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100 CHAPTER 4 Interpretations and Appraisal 4.1 Overview This chapter addresses, therefore, the following issues: Chapter 3 presents an analysis of available data that was 1. Completion of loads and parameters required to carry out mostly limited to direct correlations between the loading the calibration. The distribution functions of the lateral conditions (e.g., centric, eccentric, and so forth) and the per- load were previously developed. These are developed to formance of the bearing capacity calculation methods. The allow for calibrations of sliding resistances. Target reliabil- interpretation of the findings in the case of shallow foundations ity is also established to allow for the calibration of the is more complex than the interpretation of the findings in the resistance factors. case of deep foundations, as presented, for example, in NCHRP 2. Investigation and interpretation of the data and findings Report 507 (Paikowsky et al., 2004). The reason is that many presented in Chapter 3 of this report including sources of more parameters can contribute to the trend provided by the uncertainty, size effect, natural versus controlled soil, and data than may be apparent in the first evaluation. For example, the probabilistic approach to missing information. Section 3.8.2 of this report examined the performance of 3. Final determination of recommended resistance factors. Carter and Kulhawy's (1988) equation for the bearing capacity of foundations on rock. The database consisting of tests on shallow foundations and drilled shaft tips suggested large vari- 4.2 Uncertainty in Vertical ations between the performances of the two. The natural con- and Lateral Loading clusion could have been that the load-displacement relations 4.2.1 Overview of the tip of a rock socket cannot be applied to the examination of bearing capacity theory. However, further examination of The following discussion presents the chosen characteristics the data suggested that the investigated method (i.e., Carter for vertical and lateral loads, dead and live, acting on bridge and Kulhawy) has a bias depending on the rock quality. As the foundations. Although the subject is beyond the scope of the two examined case history databases (i.e., shallow foundations present research, establishing the lateral load distributions and and rock sockets) varied by the rock quality that predominated factors became a necessity for the calibration process and is in each, it was possible to explain the difference in the perform- therefore presented. It is expected that future experimental, ance based on rock quality rather than on the type of test. analytical, and probabilistic work will enable better analysis Similarly, the investigation of vertical loading of shallow foun- and more reliable selection of load distributions. dations on natural soils as compared to vertical loading of shal- low foundations on controlled soils, presented in Section 3.5, 4.2.2 Vertical Loads suggested large variations between the two groups. Earlier inter- pretations of the data (e.g., Paikowsky et al., 2008; Paikowsky NCHRP Report 507 (Paikowsky et al., 2004) established the et al., 2009b; Amatya et al., 2009) naturally followed these load distributions and factors used for the ULS and SLS of findings, distinguishing between the groups based on soil place- deep and shallow foundations under vertical loads. These val- ment only (i.e., natural versus controlled). Further investigation ues are based on Table F-1 of NCHRP Report 368, which pro- revealed that part of the reason for variation was the difference vides a range for live load (Nowak, 1999). The bias of live load in the friction angle of the soils in the investigated groups and has been taken as the mean of the range provided (1.101.20), the bias of the bearing capacity factor N and its dependence on and the COV is taken as 0.20 instead of 0.18, as presented in the magnitude of the internal friction angle. NCHRP Report 368. The load factors are from Tables 3.4.1-1

