NCHRP LRFD Design Specifications for Shallow Foundations TRB AFS30 Committee Meeting January 26, 2011

Transcription

1 Geotechnical Engineering Research Laboratory Dept. of Civil and Environmental Engineering University of Massachusetts Lowell. NCHRP LRFD Design Specifications for Shallow Foundations TRB AFS3 Committee Meeting January 26, 211 The lecture is based on NCHRP Report 651 LRFD DESIGN AND CONSTRUCTION OF SHALLOW FOUNDATIONS FOR HIGHWAY STRUCTURES Samuel G. Paikowsky, Mary C. Canniff, Kerstin Lesny, Aloys Kisse, Shailendra Amatya, and Robert Muganga Geosciences Testing & Research, Inc. N. Chelmsford, MA USA

2 OBJECTIVES NCHRP RESEARCH PROJECT Develop and Calibrate Procedures and Modify AASHTO s Section 1 (Foundations) Specifications for the Strength Limit State Design of Bridge Shallow Foundations. For NCHRP Research Report 651, Google NCHRP 651 2

3 Task 1: Design & Construction Practices Questionnaire - Establishing design methods, construction practices, design cases, and loads Developed and distributed to 161 State Highway Officials, TRB Representatives, and State and FHWA bridge engineers. Obtained responses from 39 states and 1 Canadian Province Previous relevant information was obtained via a questionnaire circulated in 24 for the research project NCHRP AASHTO LRFD Specifications for the Serviceability in the Design of Bridge Foundation 3

4 Design & Construction Practices - Questionnaire Foundation Alternatives Results on distribution of bridge foundation usage from our previous questionnaires conducted in 1999 and 24, and the current questionnaire (over the past 3 years, 24-26): shallow foundations driven piles drilled foundations 1999/24 14%/17% 75%/62% 11%/21% current 17% 59% 24% The average use changes significantly across the country. The use of shallow foundations in the Northeast exceeds by far all other regions of the USA, ranging from 4% in NY, NJ and ME, to 67% in CT. Other heavy users are TN (63%), WA (3%), NV (25%) and ID (2%). In contrast, out of the 39 responding states, six states do not use shallow foundations for bridges at all, and additional eight states use shallow foundations in 5% or less of the highway bridge foundations. In summary, 55.8% of the shallow foundations are built on rock (average of piers and abutments) with additional 16.8% on IGM, hence 72.6% of the foundations are build on rock or cemented soils and only 27.4% are built on soils of which 24.2% on granular soils and 3.2% on clay or silt. 4

5 TASK 2: DATABASES UML-GTR ShalFound7 Database 549 cases built in ACCESS platform, 415 cases are suitable for ULS. UML-GTR RockFound7 Capacity Database 122 Cases of load tests to failure including 61 rock sockets, 33 shallow foundations on rock surface, 28 shallow foundations below surface ShalFound7 Divided into vertical centric and eccentric, and inclined cases RockFound7 All vertical centric, shallow and drilled shafts 5

6 Database Overview UML-GTR ShalFound7 Foundation type Plate load tests B 1m Small footings 1 < B 3m Large footings 3 < B 6m Rafts & Mats B > 6m Predominant Soil Type Country Total Sand Gravel Cohesive Mix Others Germany Others Total Note: Mixed are cases with alternating layers of sand or gravel and clay or silt Others are cases with either unknown soil types or with other granular materials like loamy Scoria 1m 3.3ft Large foundations are often not loaded to ULS failure (SLS controls) 6

7 TASK 3: BC Shallow Foundations on Soil - OUTLINE 1. BC of Shallow foundations BC Factors BC modification Factors 2. Determination of ULS from case histories ULS and Modes of Failure Overview Modes of Failure 3. Failure (Ultimate Load) Criteria Minimum slope criteria (Vesić, 1963) Limited settlement criterion of.1b (Vesić, 1975) Log-log plot of load-settlement curve (DeBeer, 1967) Two-slope criterion Selection of failure criteria (representative values and minimum slope) Examples in soil & rock 4. Uncertainty Evaluation BC of Centric Vertically Loaded Footing on Granular Soils Database overview Calculated BC missing soil parameters and equations used for BC calculations 5. Calibration 6. Summary and Conclusions 7

8 Recommended Failure Criterion Minimum Slope Failure Load Criterion, Vesic (1963) Failure load interpreted were for 196 cases using each of the proposed methods Representative Failure Load defined as the mean value of all the failure loads interpreted using each criterion Mean of the ratio was.98 and Failure Loads for most cases could be interpreted using Minimum Slope criterion the criterion was chosen as the standard BC interpretation method 8

