development of a new family of normalized modulus reduction and materials dumping curves darendeli...
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DEVELOPMENT OF A NEW FAMILY OF NORMALIZED
MODULUS REDUCTION AND MATERIAL DAMPING
CURVES
by
MEHMET BARIS DARENDELI, B.S., M.S.
DISSERTATION
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
DOCTOR OF PHILOSOPHY
The University of Texas at Austin
August, 2001
249
CHAPTER 10
RECOMMENDED NORMALIZED MODULUS REDUCTION
AND MATERIAL DAMPING CURVES
10.1 INTRODUCTION
Mean values of the normalized shear modulus and the material damping
ratio (predicted by the calibrated model) at strain amplitudes ranging from 1x10-5
% to 1 % are presented in this chapter. As discussed in Chapter Nine, the mean
values of model parameters can be utilized to construct normalized modulus
reduction and material damping curves for different soil types and loading
conditions. However, the reader must use caution when a soil type or loading
condition not represented in the database is to be evaluated with these equations.
Since the impact of overconsolidation ratio is relatively small and ten
cycles at 1 Hz loading frequency closely represents the characteristics of
earthquake shaking, these parameters are fixed for the recommended curves. In
this chapter, recommended normalized modulus reduction and material damping
curves are presented for soils with a broad range of plasticities confined at a broad
range of mean effective stresses.
These curves are presented from two different perspectives so that the
reader can interpolate the data for different values of soil plasticity and confining
pressure. If the reader has to extrapolate for soil plasticities and confining
pressures not represented in the database, use of caution is suggested.
250
10.2 EFFECT OF PI AT A GIVEN MEAN EFFECTIVE STRESS
Figures 10.1 through 10.4 show the effect of PI on nonlinear soil behavior
at 0.25, 1.0, 4.0 and 16 atm, respectively. These normalized modulus and material
damping curves are presented so that the reader can interpolate these relationships
for soils with different plasticities. Also, these curves are tabulated in Tables 10.1
through 10.8. The figures and tables are organized so that the G/Gmax – log γ and
D – log γ curves are followed on the next page by the associated tables.
10.3 EFFECT OF MEAN EFFECTIVE STRESS ON A SOIL WITH GIVEN PLASTICITY
Figures 10.5 through 10.9 show the effect of mean effective stress on
nonlinear behavior of soils with 0, 15, 30, 50 and 100 % plasticity, respectively.
These normalized modulus and material damping curves are presented so that the
reader can interpolate these relationships for soil layers at different depths
confined under different mean effective stresses. Also, these curves are tabulated
in Tables 10.9 through 10.18. The figures and tables are organized so that the
G/Gmax – log γ and D – log γ curves are followed on the next page by the
associated tables.
10.4 IMPACT OF UTILIZING THE RECOMMENDED CURVES ON EARTHQUAKE RESPONSE PREDICTIONS OF DEEP SOIL SITES
The impact of utilizing the recommended curves when assigning nonlinear
soil properties in site response analyses of deep (>50 m) soil sites is discussed in
this section. This point is addressed because site response analyses are often
performed using average, pressure-independent generic curves.
