This is a further update of a presentation delivered at the 2nd Ishihara Colloquium held at San Diego State University on August 22-23, 2019.

1. Improved Analysis of Potential Lateral
Spreading Displacements in Earthquakes
By Robert Pyke Ph.D., G.E.
Robert Pyke, Consulting Engineer, Walnut Creek, CA, USA
Presented at the 2nd Ishihara Colloquium,
San Diego State University, August 22-23, 2019

2. Companion presentation which combines three papers presented at the
7ICEGE in Rome, June 2019 :
Improved Analyses of Earthquake-Induced
Liquefaction and Settlement
Available on LinkedIn and Research Gate
https://www.linkedin.com/pulse/improved-analyses-earthquake-induced-
liquefaction-settlement-pyke-1c

3. Outline
• Basics
• A parametric study
• A case history
• ASCE 7-16 code provisions

4. This is an inherently difficult problem
• Permanent displacements are very sensitive to the character and
duration of the earthquake ground motion. The same motion will
even give different displacements depending on which side of it is
applied in the downslope direction.
• And, they are strongly affected by any development, redistribution
and dissipation of excess pore pressures in saturated cohesionless
soils – about which there is commonly uncertainty in real soil profiles

5. Possible approaches to estimating
lateral spreading displacements
• Empirical methods
• Other simplified methods?
• One-dimensional nonlinear site response analyses
• Two or three-dimensional nonlinear analyses

6. Empirical methods
• In spite of the best efforts of their authors, these methods, e.g. Youd et al.
(2002) and Zhang et al. (2004), show very wide scatter in the ratio of observed
to predicted displacements to the point where one might reasonably question
the usefulness of the procedures for forward prediction
• Again, this is an inherently difficult problem! But analytical procedures also
show sensitivity of the results to the input motions and modelling of the soil
profile, and nonlinear effective stress analyses limit the depth of liquefied
material, which may be over-estimated in simplified analyses

7. Particular Issues Regarding Thin Layers
• If only seen in a single boring or CPT they may be lenses rather than layers, and the
induced stresses in a lenses are likely be lower than in the surrounding material –
see Pyke (1995)
• Both the SPT and the CPT “have a nose”. They can detect softer layers even before
they get to them. See the following slide taken from Boulanger and DeJong
(2018). A sand layer underlain by a soft clay has to be in the order of one meter
thick in order that the true peak tip resistance be recorded. Similarly, an SPT
sampler needs to have several feet of the same material below the tip to record a
meaningful blowcount.

9. Beware of automation!
• It is not only poor practice, but can be dangerous, to automate the
process of processing field data and conducting analyses without human
oversight and intervention!
• See Youd (2018) for an excellent example of the need for human
intervention and interpretation of a soil profile. The following slide, from
Youd, shows the results of using the computer program C-LIQ to estimate
potential lateral spread displacements at the BYU test site in Utah.

11. But if the geologic history and grain size characteristics
of each layer are taken into account, not one layer is
susceptible to lateral spreading!

12. One-dimensional nonlinear effective stress site response
analyses
The procedure described in this presentation is more complex and demanding of
resources than empirical or simplified analyses, but it is still simplified relative to a
full three-dimensional analysis of site response using a soil model that computes
permanent strains caused by complex cyclic loadings.
However, it provides more reasonable results and much greater insight into the
problem than the existing simplified methods.
The analysis itself can typically be conducted in a day or two, but the overall time and
cost required to execute this kind of analysis may be increased by the need to
conduct additional field and laboratory studies in order to maximize the benefits of
conducting the analysis.

13. One-dimensional nonlinear effective stress site response
analyses - continued
• The procedure requires the use of either site specific or generic data from cyclic
simple shear tests to determine the permanent shear strains that develop in
representative samples when a cyclic shear stress is applied to a test specimen
consolidated with an initial shear stress. Generic data from Pyke (1973) is the
default option in the author’s program, TESS2, but it can be replaced with site-
specific data if that is developed.
• Site-specific acceleration histories are then input to a one-dimensional nonlinear
site response analysis which uses a soil model such as that described by Pyke (1979)
which allows the development of permanent shear strains, when there is an initial
shear stress, even when the soil element is subjected to a symmetrical cyclic shear
stress.