9 Bias of Estimated BC Cases with Vertical Centric Loading Vertical Centric Loading n = 173; mean bias = 1.59, COV =.291 Natural soil conditions ( f from SPT-N counts) n = 14; no. of sites = 8 mean = 1. COV =.329 Controlled soil conditions (D r 35%) n = 159; no. of sites = 7 mean = 1.64 COV =.267 B > 1.m n = 6 no. of sites = 3 mean = 1.1 COV = < B 1.m n = 8 no. of sites = 7 mean =.99 COV =.47 B.1m n = 138 no. of sites = 5 mean = 1.67 COV = < B 1.m n = 21 no. of sites = 3 mean = 1.48 COV =.391 Figure 6 Summary of bias (measured over calculated BC) for vertical centric loading cases (Database I);.1m = 3.94in; 1m = 3.28ft. 9

10 Number of observations Frequency using Minimum Slope criterion (Vesic, 1963) (ksf) Bias of Estimated BC Cases with Vertical Centric Loading Vertical-centric loading n = 173 mean = 1.59 COV =.291 lognormal distribution normal distribution.2.1 Interpreted bearing capacity, qu,meas Vertical-centric loading Data (n = 173) Data best fit line No bias line Bias, q u,meas / q u,calc Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 61. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of vertical centrically loaded shallow foundations. 1

11 Number of observations Frequency Bias of Estimated BC using Minimum Slope criterion (Vesic, 1963) (ksf) Cases with Vertical Centric Loading 4 Controlled soil conditions n = 159 mean = 1.64 COV = lognormal distribution normal distribution Bias, q u,meas / q u,calc Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 62. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for vertical centrically loaded shallow foundations on controlled soil conditions. Interpreted bearing capacity, qu,meas Controlled soil conditions Data (n = 159) Data best fit line No bias line 11

12 Number of observations Frequency using Minimum Slope criterion (Vesic, 1963) (ksf) Bias of Estimated BC Cases with Vertical Centric Loading Natural soil conditions n = 14 mean = 1. COV =.329 normal distribution lognormal distribution Interpreted bearing capacity, qu,meas 1 1 Natural soil conditions Data (n = 14) Data best fit line No bias line Bias, q u,meas / q u,calc Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 63. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for vertical centrically loaded shallow foundations on natural soil conditions. 12

13 Bias Bias versus Footing Width B (ft) Mean bias BC (n = 172) s.d. (x) no. of cases in each interval 95% confidence interval for f (n = 135) 95% confidence interval for f (n = 37) (5) (9) (2) (3) (4) 1.5 (4) (5) (1) 1.5 (34) (1) (17) (3) (1) (2) Footing width, B (m) Figure 1. Variation of the bias in bearing resistance versus footing size for cases under vertical-centric loadings: f 43 and f <

14 q u / (.5 B s ) Uncertainty in N N from load tests; n = 125 N (Vesic, 1973) N = exp(.39 f ) (R 2 =.666) friction angle, f (deg) Comparison of bearing capacity factor calculated based on test results; N = q u / (.5 B s ) from 125 tests carried out in controlled soil conditions (tests by Perau, 1995) and N proposed by Vesic (1973) in the range of soil friction angle of 42 and 46 14

15 Uncertainty in N N = [q u / (.5 B s )] / NVesic load test data; n = 125 = exp(.25 f 8.655) (R 2 =.351) Friction Angle, f (deg) Figure 93. The ratio ( N ) between the back-calculated B.C. factor N based on experimental data to that proposed by Vesić versus soil friction angle. 15

16 Bias Uncertainty in N Data BC bias (n = 131) Bearing Capacity (BC) bias, N bias, Friction Angle, f (deg) Figure 94. The ratio between measured and calculated bearing capacity (bias ) compared to the bias in the B.C. factor N ( N ) versus the soil s friction angle for footings under vertical-centric loadings. 16

17 Bias Uncertainty in B.C Mean bias,bc (n = 172) 1 s.d. (x) no. of cases in each interval BC =.38exp(.372 f ) (R 2 =.2) % confidence interval (2) (4) (2) (3) (12) (3) (9) (2) 1. (3) (4) (4) (14).5 (2) Friction angle f (deg) Figure 13. Bearing resistance bias vs. average soil friction angle (taken f.5) including 95% confidence interval for all cases under vertical-centric loading. 17

