Homework 3 (pdf) - Geotechnical Earthquake Engineering

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suspension logger method) V s data that will not be available to us. (Dickenson used the two V s data sets, as well as a suite of empirical correlations, and then selected his V s profile.) (i) (ii) Assume reasonable unit weights for the upper fill, and calculate and plot a profile of σ v΄ vs. depth within the upper 42 feet. At depths of 10, 20, and 40 feet, estimate G max and V s using the correlations of • Seed et al., 1984 • Imai and Tonouchi, 1982 • Sykora and Stokoe, 1983 • Hardin, 1983 (Estimate that OCR ≈ 1 to 1.5 for these upper sands) (iii) (iv) (v) Plot these profiles of V s vs. depth, and on the same figure also plot the measured V s data (in the upper sands) from Figure 2. Now we have to decide how to sub-divide our soil into sub-layers. Based on the V s estimates thus far, and your notion of frequency needs and resulting wavelengths, sub-divide the upper sands into X sublayers (and explain your selection of X.) Now, based on all of this, select proposed V s values for use within each of these sublayers in your SHAKE analyses. On a full-depth profile, plot V s vs. depth. (You will continue this figure right down to the rock by the time you have finished this assignment, so scale this figure accordingly.) 2. Now consider the deposit of clayey soils immediately underlying the upper sands (from a depth of about 44.2 feet to about 95.4 feet.) This soil is San Francisco Bay Mud, a Holocene deposit of marine clay and silty clay (CH), with occasional silty and sandy lenses. The Bay Mud is a nearly normally consolidated clay (beneath the fill at our site), and is of low strength. It is also “sensitive”, and highly compressible under long-term loads too. The Bay Mud at our site has a Plasticity Index of PI ≈ 45 to 55%. (a) We will begin by estimating the undrained shear strength of the Bay Mud. Based on laboratory testing of “undisturbed” samples (UU Triaxial tests), and in-situ vane shear tests (corrected with Bjerrum’s correction), and one-dimensional laboratory consolidation tests, it appears that this deposit is essentially normally consolidated (OCR = 1.0 to 1.3), and that S u /P = 0.32 to 0.35. Does this seem reasonable? (b) Assuming a reasonable value for the unit weight of the Bay Mud, continue your profile of σ v΄ vs. depth down to the base of the Bay Mud (at a depth of 95.4 feet.) The Bay Mud is lighter than the sandy fills, and a good average estimate of unit weight is γ sat = 94 to 100 lb/ft 3 . How would the unit weight vary with depth? Would this matter for our purposes?
(c) Now, based on this effective stress profile, and S u /P = 0.32 to 0.35, plot your estimate of S u vs. depth within the Bay Mud. (d) Now, using Dickenson’s recommended correlation between S u and V s , plot your estimated profile of V s vs. depth within the Bay Mud. On the same plot, also plot the measured V s data (from Figure 2.) (e) Based on this, and considering wavelengths and frequencies, decide how to sub-divide the Bay Mud stratum into sub-layers. Explain your rationale. (f) Finally, based on all of this, select recommended values of V s within each sublayer, and plot this vs. depth (on the same figure with your chosen profile of V s within the upper sands.) (g) We will, of course, also need modulus degredation and damping curves. Make another copy of the Vucetic and Dobry curves (Figure 3.) Onto this, plot the material-specific curves for Bay Mud recommended by Dickenson (Figure 4.) How do these compare with the Vucetic and Dobry data set (at similar PI)? 3. Now, repeat the above exercises for the deeper soils (down to a depth of 298.9 feet.) The following data and information will be helpful. (a) The Bay Mud is underlain by a deposit of medium to dense, fine to medium sand and silty sand (SP, and SP/SM) to a depth of approximately 135.7 feet. These sands have been in place for at least the second half of the Holocene period, and have been shaken by many earthquakes. Based on SPT borings, corrected N-values in these sands are typically on the order of N 1,60 = 25 to 50 blows/ft. Fines contents vary, but are typically on the order of 5 to 25%, but with occasional thin silt and clay lenses. (b) These sandy strata are underlain by Old Bay Clays (CH/CL). These are pre-Holocene units, and are overconsolidated due to Bay level fluctuations and also ageing (and attendant secondary compression.) It is a bit difficult to get good undrained shear strength data on these deeper clays, as the samples tend to be disturbed by unloading. The limited data available to us (from our project borings and testing) suggests that S u is approximately 2,700 to 5,200 lb/ft 2 in this unit, but we are not very confident in this data. We also have the measured V s data from Figure 2. Think about how V s should vary with depth in this unit. Also, check the implied ratio of S u /P, and think about OCR and SHANSEP. (OCR appears to be on the order of about 3 to 7 in this unit.) (c) The Old Bay Clays are underlain, at a depth of about 248 feet, by very dense sands and gravelly sands (SP, SW). We don’t have much SPT data here, as the depth is great, the soils are dense, and the gravels impede the SPT penetrometer. You will have to make your own guesses. (We do know that this unit is dense to very dense, and expect that N 1,60 values will be on the order of about 40 to 80 or more.) Remember that we also have measured V s data (Figure 2), but we are getting rather deep for SASW.
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