251
1.2
1.0
0.8
0.6
0.4
0.2
0.0
G/Gmax G/Gmax Prediction( σo' = 0.25 atm, N = 10 cycles, f = 1 Hz, OCR = 1 )
(a)
25
20
15
10
5
0
D, %
0.0001 0.001 0.01 0.1 1
Shearing Strain, γ ,%
Material Damping PredictionPI = 0 %PI = 15 %PI = 30 %PI = 50 %PI = 100 %
(b)
Figure 10.1 Effect of PI on (a) normalized modulus reduction and (b) material damping curves at 0.25 atm confining pressure
252
Table 10.1 Effect of PI on normalized modulus reduction curve: σo’ = 0.25 atm
Shearing Strain (%) PI = 0 % PI = 15 % PI = 30 % PI = 50 % PI = 100 %1.00E-05 0.999 0.999 1.000 1.000 1.0002.20E-05 0.998 0.999 0.999 0.999 1.0004.84E-05 0.996 0.997 0.998 0.998 0.9991.00E-04 0.993 0.995 0.996 0.997 0.9982.20E-04 0.986 0.990 0.992 0.994 0.9964.84E-04 0.971 0.979 0.983 0.987 0.9911.00E-03 0.944 0.959 0.968 0.975 0.9832.20E-03 0.891 0.919 0.936 0.949 0.9664.84E-03 0.799 0.847 0.876 0.900 0.9321.00E-02 0.671 0.739 0.783 0.822 0.8762.20E-02 0.497 0.579 0.637 0.692 0.7744.84E-02 0.324 0.400 0.459 0.521 0.6251.00E-01 0.197 0.255 0.303 0.358 0.4612.20E-01 0.107 0.142 0.174 0.213 0.2934.84E-01 0.055 0.074 0.093 0.116 0.1671.00E+00 0.029 0.040 0.050 0.063 0.093
Table 10.2 Effect of PI on material damping curve: σo’ = 0.25 atm
Shearing Strain (%) PI = 0 % PI = 15 % PI = 30 % PI = 50 % PI = 100 %1.00E-05 1.201 1.489 1.778 2.164 3.1292.20E-05 1.207 1.493 1.781 2.166 3.1314.84E-05 1.226 1.506 1.791 2.174 3.1361.00E-04 1.257 1.528 1.808 2.187 3.1442.20E-04 1.330 1.579 1.848 2.217 3.1634.84E-04 1.487 1.690 1.933 2.282 3.2041.00E-03 1.792 1.906 2.101 2.411 3.2862.20E-03 2.458 2.387 2.476 2.702 3.4724.84E-03 3.762 3.358 3.249 3.310 3.8681.00E-02 5.821 4.977 4.581 4.386 4.5932.20E-02 9.097 7.778 7.010 6.441 6.0704.84E-02 12.993 11.489 10.477 9.589 8.5791.00E-01 16.376 15.064 14.088 13.137 11.7982.20E-01 19.181 18.334 17.640 16.904 15.7164.84E-01 20.829 20.515 20.208 19.849 19.2131.00E+00 21.393 21.507 21.542 21.547 21.544
253
1.2
1.0
0.8
0.6
0.4
0.2
0.0
G/Gmax G/Gmax Prediction( σo' = 1 atm, N = 10 cycles, f = 1 Hz, OCR = 1 )
(a)
25
20
15
10
5
0
D, %
0.0001 0.001 0.01 0.1 1
Shearing Strain, γ ,%
Material Damping PredictionPI = 0 %PI = 15 %PI = 30 %PI = 50 %PI = 100 %
(b)
Figure 10.2 Effect of PI on (a) normalized modulus reduction and (b) material damping curves at 1.0 atm confining pressure
254
Table 10.3 Effect of PI on normalized modulus reduction curve: σo’ = 1.0 atm
Shearing Strain (%) PI = 0 % PI = 15 % PI = 30 % PI = 50 % PI = 100 %1.00E-05 0.999 1.000 1.000 1.000 1.0002.20E-05 0.999 0.999 0.999 1.000 1.0004.84E-05 0.998 0.998 0.999 0.999 0.9991.00E-04 0.995 0.997 0.997 0.998 0.9992.20E-04 0.991 0.993 0.995 0.996 0.9974.84E-04 0.981 0.986 0.989 0.992 0.9941.00E-03 0.964 0.973 0.979 0.984 0.9892.20E-03 0.928 0.947 0.958 0.967 0.9784.84E-03 0.861 0.896 0.917 0.934 0.9561.00E-02 0.761 0.816 0.849 0.878 0.9172.20E-02 0.607 0.682 0.732 0.778 0.8434.84E-02 0.428 0.509 0.569 0.629 0.7221.00E-01 0.277 0.348 0.404 0.465 0.5712.20E-01 0.157 0.205 0.248 0.296 0.3924.84E-01 0.083 0.111 0.137 0.169 0.2381.00E+00 0.044 0.060 0.076 0.095 0.138