14. What’s the deal about the Masing Hypothesis?
• See Pyke (1979)
• The Masing hypothesis does not allow the development of permanent
deformations as a result of material behavior
• If you read Masing’s original paper (which was written in German), he said
I formulated a hypothesis, I tested it, and it didn’t hold up!
• Some complex two and three-dimensional soil models behave correctly,
e.g. “failure seeking” models, but some do not

15. An additional element of soil behavior that is key to a soil
model that accumulates permanent displacements
The results of a typical cyclic simple shear test from Pyke (1973) are shown on
the following slide. There are two points worth noting:
1. The settlement per cycle clearly decreases with an increasing
number of cycles;
2. The shear modulus increases with the number of cycles
In other words, sands “harden” under cyclic loading

17. This effect is also seen in undrained tests on saturated samples
• Careful examination of test results shows that the shear modulus
tends to increase before the development of excess pore pressures
kicks in and the shear modulus decreases
• See results from Vucetic and Mortezaie (2015) on the next slide

18. Vucetic and Mortezaie (2015)

19. So, how to account for the stiffening of a sand under cyclic
loading?
• Perhaps the best way to follow this increase in shear modulus is to
use the accumulated actual or latent settlements as a measure of the
previous loading, as suggested by Geoffrey Martin.
• This is illustrated on the next slide.

21. A confession
This effect was not included in Pyke (1979) with the result, as
noted by Peter Cundall, that the stress-strain curves motored
across the page too quickly!

23. Is this effect the same with multi-directional
shaking?
• See the following slide which shows the results of two shaking table
tests – one with uni-directional loading and one with bi-directional (in
this case gyratory) loading
• Initially the test with bi-directional loading shows a lower implied
shear modulus but it actually hardens more quickly and overall the
stiffnesses are similar (even though there is about twice the
settlement in the bi-directional test with equal amplitude
components)

25. One more thing:
The rate at which excess pore pressures develop is also affected by the
initial shear stress. The user can take this into account by modifying the
cyclic stress ratio required to cause initial liquefaction and the default
pore pressure generation curve that is built into TESS2 but, as noted by
Idriss and Boulanger (2008), “the parameter Kalpha is often omitted in
analyses of lateral spreading of level or mildly sloping sites – which is
reasonable because Kalpha is approximately unity for small values of the
initial static shear stress ratio

26. And, finally, a caveat:
• The procedure described in this presentation for evaluating lateral
spreading displacements strictly applies only to long shallow slopes
under which there are initial shear stresses on horizontal planes which
will tend to cause permanent displacements in the downslope
direction and assumes that the slope moves uniformly downhill
• Lateral spreading can also occur even for flat ground adjacent to a free
face, as illustrated on the next slide, which is taken from Youd (2018)

28. So, what to do about free faces?
• In the first place use an empirical procedure such as Youd et al (2002)
• If this indicates that significant deformations are possible, and there is sloping
ground rather than flat ground, and the free face is not very high, try the 1D
nonlinear effective stress approach. For slopes which are long relative to the depth
of liquefiable material and the height of the free face, this will likely give
reasonable results
• If the empirical procedure indicates that significant deformations are possible, and
the ground surface is flat, or the slope is short relative to the depth of liquefiable
material and the height of the free face, look at doing a 2D nonlinear effective
stress analysis

29. Part 2. A parametric study
• This study uses the soil profile for the Lum Elementary School in
Alameda, CA, that was included in the paper “Improved analyses of
earthquake-induced liquefaction and settlement”, Proc. 7th
International Conference on Earthquake Geotechnical Engineering,
Rome, June 2019
• The profile basically has five strata:
1. Hydraulically placed sand fill
2. young Bay Mud, lightly OC clayey silts and silty clays
3. Merritt Sand, late Pleistocene wind-blown sands
4. Old Bay Clay, OC clayey silts and silty clays
5. Lower Alameda Formation, very dense sands and gravels