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101 Table 49. Load factors and uncertainties in Table 50. Ranges of COV of K0nc for ranges of vertical live load and dead load. variation in soil friction angle (D'Appolonia and the University of Michigan, 2004). Load type Load factor1 Bias2 COV2 Live Load (LL) = 1.75 1.153 0.204 COV of K0nc L Dead Load (DL) 1.05 0.10 COV of f D = 1.25 Soil friction angle, 0.050.10 0.100.15 0.150.20 1 f Tables 3.4.1-1 and 3.4.1-2 (AASHTO, 2007) 2 Table F-1 of NCHRP Report 368 (Nowak, 1999) f from Lab Test f from CPT f from SPT 3 Mean of the range 1.10 to 1.20 30 0.1860.202 0.2020.227 0.2270.260 4 COV of 0.18 rounded to 0.20 35 0.1890.217 0.2170.257 0.2570.303 40 0.1950.237 0.2370.295 0.2950.364 and 3.4.1-2 of LRFD Bridge Design Specifications Section 10: Foundations (AASHTO, 2007). These load factors are listed in Table 49. K 0nc = 1 - sin f (113) Table 50 summarizes the variation in K0nc for cohesionless 4.2.3 Horizontal Loads soils, which includes the transformation uncertainty, based on 4.2.3.1 Horizontal Earth Pressure (Dead Load) the final report for NCHRP Project 12-55 (D'Appolonia and the University of Michigan, 2004). The sources of uncertainties in the horizontal earth pres- sures due to soil and surcharge are the variations in soil unit Rankine Active Earth Pressure Coefficient, Ka. The weight and the soil friction angle. Based on the study by Phoon Rankine active earth pressure coefficient is given by the et al. (1995), the final report for NCHRP Project 12-55 following: (D'Appolonia and the University of Michigan 2004) suggests the variation in soil unit weight as the following: 1 - sin f f Ka = = tan 2 45 - (114) 1 + sin f 2 Bias of soil unit weight = 1.00 COV of 0.10 for in situ (natural) soil conditions COV of 0.08 for engineered backfill (controlled) The variation of the Rankine active earth pressure coeffi- Distribution followed = Normal cient with the variation in the soil friction angle is presented in Table 51. The coefficients of variation for earth pressure Also, based on the study by Phoon et al. (1995), the final coefficients in Table 51 were obtained by generating 1,000 report for NCHRP Project 12-55 (2004) lists the variation in samples of soil friction angle following lognormal distribu- the estimation of the soil friction angle (f) as the following: tion, with COVs of 0.10, 0.15, 0.20, and 0.25, respectively, and limiting maximum soil friction angle to 47. In Table 51, these f from SPT: COVs are presented under "COV sim"; "COV calc" was Bias = 1.00 to 1.20, COV = 0.15 to 0.20 obtained using the first order approximation in the calculation f from cone penetration test (CPT) (Kulhawy and Mayne, of COV, as mentioned in the final report for NCHRP Project 1990): 12-55 (2004). It can be seen that the difference between the Bias = 1.00 to 1.15, COV = 0.10 to 0.15 estimated COV using the simulation and the first order f from Lab test: approximation increases with the increase in the soil friction Bias = 1.00 to 1.13, COV = 0.05 to 0.10 angle COV. Distribution followed = Lognormal Reasonable estimate of bias taken as 1.00 Rankine and Coulomb Passive Earth Pressure Coeffi- cients, Kp. The Rankine passive earth pressure coefficient At-Rest Earth Pressure Coefficient, K0. Based on the data assumes no friction between the wall and the soil and there- summarized by Mayne and Kulhawy (1982) for drained and fore results in a conservative estimate of the passive earth pres- undrained at-rest earth pressure coefficient K0, it was found sure coefficient, which for frictional material is given by the that the COV of the corresponding transformation, using following: Jaky's equation given below (Jaky, 1944), was 0.18 (NCHRP Project 12-55, 2004). K0nc represents K0 for normally consoli- 1 + sin f f Kp = = tan 2 45 + (115) dated cohesionless soil. 1 - sin f 2