Table 10.4 Effect of PI on material damping curve: σo’ = 1.0 atm
Shearing Strain (%) PI = 0 % PI = 15 % PI = 30 % PI = 50 % PI = 100 %1.00E-05 0.804 0.997 1.191 1.450 2.0962.20E-05 0.808 1.000 1.193 1.451 2.0974.84E-05 0.820 1.008 1.199 1.456 2.1001.00E-04 0.839 1.021 1.209 1.464 2.1052.20E-04 0.884 1.053 1.234 1.482 2.1174.84E-04 0.982 1.122 1.287 1.523 2.1431.00E-03 1.174 1.257 1.392 1.603 2.1932.20E-03 1.602 1.562 1.628 1.786 2.3094.84E-03 2.474 2.198 2.128 2.175 2.5601.00E-02 3.953 3.317 3.028 2.888 3.0292.20E-02 6.579 5.440 4.803 4.343 4.0294.84E-02 10.184 8.650 7.664 6.824 5.8761.00E-01 13.788 12.217 11.092 10.024 8.5412.20E-01 17.199 15.951 14.966 13.941 12.2794.84E-01 19.565 18.829 18.185 17.458 16.1321.00E+00 20.716 20.460 20.178 19.815 19.069
255
1.2
1.0
0.8
0.6
0.4
0.2
0.0
G/Gmax G/Gmax Prediction( σo' = 4 atm, N = 10 cycles, f = 1 Hz, OCR = 1 )
(a)
25
20
15
10
5
0
D, %
0.0001 0.001 0.01 0.1 1
Shearing Strain, γ ,%
Material Damping PredictionPI = 0 %PI = 15 %PI = 30 %PI = 50 %PI = 100 %
(b)
Figure 10.3 Effect of PI on (a) normalized modulus reduction and (b) material damping curves at 4.0 atm confining pressure
256
Table 10.5 Effect of PI on normalized modulus reduction curve: σo’ = 4.0 atm
Shearing Strain (%) PI = 0 % PI = 15 % PI = 30 % PI = 50 % PI = 100 %1.00E-05 1.000 1.000 1.000 1.000 1.0002.20E-05 0.999 1.000 1.000 1.000 1.0004.84E-05 0.998 0.999 0.999 0.999 1.0001.00E-04 0.997 0.998 0.998 0.999 0.9992.20E-04 0.994 0.996 0.997 0.997 0.9984.84E-04 0.988 0.991 0.993 0.995 0.9961.00E-03 0.976 0.983 0.986 0.989 0.9932.20E-03 0.952 0.965 0.972 0.978 0.9864.84E-03 0.906 0.931 0.945 0.956 0.9711.00E-02 0.832 0.873 0.898 0.918 0.9452.20E-02 0.706 0.770 0.810 0.845 0.8934.84E-02 0.538 0.618 0.673 0.725 0.8021.00E-01 0.374 0.454 0.514 0.575 0.6752.20E-01 0.225 0.287 0.339 0.396 0.5014.84E-01 0.123 0.163 0.199 0.241 0.3271.00E+00 0.067 0.091 0.113 0.140 0.200
Table 10.6 Effect of PI on material damping curve: σo’ = 4.0 atm
Shearing Strain (%) PI = 0 % PI = 15 % PI = 30 % PI = 50 % PI = 100 %1.00E-05 0.539 0.668 0.798 0.971 1.4042.20E-05 0.541 0.670 0.799 0.972 1.4054.84E-05 0.548 0.675 0.803 0.975 1.4071.00E-04 0.560 0.683 0.809 0.980 1.4102.20E-04 0.588 0.703 0.824 0.991 1.4174.84E-04 0.649 0.745 0.857 1.016 1.4331.00E-03 0.769 0.829 0.922 1.066 1.4642.20E-03 1.039 1.021 1.070 1.180 1.5374.84E-03 1.607 1.428 1.388 1.426 1.6931.00E-02 2.618 2.173 1.977 1.886 1.9912.20E-02 4.572 3.684 3.206 2.871 2.6484.84E-02 7.621 6.235 5.387 4.693 3.9341.00E-01 11.134 9.482 8.357 7.333 5.9722.20E-01 14.946 13.400 12.231 11.056 9.2264.84E-01 17.990 16.866 15.935 14.917 13.1181.00E+00 19.792 19.158 18.571 17.876 16.513
