Fundamentals of the Behavior of Sands Under Cyclic Loading.pdf
- 1. Fundamentals of the Behavior of Sands Under Cyclic Loading by Robert Pyke PhD, GE June 7, 2025 This article is intended to be a companion to my article on the Limitations of Simplified Methods for Evaluating Earthquake-Induced Liquefaction and its Consequences https://www.linkedin.com/pulse/one-more-update-limitations-simplified-methods- evaluating-robert-pyke-wchic. At one point I intended to include this material in that article to further explain a more obscure limitation of simplified methods, which is that the continued equivalencing of irregular shear stress or shear strain histories to an equivalent number of uniform cycles obscures the importance of the shear stress and strain histories to the rate at which excess pore pressures, latent or actual settlements, and hardening (an increase in the shear modulus) occur. Like other aspects of simplified methods, this approximation made perfect sense in 1969, when the original Seed and Idriss simplified method was first published, but it makes much less sense 50 years later when ready access to personal computers makes more detailed and accurate analyses possible. But the other article was already getting too long for most readers to digest, hence this separate article. The figures that follow in this article are taken from the EERC reports on the shaking table tests conducted by myself (Pyke et al., 1974) and Pedro De Alba (De Alba et al., 1975), under the supervision of Harry Seed and with the active assistance of Clarence Chan. Pedro and I shared use of the same spreader box for preparing the beds of sand that were tested at a wide range of different relative densities. Note that these results directly apply to only pluviated, washed, and screened Monterey No. 0 sand. This is what Professor Michele Jamiolkowski used to refer to as “baby sand”. The magnitudes of the observed cyclic shear strains, excess pore pressures, and settlements will likely be much less for real soils. Even for Monterey No.0 sand, I had found that it made a difference how you prepare the sample and it was well known that the boundary conditions of the test device make a difference. Additionally, pre-straining, initial shear stresses, overconsolidation, and other aspects of ageing all make a difference. However, notwithstanding the importance of the soil fabric, these well-controlled and repeatable laboratory tests show some aspects of fundamental behavior that are likely also important in natural soils. Dry or non-saturated sands Figures 1 and 2, taken from Pyke et al. (1974) and Pyke (2022), show that when the data was reduced to show the settlement of a dry sand per cycle or the average shear modulus
- 2. per cycle as a function of both the cyclic shear strain and the accumulated previous settlement to that point, the accumulated previous settlement had a significant effect. Figure 1 – Settlement Per Cycle as a Function of Cyclic Shear Strain and Accumulated Settlement Figure 2 – Shear Modulus as a Function of Cyclic Shear Strain and Accumulated Settlement
- 3. This use of the accumulated previous settlement as a measure of the previous strain history or “energy” imparted into the soil, had been suggested by Geoffrey Martin, and is one of the keys to modeling the linking of the development of excess pore pressures in a fully saturated sand under cyclic loading to the settlement of a dry sand under cyclic loading (see Martin et al., 1975). It is also key to calculating the settlement of dry or non- saturated sands more accurately (Pyke, 2022). Neither of these things can be done if you are still thinking in terms of the equivalent number of uniform cycles of shear stress. Figure 3, also taken from Pyke et al. (1974), shows the effect of multi-directional shaking on the settlement of dry sand. Neither Professor Seed nor I knew exactly what to expect when we planned this experiment, but it turned out that when two orthogonal components of motion were run simultaneously, the settlement was approximately equal to the sum of the settlements observed when the components were run individually. Figure 3 – The Effect of Multi-Directional Shaking on Settlement But this does not mean that you should “double the predicted settlement” to account for multi-directional shaking. That is a misconception that arose from the paper by Seed et al. (1978) and would apply at best only when you have two identical components of motion. Because of various nonlinearities in the relationship between the cyclic stress ratio causing triggering of liquefaction and the settlement of a dry sand, the reduction in the cyclic stress ratio causing triggering of liquefaction turns out to be fairly modest.