18 Final Resistance Factors Controlled Conditions Table 66 Recommended resistance factors for shallow foundations on granular soils placed under controlled conditions Soil friction angle f Vertical-centric or -eccentric Loading conditions Inclined-centric Inclined-eccentric Positive Negative Notes: 1) f determined by laboratory testing 2) compacted controlled fill or improved ground are assumed to extend below the base of the footing to a distance to at least two (2.) times the width of the foundation (B). If the fill is less than 2B thick, but overlays a material equal or better in strength than the fill itself, then the recommendation stands. If not, then the strength of the weaker material within a distance of 2B below the footing; prevails. 3) The resistance factors were evaluated for a target reliability T =

19 Final Resistance Factors Natural Conditions Table 67 Recommended resistance factors for shallow foundations on natural deposited granular soil conditions Loading conditions Soil friction angle f Vertical-centric or -eccentric Inclined-centric Inclined-eccentric Positive Negative Notes: 1) f determined from Standard Penetration Test results 2) granular material is assumed to extend below the base of the footing at least two (2.) times the width of the foundation. 3) The resistance factors were evaluated for a target reliability T =

20 Intermediate Conclusions and Summary It was found that for the footings of larger sizes (B>3m (9.9ft)), the load tests were not carried out to the failure load Biases for the tests in Natural Soil Condition and Controlled Soil Conditions were analyzed separately For the footing sizes in similar ranges (.1m < B 1.m), the scatter of bias was larger for footings on/in natural soil conditions The majority of the relevant data refers to small size foundations (B 3.3ft (1.m)) on controlled compacted material. Many of the highway shallow foundations on soils are built on compacted materials and hence, the statistical data of the uncertainty can be used for that purpose There appears to be a trend of increase in bias with the footing size within the range of footing sizes available for testing (which seems to conform with the observation made by Vesic (1969)) 2

21 ULS of Inclined Loading x 2 F 1 M1 M2 F 1 M 2 x 2 D D M 1 F2 M3 F 2 M 3 F 3 F 3 b 2 L x 3 x 3 B b 3 x 1 x 1 g f (a) Loading convention F 1 F 1 F F 1 1,const. = const. F 3 arctan e = const M 2 increasing F 3 (b) Radial load path (c) Step-like load path Figure 4.7. Loading convention and load paths used during tests Figure 64. Loading convention and load paths used during tests. 21

22 Vertical displacement, u 1 (mm) u 1 (in) Horizontal displacement, u 3 (mm) u 3 (in) ULS of Inclined Loading Vertical load, F 1, F 1 (kn) Horizontal load, F 3 (kn) MoD2.1 = MoD2.2 = 8 MoD2.3 = MoD2.1 = 3 MoD2.2 = MoD2.3 = 14 MoA2.1 = F F 1 (kips) F 3 (kips).2 Figure 65. Load displacements curves for model tests conducted by Montrasio (1994) with varying load inclination: (a) vertical load vs. vertical displacement and (b) horizontal load vs. horizontal displacement. 22

23 Number of observations Frequency using Minimum Slope criterion (Vesic, 1963) (ksf) Bias of Estimated BC Cases with Vertical-Eccentric Loading (using B) Vertical-eccentric loading n = 43 mean = 1.83 COV =.351 lognormal distribution normal distribution Interpreted bearing capacity, qu,meas Vertical-eccentric loading Data (n = 43) Data best fit line No bias line Bias, q u,meas / q u,calc Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 66. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of vertical eccentrically loaded shallow foundations..1 23

24 Bias Bias of Estimated BC Cases with Vertical-Eccentric Loading 3. n = 43 (4) (7) (2) (11) Mean bias, BC 1 s.d. (x) no. of cases in each interval BC = exp( f ) (R 2 =.1) 95% confidence interval (6) (9) (4) Friction angle f (deg) Figure 15. Bearing resistance bias versus soil friction angle for cases under vertical-eccentric loadings; seven cases for f = 35 (all from a single site) have been ignored for obtaining the best fit line. 24

25 Number of observations Frequency 12 8 using Minimum Slope criterion (Vesic, 1963) (ksf) Bias of Estimated BC Cases with Inclined-Centric Loading 4 Inclined-centric loading n = 39 mean = 1.43 COV =.295 lognormal distribution normal distribution Interpreted bearing capacity, qu,meas Inclined-centric loading Data (n = 39) Data best fit line No bias line Bias, q u,meas / q u,calc Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 67. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of inclined centric loaded shallow foundations. 25