257
1.2
1.0
0.8
0.6
0.4
0.2
0.0
G/Gmax G/Gmax Prediction( σo' = 16 atm, N = 10 cycles, f = 1 Hz, OCR = 1 )
(a)
25
20
15
10
5
0
D, %
0.0001 0.001 0.01 0.1 1
Shearing Strain, γ ,%
Material Damping PredictionPI = 0 %PI = 15 %PI = 30 %PI = 50 %PI = 100 %
(b)
Figure 10.4 Effect of PI on (a) normalized modulus reduction and (b) material damping curves at 16 atm confining pressure
258
Table 10.7 Effect of PI on normalized modulus reduction curve: σo’ = 16 atm
Shearing Strain (%) PI = 0 % PI = 15 % PI = 30 % PI = 50 % PI = 100 %1.00E-05 1.000 1.000 1.000 1.000 1.0002.20E-05 1.000 1.000 1.000 1.000 1.0004.84E-05 0.999 0.999 0.999 1.000 1.0001.00E-04 0.998 0.999 0.999 0.999 0.9992.20E-04 0.996 0.997 0.998 0.998 0.9994.84E-04 0.992 0.994 0.996 0.997 0.9981.00E-03 0.985 0.989 0.991 0.993 0.9962.20E-03 0.969 0.977 0.982 0.986 0.9914.84E-03 0.938 0.954 0.964 0.972 0.9811.00E-02 0.885 0.915 0.932 0.946 0.9642.20E-02 0.789 0.839 0.869 0.895 0.9294.84E-02 0.645 0.716 0.763 0.804 0.8631.00E-01 0.482 0.564 0.623 0.679 0.7642.20E-01 0.311 0.386 0.444 0.506 0.6104.84E-01 0.179 0.233 0.279 0.331 0.4311.00E+00 0.101 0.135 0.166 0.203 0.280
Table 10.8 Effect of PI on material damping curve: σo’ = 16 atm
Shearing Strain (%) PI = 0 % PI = 15 % PI = 30 % PI = 50 % PI = 100 %1.00E-05 0.361 0.448 0.534 0.650 0.9412.20E-05 0.362 0.449 0.535 0.651 0.9414.84E-05 0.367 0.452 0.538 0.653 0.9421.00E-04 0.374 0.457 0.541 0.656 0.9442.20E-04 0.391 0.469 0.551 0.663 0.9494.84E-04 0.429 0.495 0.571 0.678 0.9581.00E-03 0.503 0.547 0.611 0.709 0.9782.20E-03 0.673 0.667 0.704 0.780 1.0234.84E-03 1.035 0.924 0.903 0.934 1.1201.00E-02 1.702 1.407 1.281 1.227 1.3082.20E-02 3.075 2.433 2.100 1.871 1.7294.84E-02 5.449 4.318 3.659 3.138 2.5891.00E-01 8.573 7.021 6.022 5.151 4.0492.20E-01 12.483 10.780 9.557 8.381 6.6514.84E-01 16.070 14.619 13.472 12.268 10.2411.00E+00 18.528 17.522 16.655 15.677 13.847
259
1.2
1.0
0.8
0.6
0.4
0.2
0.0
G/Gmax G/Gmax Prediction( PI = 0 %, N = 10 cycles, f = 1 Hz, OCR = 1 )
(a)
25
20
15
10
5
0
D, %
0.0001 0.001 0.01 0.1 1
Shearing Strain, γ ,%
Material Damping Predictionσo' = 0.25 atmσo' = 1 atmσo' = 4 atmσo' = 16 atm
(b)
Figure 10.5 Effect of mean effective stress on (a) normalized modulus reduction and (b) material damping curves of a nonplastic soil
260