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102 Table 51. COV of lateral earth pressure coefficients for different COVs and soil friction angles. Soil friction Coulomb passive, Kp Rankine active, Ka Rankine passive, Kp angle, f f = 2/3 = 0.5 f f = 0.4 f = 0.3 f = 0.2 f = 0.1 f = 0.0 Mean COV COV sim COV calc COV sim COV calc COV sim COV sim COV sim COV sim COV sim COV sim COV sim 0.10 0.09 0.10 0.10 0.09 0.20 0.17 0.15 0.14 0.12 0.11 0.10 0.15 0.14 0.15 0.15 0.13 0.34 0.27 0.24 0.21 0.19 0.17 0.15 25 0.20 0.19 0.21 0.22 0.17 0.64 0.45 0.38 0.33 0.28 0.25 0.22 0.25 0.22 0.27 0.27 0.21 1.04 0.61 0.49 0.41 0.35 0.31 0.27 0.10 0.12 0.13 0.13 0.11 0.36 0.27 0.23 0.20 0.17 0.15 0.13 0.15 0.17 0.19 0.19 0.16 0.70 0.43 0.35 0.30 0.26 0.22 0.19 30 0.20 0.23 0.27 0.26 0.21 1.05 0.63 0.50 0.42 0.35 0.30 0.26 0.25 0.27 0.34 0.33 0.25 1.39 0.84 0.67 0.55 0.46 0.39 0.33 0.10 0.15 0.16 0.16 0.14 0.58 0.37 0.30 0.25 0.22 0.18 0.16 0.15 0.22 0.24 0.24 0.20 0.97 0.59 0.48 0.39 0.33 0.28 0.24 35 0.20 0.28 0.33 0.30 0.25 1.13 0.73 0.59 0.49 0.42 0.35 0.30 0.25 0.31 0.43 0.34 0.30 1.19 0.80 0.65 0.55 0.46 0.39 0.34 0.10 0.16 0.17 0.17 0.15 0.67 0.42 0.34 0.28 0.24 0.20 0.17 0.15 0.22 0.26 0.24 0.21 0.97 0.61 0.49 0.40 0.34 0.28 0.24 37 0.20 0.27 0.36 0.29 0.27 1.07 0.69 0.56 0.47 0.39 0.34 0.29 0.25 0.32 0.47 0.33 0.32 1.09 0.75 0.62 0.52 0.44 0.38 0.33 0.10 0.17 0.19 0.17 0.16 0.68 0.42 0.34 0.28 0.24 0.20 0.17 0.15 0.23 0.30 0.23 0.23 0.84 0.55 0.45 0.37 0.32 0.27 0.23 40 0.20 0.28 0.41 0.27 0.29 0.91 0.63 0.52 0.44 0.37 0.32 0.27 0.25 0.33 0.53 0.30 0.35 0.93 0.66 0.55 0.47 0.40 0.35 0.30 Notes: * "COV sim" of earth pressure coefficients calculated from 1000 samples of friction angles assumed to follow lognormal distribution f is limited to a maximum of 47degrees * COV calc: First order COV of earth pressure coefficients estimated as (D'Appolonia and the University of Michigan, 2004): K( f ) K( f ) where f and are the mean and standard deviation of f K( f ) The Coulomb passive earth pressure coefficient is used more Coulomb passive earth pressure has been presented for = 90 commonly and is given by the following: and = 0, i.e., vertical wall and level backfill. Table 52 summarizes the COV results presented in Tables 50 sin 2 ( - f ) and 51 for lateral earth pressure coefficients; these COVs can Kp = (116) be used for at-rest and Rankine active and passive earth pres- sin ( f + ) i sin ( f + ) 2 sin 2 i sin ( + ) 1 - sure coefficients. sin ( + ) i sin ( + ) For the Coulomb passive earth pressure coefficient, one can choose a reasonable COV, as has been presented in Table 52, where for each ratio of interface friction angle to soil friction angle. = angle of wall/interface surface to soil with vertical, For example, for a granular fill material with the ratio of inter- = friction angle between wall/interface and soil, and face friction angle to soil friction angle of about 2/3, when the = angle of soil backfill surcharge with the horizontal. soil friction angle is estimated from SPT readings, the COV lies in the range of 0.70 to about 1.1. One may choose a rea- Table 51 presents variations in active and passive earth pres- sonable COV as 0.85. It should be noted that in Table 51 the sures for a range of soil friction angles and their COVs. maximum conceivable soil friction angle is assumed to be 47, Table 52. Summary of COVs of earth pressure coefficients. COV 30 < f 40 K0nc Rankine Ka Rankine Kp Range Reasonable Range Reasonable Range Reasonable f from Lab 0.200.22 0.20 0.120.17 0.15 0.120.17 0.15 Test f from CPT 0.220.26 0.25 0.170.23 0.20 0.190.23 0.20 f from SPT 0.250.33 0.30 0.230.28 0.25 0.230.28 0.25

