation (79): ( ) N tan φ = + =.33 qult qu N φ ( ) = + (79) where q u = uniaxial compressive strength of the intact rock Substituting q u and N φ values into equation (79): qult ( ) = = 98.65ksf The bias of Goodman s (989) method in case no. 9: λ = measured capacity ql calculated capacity = q = = ult G-4

18 G.7 BIAS DETERMINATION FOR BEARING CAPACITY OF A FOOTING ON ROCK USING CARTER AND KULHAWY (988) METHOD FOR G.7. Given Data: UML/GTR RockFound07 Database Table: E- of Appendix E Database Case No.: Type of Load Test: Plate Load Test Rock Description: Fractured sandstone Rock Quality: Good Interpreted Foundation Capacity (q L ): ksf Uniaxial Compressive Strength (q u ): ksf Rock Type: C = Arenaceous rocks with strong crystals and poorly developed crystal cleavage sandstone and quartzite (see Table -5 (AASHTO, 007 Table ) Strength Parameters of the Rockmass: m =.3 and s = Table -5, (AASHTO, 007 Table ) Using Equation (8): ult ( ) q = m+ s q (8) u where q u = uniaxial compressive strength of the intact rock s and m = empirically determined strength parameters for the rockmass, which are somewhat analogous to c and φ of the Mohr-Coulomb failure criterion Substituting q u, m and s values into Equation (8): qult ( ) = = 07.36ksf The bias of Carter and Kulhawy s (988) method in case no. : λ = measured capacity ql calculated capacity = q = = ult G-5

19 References: AASHTO (007). LRFD Bridge Design Specifications Section 0: Foundations, American Association of State Highway & Transportation Officials, Washington, DC. Briaud, J. and Gibbens, R. (994). Predicted and measured behavior of five spread footings on sand, Proc. of a prediction symposium sponsored by the Federal Highway Administration on the occasion of Settlement '94 ASCE Conference at Texas A&M University, June 6-8, 994, (eds. J. Briaud and R. Gibbens), Geotechnical Special Publication No.4, ASCE. Carter, J.P., and F.H. Kulhawy (988). Analysis and Design of Foundations Socketed into Rock. Report No. EL-598, Empire State Electric Engineering Research Corporation and Electric Power Research Institute, New York, NY, p. 58. Goodman, R.E. (989) Introduction to Rock Mechanics. Second Edition, John Wiley & Sons. Gottardi, G. (99). Modellazione del comportamento di fondazoni superficiali su sabbia soggette a diverse condizioni di carico, Dottorato di ricerca in ingegneria geotecnica, Instituto di Costruzioni Marittime e di Geotecnica, Universita di Padova Perau, E. (995). Ein systematischer Ansatz zur Berechnung des Grundbruchwiderstands von Fundamenten. Mitteilungen aus dem Fachgebiet Grundbau und Bodenmechanik der Universität Essen, Heft 9, Hrsg.: Prof. Dr.-Ing. W. Richwien, Essen: Glückauf-Verlag Vesic, A. (963) Bearing capacity of deep foundations in sand, Highway Research Record, 39, National Academy of Sciences, National Research Council, pp.-53 Vesić, A. (975). Bearing Capacity of Shallow Foundations, Foundation Engineering Handbook (eds. H.F. Winterkorn and H.Y. Fang), Van Nostrand Reinhold, New York, pp.-47. G-6