31. TESS2 - bi-directional, nonlinear,
effective stress site response analyses
• The same explicit finite difference solutions for response and redistribution
and dissipation of excess pore pressures as TESS
• Simple hyperbolic soil model – see Pyke (1979, 1993, 2004,2020) – complies
with Cundall-Pyke hypothesis and therefore develops permanent
deformations when there is an initial shear stress
• Excess pore pressures following Seed, Martin and Lysmer (1976)
• Settlements following Pyke (1973) and Seed, Pyke and Martin (1978)
• Runs two horizontal components simultaneously and adds excess pore
pressures and settlements or latent settlements

32. Basic site response
• Five pairs of horizontal input motions were fitted to the ASCE 7-16 Site Class
C response spectrum for the site and were input at a depth of 100 feet, that
is, the top of the Lower Alameda formation.
• The spectra of the computed surface acceleration histories are shown in the
next slide. It may be seen that the ligher frequency motion is heavily
damped, not only a a result of liquefaction of one layer in the sand fill but
also because of the deep Old Bay Clays
• One of the three three-foot thick layers of saturated sand fill in the model
completely liquefied, but another almost liquefied

33. Input motions
Ground surface motions

34. Computed permanent displacements of the ground surface:
• Are shown on the next slide
• Shows the scatter in computed displacements even when
all the input motions are fitted to the same target spectrum
and are relatively near field motions for around M = 7
earthquakes

35. 0
1
2
3
4
5
6
0 1 2 3 4 5 6
PermanentDisplacement,infeet
Slope, in percent

36. Computed displacement profile:
• Is shown on the next slide
• Shows that most of the permanent displacement occurs in the one layer that
reached initial liquefaction
• Explains why simplified methods that assume more layers will liquefy can be
very conservative. For instance, if the simplified analysis suggests that five layers
will liquefy, the computed ground surface displacement might be 15 feet rather
than 3 feet

37. -100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Final displacement profile for 5% slope - feet

38. Part 3. A case history
• Involves a now hypothetic land development in Northern Los Angeles County.
Planning scenario has now changed
• But study was done in 2007-2008 by ENGEO Incorporated, with input from the
author, to determine feasibility of limiting potential lateral spreading in a broad,
gently sloping valley filled with both Pleistocene and Holocene alluvium
• Extensional cracking, or “lurching”, occurred at several locations around the
perimeter of the fill in the 1994 Northridge earthquake as a result of the Holocene
alluvium tending to move downslope

40. Approach to problem
• Take high quality undisturbed samples
• Conduct cyclic simple shear tests with initial shear stresses on
normally re-consolidated and over-consolidated test specimens
• Develop appropriate input acceleration histories
• Fit HDCP soil model to laboratory test results
• Conduct site response analyses using the earlier program TESS

41. Limitations of study
• Variability of alluvium difficult to model (even in 2 or 3D)
• Difficult to obtain truly representative samples
• Possible sample disturbance
• Analysis is for “unconstrained” or existing condition – actual
development would have toe buttresses as necessary.

45. A warning
• Beware of spending too much time trying to fit laboratory data precisely.
It may not represent the field condition!
• Remember Terzaghi:
“Nature has no contract with mathematics – she has even less of an
obligation to laboratory test procedures and results”.