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103 hence, there is a drop in the COV calculated for a higher fric- Earth Pressure after Compaction (psf) tion angle (40). 0 400 800 1200 1600 2000 The topic of lateral passive earth pressure is complex as it is 0 often associated with the limiting displacement that controls Roller load = 500lb/in Roller 6in from wall the development of the pressure rather than the theoretical At 5 Lift thickness = 6in -re = 125lb/ft3 st pressures associated with the coefficient. As such, the discus- ea = 35o rth sion in this section is limited in its scope and addresses solely 10 c=0 pre s the current limited needs. su re Depth (ft) With the reasonable estimates of the COVs of soil unit (K 15 o =0 weight and earth pressure coefficients, the lateral pressure due .4) to, for example, active earth pressure can be calculated as 20 Ea = 0.5h i K a 25 (where Ea is active earth pressure and h is height of soil) with 30 a bias of 1.00. This implies that the combined statistics for the mean and standard deviation are the following: 35 Ea = 0.5h i Ka and ( 0.5h K a ) + Ka ( 0.5h ) 2 2 Ea 2 2 i 2 i Figure 90. Residual earth pressure after compaction of backfill behind an Hence unyielding wall (based on Clough and Duncan, 1991). COVEa = COV2 + COVKa 2 (117) depth of 5 ft. When the measured soil friction angle has a When soil friction angles are based on SPT readings, COVs COV of 0.20, based on the multiplier factors in Table 53, this of the horizontal dead load due to at-rest (K0) or active earth residual stress can vary from 704 psf (800 0.88) to 952 psf pressure (Ka) can be calculated as 0.27 to 0.35. As such, a prac- (800 1.19). tical use of a bias of 1.00 and COV of 0.30 is a reasonable rep- To estimate the uncertainty in the establishment of the resid- resentation of a large range of possibilities for lateral dead load ual lateral pressure curve obtained based on a solution proposed due to earth pressure and can be considered to follow a lognor- by Duncan and Seed (1986) and shown in Figure 90, the bias of mal distribution. the measured lateral earth pressure versus the calculated lateral earth pressure was studied (see Figure 91). The measured earth Earth Pressure Due to Compaction. A typical distribu- pressures are from the experimental study by Carder et al. tion of residual earth pressure after compaction of backfill (1977). The residual earth pressures on a concrete retaining wall behind an unyielding wall with depth is given in Figure 90. A due to compaction of sand backfill were measured at differ- particular example of granular soil with f of 35, of 125 pcf, ent depths. The calculated earth pressures are, as presented by and roller load of 500lb/in. compacting a lift thickness of Duncan and Seed (1986), based on an "incremental solution." 6 in. when at a distance of 6 in. away from the wall has been presented. It can be seen that the residual earth pressure increases rapidly with depth, with a maximum pressure at Table 53. Range of multiplier factor R for the around 5 ft below the compacted surface for this example. estimation of earth pressure due to compaction Table 53 summarizes the variation of the multiplier factor at a depth of 5 ft of compacted soil for f = 35, R with the COV of a soil friction angle f of 35, specifically = 125 pcf, roller load = 500 lb/in, distance for one standard deviation change in f. This range of multi- from wall = 6 in, lift thickness = 6 in, mean of plier (adjustment) factors was based on the tables of adjust- R = 1.00. ment factors by Williams et al. (1987). It is to be noted that f = 35 Range of R at 5 ft depth for a variation of 1 s.d. in f these adjustment factors themselves are empirical in nature COV Roller Vibrator plates/ rammers and are approximate representations of test results with large 0.10 0.94 1.10 0.97 1.05 scatters. 0.15 0.91 1.14 0.96 1.09 From Figure 90, it can be seen that the lateral earth pres- 0.20 0.88 1.19 0.95 1.17 sure after compaction (residual lateral stress) is 800 psf at a 0.25 0.85 1.24 0.94 1.24