Table 10.9 Effect of σo’ on normalized modulus reduction curve: PI = 0 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 0.999 0.999 1.000 1.0002.20E-05 0.998 0.999 0.999 1.0004.84E-05 0.996 0.998 0.998 0.9991.00E-04 0.993 0.995 0.997 0.9982.20E-04 0.986 0.991 0.994 0.9964.84E-04 0.971 0.981 0.988 0.9921.00E-03 0.944 0.964 0.976 0.9852.20E-03 0.891 0.928 0.952 0.9694.84E-03 0.799 0.861 0.906 0.9381.00E-02 0.671 0.761 0.832 0.8852.20E-02 0.497 0.607 0.706 0.7894.84E-02 0.324 0.428 0.538 0.6451.00E-01 0.197 0.277 0.374 0.4822.20E-01 0.107 0.157 0.225 0.3114.84E-01 0.055 0.083 0.123 0.1791.00E+00 0.029 0.044 0.067 0.101
Table 10.10 Effect of σo’ on material damping curve: PI = 0 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 1.201 0.804 0.539 0.3612.20E-05 1.207 0.808 0.541 0.3624.84E-05 1.226 0.820 0.548 0.3671.00E-04 1.257 0.839 0.560 0.3742.20E-04 1.330 0.884 0.588 0.3914.84E-04 1.487 0.982 0.649 0.4291.00E-03 1.792 1.174 0.769 0.5032.20E-03 2.458 1.602 1.039 0.6734.84E-03 3.762 2.474 1.607 1.0351.00E-02 5.821 3.953 2.618 1.7022.20E-02 9.097 6.579 4.572 3.0754.84E-02 12.993 10.184 7.621 5.4491.00E-01 16.376 13.788 11.134 8.5732.20E-01 19.181 17.199 14.946 12.4834.84E-01 20.829 19.565 17.990 16.0701.00E+00 21.393 20.716 19.792 18.528
261
1.2
1.0
0.8
0.6
0.4
0.2
0.0
G/Gmax G/Gmax Prediction( PI = 15 %, N = 10 cycles, f = 1 Hz, OCR = 1 )
(a)
25
20
15
10
5
0
D, %
0.0001 0.001 0.01 0.1 1
Shearing Strain, γ ,%
Material Damping Predictionσo' = 0.25 atmσo' = 1 atmσo' = 4 atmσo' = 16 atm
(b)
Figure 10.6 Effect of mean effective stress on (a) normalized modulus reduction and (b) material damping curves of a soil with PI = 15 %
262
Table 10.11 Effect of σo’ on normalized modulus reduction curve: PI = 15 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 0.999 1.000 1.000 1.0002.20E-05 0.999 0.999 1.000 1.0004.84E-05 0.997 0.998 0.999 0.9991.00E-04 0.995 0.997 0.998 0.9992.20E-04 0.990 0.993 0.996 0.9974.84E-04 0.979 0.986 0.991 0.9941.00E-03 0.959 0.973 0.983 0.9892.20E-03 0.919 0.947 0.965 0.9774.84E-03 0.847 0.896 0.931 0.9541.00E-02 0.739 0.816 0.873 0.9152.20E-02 0.579 0.682 0.770 0.8394.84E-02 0.400 0.509 0.618 0.7161.00E-01 0.255 0.348 0.454 0.5642.20E-01 0.142 0.205 0.287 0.3864.84E-01 0.074 0.111 0.163 0.2331.00E+00 0.040 0.060 0.091 0.135
Table 10.12 Effect of σo’ on material damping curve: PI = 15 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 1.489 0.997 0.668 0.4482.20E-05 1.493 1.000 0.670 0.4494.84E-05 1.506 1.008 0.675 0.4521.00E-04 1.528 1.021 0.683 0.4572.20E-04 1.579 1.053 0.703 0.4694.84E-04 1.690 1.122 0.745 0.4951.00E-03 1.906 1.257 0.829 0.5472.20E-03 2.387 1.562 1.021 0.6674.84E-03 3.358 2.198 1.428 0.9241.00E-02 4.977 3.317 2.173 1.4072.20E-02 7.778 5.440 3.684 2.4334.84E-02 11.489 8.650 6.235 4.3181.00E-01 15.064 12.217 9.482 7.0212.20E-01 18.334 15.951 13.400 10.7804.84E-01 20.515 18.829 16.866 14.6191.00E+00 21.507 20.460 19.158 17.522