- 4. Seed et al. (1978) wrote: “Both qualitative use of the results of shaking table tests on dry sand and the results of a quantitative evaluation using data from cyclic simple shear tests indicate that the shear stresses causing liquefaction under multi-directional shaking with two equal components are 10 to 20 percent less than the shear stresses causing liquefaction under one-directional shaking. Since in practice it is unlikely that a second component of motion would be equal to the single component used for design purposes, it is suggested that a reduction of 10 percent in the shear stresses causing liquefaction is a suitable general procedure for accounting for the effects of multi- directional shaking.” The best way to account for multi-directional shaking is therefor to conduct bi- directional, nonlinear, effective stress site response analyses, tracking the development of excess pore pressures and immediate or latent settlements for each half cycle in each of two orthogonal directions, thus accounting for the effects of previous loading on excess pore pressure development and settlement, and eliminating the need to make approximations about the effects of multi-directional shaking. Because the rate of settlement decreases markedly with increasing accumulated volume change, the ultimate or maximum settlement is not that much different under multi- directional shaking than it would be under uni-directional shaking. The data in Pyke et al. (1974) suggests that, even for relatively loose sands, free-field settlement of non- saturated sands will not exceed about 0.5 percent of the layer height. Saturated sands Figures 4 and 5, taken from De Alba et al. (1975), show findings that are very significant to evaluating the consequences of liquefaction. Simplified methods for evaluating the potential for liquefaction have generally focused on triggering of liquefaction, defined as 100 percent excess pore pressure or some small level of cyclic shear strains in laboratory tests, or surface manifestations such as sand or silt boils or minor cracking of soils or hardscape in case histories. But in practice most engineers are concerned with free-field settlements or lateral spreading, which are evaluated using add-ons to the basic simplified methods, and it is these add-ons which frequently give very large and unreasonable results. While it is true that layers that are characterized as “dense” may still be susceptible to excess pore pressure development under strong shaking, few if any adverse consequences of liquefaction have been observed when the normalized clean sand SPT blowcount exceeds 15. See for instance Ishihara (1993) and Youd et al. (2002). The reason for this is illustrated by the results shown in Figure 4. This figure shows that
- 5. while denser sands can still “trigger”, the consequent cyclic strains are very much limited as the relative density increases. Figure 4 – CSR and Limiting Strains as a Function of Relative Density One of the issues created by being overly conservative in predicting the consequences of liquefaction in denser sands is that ground improvement might be called for when in fact it is not required and it is very difficult to further densify the sand in question. Not only that, but the soil fabric may well be disrupted so that some measures such as penetration resistance and shear wave velocity might go down, at least in the short term, which makes the situation even messier. A specific example of this lack of consequences following “triggering” in denser sands is provided in Figure 5 which shows the decrease in the rate of settlement of a miniature footing as the relative density increases.
- 6. Figure 5 – Rate of Footing Settlement as a Function of Relative Density Concluding Remarks Although these laboratory tests on “baby sands” do not capture all the elements of soil behavior in the field, which usually include a complex distribution of soils in layers and lenses of various thicknesses, and soil fabric which reflects both the initial method of deposition and changes over time, they do capture important elements of the behavior of cohesionless soil under the cyclic loadings produced by earthquake ground motions. These include the effect of the prior loading within the same event, the effect of multi- directional loadings, and the diminishing likelihood of adverse consequences as the density increases. The tests reported above suggest that while earthquake loadings do very little to increase the density of a given deposit, in the absence of complete liquefaction they are likely strengthen the soil by repeated earthquake loadings. However, accumulated experience, supported by some laboratory experiments, suggests that stiffer and stronger soil fabrics can be wiped out by repeated episodes of liquefaction if they do occur, so that sites with significant looser deposits, indicated by normalized clean sand SPT blowcounts of less than about 15, do require deep foundations or ground improvement if they are to support facilities of any importance.
- 7. References De Alba, P., Chan, C.K., and Seed, H.B., “Determination of Soil Liquefaction Characteristics by Large-Scale Laboratory Tests”, Report No. EERC 75-14, May 1975 Ishihara, K., “Liquefaction and flow failure during earthquakes”, Geotechnique, Vol.43, No. 3, 1993 Martin, G.R., Seed, H.B., and Finn, W.D.L., “Fundamentals of Liquefaction under Cyclic Loading”, Journal of the Geotechnical Engineering Division, ASCE, Volume 101, No. GT5, May 1975 Pyke, R., “Lessons learned from the observed seismic settlement at the Jensen Filtration Plant in the San Fernando Earthquake”, ASCE Lifelines 21-22 Conference, Los Angeles, February 2022 Pyke, R., Chan, C.K., and Seed, H.B., “Settlement and Liquefaction of Sands Under Multi-Directional Shaking”, Report No. EERC 74-2, February 1974 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, Volume 104, No. GT1, January 1978 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