26 Number of observations Frequency using Minimum Slope criterion (Vesic, 1963) (ksf) Bias of Estimated BC Cases with Inclined-Eccentric Loading Inclined-eccentric loading n = 29 mean = 2.43 COV =.58 lognormal distribution normal distribution Bias, q u,meas / q u,calc Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 68. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of inclined eccentrically loaded shallow foundations. Interpreted bearing capacity, qu,meas Inclined-eccentric loading Data (n = 29) Data best fit line No bias line 26

27 Loading Directions for Inclined-Eccentric Loadings F 1 e 3 b Moment acting 3 in direction opposite to the lateral 3 loading negative b e 3 F 1 F 3 F 3 eccentricity Moment acting 3in the same direction as the lateral 3 loading positive eccentricity (a) along footing width b b F F M 2 1 F M F F 1 e 2 b b e 2 F 1 F 2 Moment acting 2 in direction opposite to the lateral 2 loading negative F 2 eccentricity Moment acting 2 in the same direction as the lateral 2 loading positive eccentricity b b F 1 F 1 M 3 M 3 (b) along footing length + - F + 2 F + 2 Figure 69. Loading directions for the case of inclined-eccentric loadings: (a) along footing width and (b) along footing length 27

28 Number of observations Frequency using Minimum Slope criterion (Vesic, 1963) (ksf) Bias of Estimated BC Cases with Inclined-Eccentric Loading Inclined-eccentric loading Negative eccentricity n = 7 mean = 3.43 COV =.523 lognormal distribution normal distribution Bias, q u,meas / q u,calc Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 71. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of inclined eccentrically loaded shallow foundations under negative eccentricity. Interpreted bearing capacity, qu,meas Inclined-eccentric loading Negative eccentricity Data (n = 7) Data best fit line No bias line 28

29 Final Resistance Factors Natural Conditions Table 67 Recommended resistance factors for shallow foundations on natural deposited granular soil conditions Loading conditions Soil friction angle f Vertical-centric or -eccentric Inclined-centric Inclined-eccentric Positive Negative Notes: 1) f determined from Standard Penetration Test results 2) granular material is assumed to extend below the base of the footing at least two (2.) times the width of the foundation. 3) The resistance factors were evaluated for a target reliability T =

30 Conceptual Design Influence of Serviceability s based on Serviceability Limit States Developed as a part of Project NCHRP Bias = measured load / calculated load for a given settlement For reliability index = 1.28 (p f factors taken as unity Bias of LL = 1.15, COV QL =.2 Bias of DL = 1.5, COV QD =.1 = 1%), and load Method AASHTO Range of Settlement (inch) Resistance Factor Efficiency Factor /. < < <

31 Conceptual Design Granular Soils Example 2 NCHRP Report 651: Known Load and Settlement Central Pier of a bridge in Billerica (Rangeway Rd over Rte.3) (B-12-25) Design (factored) load is kips for ultimate limit state and 275kips for service limit state (unfactored) Allowable settlement 1.5inches 31

32 Factored ultimate limit state and unfactored service limit state (MN) Factored ultimate limit state and unfactored service limit state (ksf) Factored ultimate limit state and unfactored service limit state (MPa) Factored ultimate limit stat unfactored service limit state.75 Conceptual Design Granular Soils.5 Factored Resistances (ksf) Effective footing width, B (ft) Strength LS, C2 load Strength LS, C7 load Strength LS AASHTO, 27) Service LS AASHTO (27) Service LS Schmertmann (1978) Service LS Hough (1959) Service I loading Strength I, C2 loading Strength I, C7 loading Effective footing width, B (m) Effective footing width, B (m) Effective footing width, B (ft) 15 Strength LS, C2 load Figure H-6 Variation of factored bearing resistance for Strength-I and Strength LS, C7 load unfactored resistance for Service-I limit state with effective footing width for Strength LS AASHTO, 27) 1 Example 2 (NCHRP Report Service LS 651) AASHTO (27) Service LS Schmertmann (1978) Service LS Hough (1959) 32