263
1.2
1.0
0.8
0.6
0.4
0.2
0.0
G/GmaxG/Gmax Prediction( PI = 30 %, N = 10 cycles, f = 1 Hz, OCR = 1 )
(a)
25
20
15
10
5
0
D, %
0.0001 0.001 0.01 0.1 1
Shearing Strain, γ ,%
Material Damping Predictionσo' = 0.25 atmσo' = 1 atmσo' = 4 atmσo' = 16 atm
(b)
Figure 10.7 Effect of mean effective stress on (a) normalized modulus reduction and (b) material damping curves of a soil with PI = 30 %
264
Table 10.13 Effect of σo’ on normalized modulus reduction curve: PI = 30 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 1.000 1.000 1.000 1.0002.20E-05 0.999 0.999 1.000 1.0004.84E-05 0.998 0.999 0.999 0.9991.00E-04 0.996 0.997 0.998 0.9992.20E-04 0.992 0.995 0.997 0.9984.84E-04 0.983 0.989 0.993 0.9961.00E-03 0.968 0.979 0.986 0.9912.20E-03 0.936 0.958 0.972 0.9824.84E-03 0.876 0.917 0.945 0.9641.00E-02 0.783 0.849 0.898 0.9322.20E-02 0.637 0.732 0.810 0.8694.84E-02 0.459 0.569 0.673 0.7631.00E-01 0.303 0.404 0.514 0.6232.20E-01 0.174 0.248 0.339 0.4444.84E-01 0.093 0.137 0.199 0.2791.00E+00 0.050 0.076 0.113 0.166
Table 10.14 Effect of σo’ on material damping curve: PI = 30 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 1.778 1.191 0.798 0.5342.20E-05 1.781 1.193 0.799 0.5354.84E-05 1.791 1.199 0.803 0.5381.00E-04 1.808 1.209 0.809 0.5412.20E-04 1.848 1.234 0.824 0.5514.84E-04 1.933 1.287 0.857 0.5711.00E-03 2.101 1.392 0.922 0.6112.20E-03 2.476 1.628 1.070 0.7044.84E-03 3.249 2.128 1.388 0.9031.00E-02 4.581 3.028 1.977 1.2812.20E-02 7.010 4.803 3.206 2.1004.84E-02 10.477 7.664 5.387 3.6591.00E-01 14.088 11.092 8.357 6.0222.20E-01 17.640 14.966 12.231 9.5574.84E-01 20.208 18.185 15.935 13.4721.00E+00 21.542 20.178 18.571 16.655
265
1.2
1.0
0.8
0.6
0.4
0.2
0.0
G/GmaxG/Gmax Prediction( PI = 50 %, N = 10 cycles, f = 1 Hz, OCR = 1 )
(a)
25
20
15
10
5
0
D, %
0.0001 0.001 0.01 0.1 1
Shearing Strain, γ ,%
Material Damping Predictionσo' = 0.25 atmσo' = 1 atmσo' = 4 atmσo' = 16 atm
(b)
Figure 10.8 Effect of mean effective stress on (a) normalized modulus reduction and (b) material damping curves of a soil with PI = 50 %
266
Table 10.15 Effect of σo’ on normalized modulus reduction curve: PI = 50 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 1.000 1.000 1.000 1.0002.20E-05 0.999 1.000 1.000 1.0004.84E-05 0.998 0.999 0.999 1.0001.00E-04 0.997 0.998 0.999 0.9992.20E-04 0.994 0.996 0.997 0.9984.84E-04 0.987 0.992 0.995 0.9971.00E-03 0.975 0.984 0.989 0.9932.20E-03 0.949 0.967 0.978 0.9864.84E-03 0.900 0.934 0.956 0.9721.00E-02 0.822 0.878 0.918 0.9462.20E-02 0.692 0.778 0.845 0.8954.84E-02 0.521 0.629 0.725 0.8041.00E-01 0.358 0.465 0.575 0.6792.20E-01 0.213 0.296 0.396 0.5064.84E-01 0.116 0.169 0.241 0.3311.00E+00 0.063 0.095 0.140 0.203
