Homework 3 (pdf) - Geotechnical Earthquake Engineering

CE 275: Geotechnical Earthquake Engineering
Fall Semester, 2006
Prof. R. Seed
Assignment 3
This assignment will serve as an introduction to performing one-dimensional seismic site
response analyses. Assignment 3 is a general suite of questions regarding elements of modelling
of dynamic soil properties and behavior, and is directed towards developing models for elements
of the Treasure Island project site that is one of the two hypothetical projects we are considering
as class exercises. Assignment 4 will then ask that you actually perform site response analyses
of the Treasure Island site, using “SHAKE”. Both assignments are to be done as group efforts
(turn in only one copy of each.)
Part I: General:
Figure 1 shows an enhanced set of data and information regarding subsurface conditions at our
Treasure Island project site. Figure 2 shows measured shear wave velocities (solid lines), and
the shear wave velocity profile used by Dickenson (1992) for response analyses of this site.
(Note the scale in meters.) The measured V s values were obtained by the SASW method, and so
do not necessarily provide ideal discretization, and are increasingly approximate at greater
depths.
1. Consider the stratum of sandy soil at the surface of the site, as shown in Figures 1 and 2. The
soil (down to a depth of approximately 36.1 ft.) is an uncompacted hydraulically-placed fill,
consisting mainly of loose, fine to medium silty sand (SP, SP-SM, and SM), with occasional
silty clayey sand. Fines content in this stratum is variable, ranging between about 5% to
95%, but a majority of the soil has fines contents of between about 10% to 40%. The fines
are mainly low plasticity silt (ML), though some are more clayey (CL and even occasionally
CH). These fill soils were dredged from the floor of the Bay, and were then transported to
the site in hydraulic suspension (in pipes) and then placed by pluviation through standing
water. SPT were performed in several borings at our site, and the N-values (after correction
for energy, procedure, short rod, and overburden effects) are on the order of N 1,60 = 3 to 15
blows/ft. The soils below this are also fine, silty sands, either representing additional
hydraulic fill or the natural sand bar deposit upon which the fill was placed. These lower
sandy soils extend to a depth of about 44.2 feet, and are very similar to the upper fill. We
will treat this as a single stratum (all the same soil) from the surface to a depth of 44.2 feet.
The water table occurs at a depth of approximately 5 feet within the fill.
(a) Based on this data and information, we need to select modulus degredation and damping
relationships (as a function of shear strain) for this stratum. Make a copy of the “Vucetic and
Dobry” curves for G/G max vs. γ and B vs. γ, and arrange these one above the other on the
same page (use Figure 3, but make a copy). Now, on this composite figure, draw the
modulus and damping curves that you would recommend to model the surface fill soils at our
project site. Label these clearly.
(b) We also need to assign initial values of either G max or V s within this stratum. Dickenson’s
“estimated” V s profile (in Figure 2) had the benefit of additional downhole (by the OYO

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.

(d) The deep, dense gravelly sands are underlain by additional Old Bay Clays (CH/CL). These
are even older, and so are even stiffer and stronger. Treat these as an extension of the Old
Bay Clay unit from above the gravelly sands. Again, remember that we also have V s data,
but that SASW does not work well in the “shadow” just below a stiffer layer (e.g. the
gravelly sands), and that we are very deep for SASW!
(e) Our site investigations (both borings and testing, as well as SASW) provided essentially no
useful, quantitive data regarding the weathered shale and the harder, more intact sandstone
“bedrock” underlying the deep clays. Refer to Figures 1 and 2. Dickenson assigned Vs =
730 m/sec to the weathered shale, and treated the sandstone as an elastic halfspace with Vs =
1,220 m/sec. Do these values seem reasonable? Now, feel free to choose your own.
4. Finally, prepare a full proposed site profile, divided into sub-layers, for your response
analyses. Show the proposed profile of V s vs. depth, and provide figures showing your
proposed relationships for G/Gmax vs. γ and B vs. γ for each soil and/or “rock” unit,
including the base “rock”.