46. TESS analyses
• 13 profiles
• 11 input motions fitted to 475-year UHS, plus reconstruction of 1994
deformations using the USC56 record of Northridge earthquake
• One partner jumped up and down saying “not enough near-field
motions”, but it turned out that further afield motions with more
cycles produced larger permanent displacements!
• Analyses with USC56 record produced deformations of 1 to 2 feet in
the downslope direction, consistent with 1994 observations

47. Stress strain loops
• The next three slides show shear stress – shear strain loops generated
by the HDCP soil model that is used in TESS and TESS2
• The first slide shows the response under a sinusoidal loading
replicating a laboratory test
• The second and third slides show the response to an irregular loading
without an initial shear stress and then with an initial shear stress

51. Response spectra of input motions
• 475-year Uniform Hazard Spectrum
• For USC56 recording of the 1994 Northridge earthquake
and the Newhall record … also ran analyses for these
records unmodified

53. Results
• For samples reconsolidated to the in-situ vertical stress, i.e. OCR = 1, the computed
deformation of the USC56 record were in the order of 1-2 feet, consistent with the
observations of movement in the Northridge earthquake
• For the motions fitted to the 475-year UHS, lateral deformations at the ground surface
were in the order of 5 feet for sample reconsolidated to the in-situ vertical stress
• For a 2 percent slope and OCR = 2, there was generally less than 1 foot of deformation
at ground surface – see next slide
• There is a wide variation in the computed displacements using different acceleration
histories as the input motion
• The larger values are for more distant earthquakes with longer durations and more
cycles, which would not in reality have the same amplitudes as the near-field motions

55. ASCE 7-16 Code Provisions
• For the first time, ASCE 7-16, which will be adopted by many US states in their state
building codes as of 1/1/2020, specifies the maximum lateral spread displacements for
which shallow foundations can be employed.
• Because geotechnical engineers may not be familiar with the Risk Categories in ASCE 7-
16, these are listed on the left of the next slide
• The upper limit on lateral spread displacements for which shallow foundations can be
employed are listed as a function of the Risk Categories on the upper right of the slide
and the more general requirements for the use of shallow foundations are listed on the
lower right of the slide

57. Significance of these code provisions
• The upper limits on the computed lateral spreading displacements if shallow
foundations are to be employed are very tight
• Any conservatism in lateral spreading evaluations will force the use of either
ground improvement or deep foundations and add significantly to the cost of a
project
• Use of TESS2 will help limit the conservatism in evaluating excess pore presuures,
seismic settlements, and lateral spreading displacements, and the cost of using
TESS2 is trivial when compared to the cost of ground improvement or deep
foundations

58. Conclusions
• TESS, and now TESS2, provide a reasonably simple way to
estimate downslope movements of shallow slopes cause by
earthquakes
• Excess pore pressure development, redistribution and
dissipation are properly taken into account
• Potential settlements can also be estimated at the same time
• The Potrero Canyon case history indicates that the method is
consistent with at least one set of observations

59. Conclusions 2
• But the results will always be sensitive to the accuracy of the representation of
the field conditions in the model and the character of the acceleration histories
that are used as input
• Rather than designing a project around a predicted displacement, the only
practical approach is to adopt a design that limits any potential displacements to
acceptably small values
• This was accomplished in the case history by the plan to overconsolidate the
Holocene alluvium with a minimum OCR of 2.0

60. Conclusions 3
• There is no single correct way to evaluate potential lateral spreading
displacements. In different circumstances any of the four general approaches
listed at the outset might be appropriate.
• But for routine land development and building construction in California, the
optimum approach might be first to use an empirical procedure, preferable Youd
et al. (2002), but the CPT approach might be used if you examine the data very
carefully, and then, if a problem is indicated, use the approach described in this
presentation (which may require additional field and laboratory studies).
• But note that if you use this approach, you also get a better evaluation of site
response, liquefaction and seismic settlement as part of the process!