Table 10.16 Effect of σo’ on material damping curve: PI = 50 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 2.164 1.450 0.971 0.6502.20E-05 2.166 1.451 0.972 0.6514.84E-05 2.174 1.456 0.975 0.6531.00E-04 2.187 1.464 0.980 0.6562.20E-04 2.217 1.482 0.991 0.6634.84E-04 2.282 1.523 1.016 0.6781.00E-03 2.411 1.603 1.066 0.7092.20E-03 2.702 1.786 1.180 0.7804.84E-03 3.310 2.175 1.426 0.9341.00E-02 4.386 2.888 1.886 1.2272.20E-02 6.441 4.343 2.871 1.8714.84E-02 9.589 6.824 4.693 3.1381.00E-01 13.137 10.024 7.333 5.1512.20E-01 16.904 13.941 11.056 8.3814.84E-01 19.849 17.458 14.917 12.2681.00E+00 21.547 19.815 17.876 15.677
267
1.2
1.0
0.8
0.6
0.4
0.2
0.0
G/GmaxG/Gmax Prediction( PI = 100 %, N = 10 cycles, f = 1 Hz, OCR = 1 )
(a)
25
20
15
10
5
0
D, %
0.0001 0.001 0.01 0.1 1
Shearing Strain, γ ,%
Material Damping Predictionσo' = 0.25 atmσo' = 1 atmσo' = 4 atmσo' = 16 atm
(b)
Figure 10.9 Effect of mean effective stress on (a) normalized modulus reduction and (b) material damping curves of a soil with PI = 100 %
268
Table 10.17 Effect of σo’ on normalized modulus reduction curve: PI = 100 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 1.000 1.000 1.000 1.0002.20E-05 1.000 1.000 1.000 1.0004.84E-05 0.999 0.999 1.000 1.0001.00E-04 0.998 0.999 0.999 0.9992.20E-04 0.996 0.997 0.998 0.9994.84E-04 0.991 0.994 0.996 0.9981.00E-03 0.983 0.989 0.993 0.9962.20E-03 0.966 0.978 0.986 0.9914.84E-03 0.932 0.956 0.971 0.9811.00E-02 0.876 0.917 0.945 0.9642.20E-02 0.774 0.843 0.893 0.9294.84E-02 0.625 0.722 0.802 0.8631.00E-01 0.461 0.571 0.675 0.7642.20E-01 0.293 0.392 0.501 0.6104.84E-01 0.167 0.238 0.327 0.4311.00E+00 0.093 0.138 0.200 0.280
Table 10.18 Effect of σo’ on material damping curve: PI = 100 %
Shearing Strain (%) σo' = 0.25 atm σo' = 1.0 atm σo' = 4.0 atm σo' = 16 atm1.00E-05 3.129 2.096 1.404 0.9412.20E-05 3.131 2.097 1.405 0.9414.84E-05 3.136 2.100 1.407 0.9421.00E-04 3.144 2.105 1.410 0.9442.20E-04 3.163 2.117 1.417 0.9494.84E-04 3.204 2.143 1.433 0.9581.00E-03 3.286 2.193 1.464 0.9782.20E-03 3.472 2.309 1.537 1.0234.84E-03 3.868 2.560 1.693 1.1201.00E-02 4.593 3.029 1.991 1.3082.20E-02 6.070 4.029 2.648 1.7294.84E-02 8.579 5.876 3.934 2.5891.00E-01 11.798 8.541 5.972 4.0492.20E-01 15.716 12.279 9.226 6.6514.84E-01 19.213 16.132 13.118 10.2411.00E+00 21.544 19.069 16.513 13.847
269
To illustrate the impact of utilizing the recommended curves on site
response analyses, a 100-m thick silty sand (SM) deposit was modeled in twenty
six layers and analyzed using the shareware version of ProShake (EduPro, 1998).
A confining-pressure-dependent shear wave velocity, Vs, profile was used (as