33 Factored ultimate limit state and unfactored service limit state (kips) Factored ultimate limit state and unfactored service limit state (kips) Factored ultimate limit state and unfactored service limit state (MN) F un Service LS Hough (1959) Conceptual Service Design I loading Granular Soils Factored Resistances (kips) Service LS Schmertmann (1978) Strength I, C2 loading Strength I, C7 loading Effective footing width, B (m) Effective footing width, B (ft) Strength Limit State loading 3688kips (phi=.45) B = 8.9ft (B =7.9ft+2x.5) Service Limit state of 275kips B=4.5ft (B =3.5+2x.5) Effective footing width, B (ft) Figure H-6 cont. Variation of factored bearing resistance for Strength-I and unfactored resistance for Service-I limit state with effective footing width for Example 2 (NCHRP Report 651) Effective footing width, B (ft) Strength LS, C2 load Strength LS, C7 load Strength LS AASHTO, 27) Service LS AASHTO (27) Service LS Schmertmann (1978) Service LS Hough (1959) Service I loading Strength I, C2 loading Strength I, C7 loading Effective footing width, B (m)

34 Intermediate Conclusions The Strength Limit State governs the footing dimensions in this design example with a requirement for B=8.9ft vs. B=4.5ft for the service limit state The bridge was designed with B=13.1ft most likely due to the differences in design procedures (especially settlement) 34

35 Task 3: BC Shallow Foundations on Rock - OUTLINE 1. Broad Objectives 2. Database UML/GTR RockFound7 3. Rock Classification and Properties 4. Methods of Analyses Selected for Establishing the Uncertainty in B.C. of Foundations on Rock 5. Calibration evaluation of resistance factors 6. Summary and Conclusions 35

36 2. DATABASE UML/GTR RockFound 7 Comprised of 122 foundation case histories of load tests in/on rock and IGM s. The database has 61 footings cases (28 cases D>, 33 cases D=) and 61 rock socket cases for which the base behavior (load and displacement) under loading was monitored. 89 of the 122 cases were used for the uncertainty determination of the settlement of foundations on rock. 36

37 Hirany and Kulhawy (1988) Failure criterion Hirany and Kulhawy (1988) proposed the L1-L2 method for interpreting the "failure" load or "ultimate" capacity of foundations from loaddisplacement curves. The unique peak or asymptote value in the curves is taken as the measured or interpreted capacity (QL2=qL2). For 79 cases ql2 could be evaluated, 43 cases are based on reported failure load. 37

38 Carter and Kulhawy (1988) - B.C. of Foundations on Rock Using the limit-equilibrium approach, Carter and Kulhawy (1988) developed a lower bound to the B.C. for strip and circular footings on jointed rock masses presented below. q ult m s qu (2) 38

39 Interpreted Foundation Capacity q L2 (ksf) Carter and Kulhawy (1988) - B.C. of Foundations on Rock 1 1 q L2 = q ult ).619 (n = 119; R 2 =.921) q L2 = q ult ).6 (Revised) (n = 119; R 2 =.917) q L2 = q ult Footings cases 61 Rock Socket cases 119 All cases with revised equation Carter and Kulhawy (1988) Bearing Capacity q ult (ksf) Relationship between Carter and Kulhawy (1988) calculated bearing capacity (q ult ) using two variations (equations 82a and 82b) and the interpreted bearing capacity (q L2 ). 39

40 Carter and Kulhawy (1988) - B.C. of Foundations on Rock Table 69 Calibrated resistance factors for different datasets of resistance bias obtained using Carter and Kulhawy s (1988) method Dataset No. of cases Bias Resistance factor ( T = 3) Mean COV MCS Recommended All cases RMR RMR < RMR < RMR <

41 Goodman (1989) - B.C. of Foundations on Rock The lower bound is represented by the following Equation: in which q N ult tan q u N (3) (4) Goodman (1989) developed the B.C. Equation 5 for footings resting on orthogonal vertical joints each spaced distance s in which lateral stress transfer is nil. q ult q u N 1 N 1 S B N 1 N 1 (5) 41

42 Goodman (1989) - B.C. of Foundations on Rock Summary of the statistics for the Ratio of Measured to Calculated B.C. using Goodman s (1989) Method Cases n No. of Sites Mean of Bias m Standard Deviation s COV All Foundations All rock sockets All footings Sub-categorization suggests that if more details of rock measurements are available, the uncertainty is reduced Rock Socket cases with measured discontinuity spacing had a COV l = Rock Socket cases with measured discontinuity spacing and friction angle had a COV l =

43 Interpreted Foundation Capacity q L2 (ksf) Goodman (1989) - B.C. of Foundations on Rock 1 1 q L2 = 2.16 q ult ).868 (n = 119; R 2 =.897) q L2 = q ult Footings cases 61 Rock Socket cases Goodman (1989) Bearing Capacity q ult (ksf) Figure 78. Relationship between Goodman s (1989) calculated bearing capacity (q ult ) and the interpreted bearing capacity (q L2 ). 43