61. References
• Dahl, K.R., et al., “Characterization of an alluvial silt and clay deposit for monotonic, cyclic, and post-cyclic behavior”, Canadian
Geotechnical Journal, Volume 51, pp.432-440. 2014
• Idriss, I.M., and Boulanger, R.W., “Soil Liquefaction During Earthquakes”, EERI Monograph MNO-12, 2008
• Martin, G.R., Seed, H.B., and Finn, W.D.L., “Fundamentals of Liquefaction under Cyclic Loading”, Journal of the Geotechnical
Engineering Division, ASCE, Vol.101, No. GT5, May 1975
• Pyke, R., "Settlement and Liquefaction of Sands Under Multi-Directional Loading," Ph.D. Thesis, University of California, Berkeley,
1973
• Pyke, R., "Non-linear Soil Models for Irregular Cyclic Loadings," Journal of the Geotechnical Engineering Division, ASCE, Volume
105, No. GT6, June 1979.
• Pyke, R., 2004, “Evolution of Soil Models Since the 1970s.”, Opinion Paper, International Workshop on Uncertainties in Nonlinear
Soil Properties and their Impact on Modeling Dynamic Soil Response, Sponsored by the National Science Foundation and PEER
Lifelines Program PEER Headquarters, UC Berkeley, March 18-19, 2004.
• Pyke, R., et al., “Modeling of Dynamic Soil Properties”, Appendix 7.A, Guidelines for Determining Design Basis Ground Motions,
Report No. TR-102293, Electric Power Research Institute, November 1993
• Pyke, R., 2004, “Evolution of Soil Models Since the 1970s.”, Opinion Paper, International Workshop on Uncertainties in Nonlinear
Soil Properties and their Impact on Modeling Dynamic Soil Response, Sponsored by the National Science Foundation and PEER
Lifelines Program PEER Headquarters, UC Berkeley, March 18-19, 2004.

62. References 2
• Pyke, R., et al., “Modeling of Dynamic Soil Properties”, Appendix 7.A, Guidelines for Determining Design Basis Ground Motions,
Report No. TR-102293, Electric Power Research Institute, November 1993
• Rymer, M.J., Fumal, T.E., Schwartz, D.P., Powers, T.J., and Cinti, F.R., “Distribution and recurrence of surface fractures in Potrero
Canyon associated with the 1994 Northridge, California, earthquake.” The Northridge, California, Earthquake of 17January
1994. Woods, M.C., and Seiple, W.R., eds. California Division of Mines and Geology Special Publication 116, p. 133–146, 1995
• Seed, H.B., Martin, P.P., and Lysmer, J., “Pore Pressure Changes During Soil Liquefaction”, Journal of the Soil Mechanics and
Foundations Division, ASCE, Vol. 102, No.GT4, April 1976
• Seed, H.B., Pyke, R., and Martin, G.R., "Effect of Multi-directional Shaking on Pore Pressure Development in Sands," Journal of the
Geotechnical Engineering Division, ASCE, Vol. 104, No. GT1, January 1978.
• Vucetic, M., and Mortezaie, A., “ Cyclic secant shear modulus versus pore water pressure in sands at small cyclic strains”, Soil
Dynamics and Earthquake Engineering, Volume 70, pp. 60-72, 2015
• Youd, T.L., Hansen C.M., and Bartlett, S.F., “Revised Multilinear Regression Equations for Prediction of lateral Spread
Displacements”, Journal of Geotechnical and GeoEnvironmental Engineering, ASCE, Vol. 128, No.128, December 2002
• Youd, T.L.., “Application of MLR Procedure for Prediction of Liquefaction-Induced Lateral Spread Displacement”, Journal of the
Geotechnical and GeoEnvironmental Division, ASCE, Vo. 144, No. 6, 2018
• Zhang, G., Robertson, P.K., and Brachman, R.W.I., “Estimating Liquefaction-Induced Lateral Displacements Using the Standard
Penetration Test or Cone Penetration Test”, Journal of Geotechnical and GeoEnvironmental Engineering, ASCE, Vol. 130, No. 8,
August 2004.

63. Acknowledgements
• In addition to the valuable input provided by Jason DeJong and Katrina Dahl at UC
Davis, much of the work on the Potrero Canyon study was carried out by Pedro
Espinosa and Douglas Wahl. The input motions for that study were developed by
Jennie Watson-Lamprey.
• This updated presentation has benefitted greatly from the discussion sessions at
the 2nd Ishihara Colloquium and from the presentation by Les Youd, which was
based on his 2018 paper.

64. The End!
For more information write to me at bobpyke@attglobal.net