shown in Figure 10.10) along with 1500-m/sec Vs at the half space. The Topanga
motion (Maximum Horizontal Acceleration, MHA, = 0.33 g) recorded during the
1994 Northridge earthquake was used as the input “rock” motion.
100
80
60
40
20
0
Depth, m
10008006004002000
Vs, m/sec
Figure 10.10 Shear wave velocity profile assumed for the 100-m thick silty sand deposit
270
In Figure 10.11, the acceleration response spectra from two analyses are
presented: 1) using the average generic curves (Seed et al., 1986) to model all
layers, and 2) using the recommended nonlinear curves interpolated for each soil
layer. The response spectrum of the input motion is also shown in this figure. The
response spectra indicate that the recommended nonlinear curves produce an
MHA much higher than that predicted by the average generic curves (0.54 g vs.
0.37 g). Additionally, larger spectral accelerations (typically 30 % to 50 % higher)
are calculated at all periods less than 1 sec for the analysis utilizing the
recommended nonlinear curves.
As discussed in Darendeli et al. (2001) the impact of utilizing a family of
confining-pressure-dependent curves is expected to be more pronounced for
deeper sites subjected to higher intensity input motions due to lower damping
introduced by the confining-pressure-dependent curves. At longer spectral periods
(T > 1 sec), the response is dominated by the overall stiffness of the site. As a
result, the confining-pressure-dependent analyses may tend to predict a smaller
response at longer periods due to the more linear response modeled by these
curves.
271
2.5
2.0
1.5
1.0
0.5
0.0
Spec
tral A
ccel
erat
ion,
S a ,
g
0.01 0.1 1 10Period, T, sec
This Study (a family of mean curves for PI = 0 %)Seed et al., 1986 (mean curve for sands)Input Motion
5 % Damping
Figure 10.11 An example of utilizing the recommended normalized modulus reduction and material damping curves and its impact on estimated nonlinear site response
272
10.5 SUMMARY
In this chapter, recommended normalized modulus reduction and material
damping curves are presented for soils with a broad range of plasticities confined
over a broad range of mean effective stresses.
The impact of utilizing the recommended curves when assigning nonlinear
soil properties in site response analyses is illustrated by analyzing a 100-m thick
silty sand (SM) deposit using average generic curves (Seed et al., 1986) to model
all twenty six layers, and the recommended nonlinear curves interpolated for each
soil layer. Larger spectral accelerations (typically 30 % to 50 % higher) are
calculated at all periods less than 1 sec for the analysis utilizing the recommended
nonlinear curves than those calculated for the analysis utilizing average generic
curves.