44 Number of observations Goodman (1989) - B.C. of Foundations on Rock Frequency Number of observations Frequency Rock-sockets and Footing cases Goodman (1989) mean = 1.35 COV = Foundation cases on Fractured Rocks Goodman (1989) mean = 1.24 COV = lognormal distribution normal distribution lognormal distribution normal distribution Bias, q u,meas / q u,calc Bias, q u,meas / q u,calc Figure 79. Distribution of the ratio of the interpreted bearing capacity (q L2 ) to the bearing capacity (q ult ) calculated using Goodman s (1989) method for the rock sockets and footings in database UML-GTR RockFound7. Figure 8. Distribution of the ratio of the interpreted bearing capacity (q L2 ) to the bearing capacity (q ult ) calculated using Goodman s (1989) method for foundations on fractured rock in database UML-GTR RockFound7 44

45 Standard normal quantile Goodman (1989) - B.C. of Foundations on Rock 4 = 1.35 COV = B.C. using Goodman (1989) All data Total data (n = 119) Normal distribution Lognormal distribution Bias Figure 113. Comparison of the unfiltered bias for BC calculated using Goodman (1989) method for all data and the theoretical normal and lognormal distributions. 45

46 Goodman (1989) - B.C. of Foundations on Rock Table 68 Calibrated resistance factors for different datasets of resistance bias obtained using Goodman s (1989) method Dataset No. of cases Bias Resistance factor ( T = 3) Mean COV MCS Recommended All data Measured friction angle f Measured spacing s Measured friction angle f and s

47 Calibration of Resistance Factors Table 7 Recommended resistance factors for foundations in/on rock based on T = 3. (p f =.135%) Method of Analysis Equation Application Efficiency Factor / (%) Carter and Kulhawy (1988) Goodman (1989) ult q q m s For fractured rocks: For non-fractured rocks: u qult qu N 1 s qult qu N N 1 B 1 ( N 1) N 1 All RMR RMR < RMR < RMR < All Measured f Measured s Measured s and f

48

49 Bias Resistance factor, Uncertainty in B.C % confidence interval for 2.5 Resistance factor based on database (x) no. of cases in each interval Recommended f for Controlled soil conditions (3) Recommended f for Natural soil conditions (2) (3) (4) (12) (4) (14) (3) (9) (2) (2) (4) (2) n = Friction angle f (deg).2. Figure 14. Recommended resistance factors for soil friction angles (taken f.5) between 3 and 46, with comparisons to 95% confidence interval and resistance factors obtained for the cases in the database; the bubble size represents the number of data cases in each subset. 49

50 Carter and Kulhawy (1988) - B.C. of Foundations on Rock Table 38 Summary of the statistics for the ratio of measured (q L2 ) to calculated bearing capacity (q ult ) of rock sockets and footings on rock using Carter and Kulhawy (1988) method No. of Cases n m Sites s COV All rock sockets All rock sockets on fractured rock All rock sockets on non-fractured rock Rock sockets on non-fractured rock with measured discontinuity spacing (s') Rock sockets on non-fractured rock with s' based on AASHTO (27) All footings All footings onfractured rock All footings onnon-fractured rock Footings on non-fractured rock with measured discontinuity spacing (s') Footings on non-fractured rock with s' based on AASHTO (27) n = number of case histories m = mean of biases s = standard deviation COV = coefficient of variation Calculated capacity based on equation (82a) 5

51 Goodman (1989) - B.C. of Foundations on Rock Table 4 Summary of the statistics for the ratio of measured (q L2 ) to calculated bearing capacity (q ult ) of rock sockets and footings on rock using Goodman (1989) method Cases n No. of Sites m s COV All Measured discontinuity spacing (s') and friction angle ( f ) Measured discontinuity spacing (s') Measured friction angle ( f ) Fractured Fractured with measured friction angle ( f ) Non-fractured Non-fractured with measured s' and measured f Non-fractured with measured discontinuity spacing (s') Non-fractured with measured friction angle ( f ) Spacing s' and f, both based on AASHTO (27) Discontinuity spacing (s') based on AASHTO (27) Friction angle ( f ) based on AASHTO (27) n = number of case histories m = mean of biases s = standard deviation COV = coefficient of variation 51