Liquefaction - principles

Transcription

1 Liquefaction - principles Consider a box of dry sand, subjected to cycles of shear strain. On initial loading, sand usually compacts and then dilates. On unloading, the sand follows a similar path to loading, but some residual volume strain remains at zero strain. Depending on the initial porosity, this can represent a net compaction. expansion compaction Now suppose the pores are filled with water. For a constant-volume test, the effective stress decreases, but the pore pressure remains constant. For a constant-applied-load test (e.g., normal load on box is fixed), the pore pressure increases and the effective stress decreases. Liquefaction occurs when the effective stress becomes zero.

2 Liquefaction principles (2) Thus, pore-pressure increase is not the primary cause of liquefaction; it is the decrease in effective stress due to lower contact forces between particles (after re-arrangement). Pore pressure does increase in some cases: e.g., if there is a constant overburden (total) stress. With a comprehensive constitutive model (such as the BSHP model) the process of liquefaction would occur automatically, with the associated pore pressure changes being handled by FLAC s fully coupled calculation. However, with a simple Mohr Coulomb model, we can treat liquefaction by simplified procedures, in which volume strains are added to elements, as a function of cyclic strain amplitude.

3 Simple models Two simple volume-change models are built into FLAC 4.0: Martin, Finn & Seed (1975) Byrne (1991) Shear strain ε vd ε vd γ is the incremental volume strain is the accumulated volume strain is the amplitude of the last cycle of strain time These relations are incorporated into a Mohr Coulomb constitutive model, with an algorithm for detecting when a strain reversal has occurred, and what was the amplitude of the last cycle. (The model is a DLL, automatically loaded.)

4 Use of Martin or Byrne models The determination of the four constants for the the Martin et al formula is awkward, because it is necessary to simulate a cyclic test with FLAC, and adjust the constants iteratively, to obtain a match to the known liquefaction data (e.g., cycles to liquefaction). For the Byrne formula, some guidance is given in his 1991 paper, in which the two constants are related to relative densities and SPT results: Liquefaction tests may still be simulated with FLAC, to verify that these empirical relations lead to a match with the data, and used to adjust the constants if there are differences.

5 Simulation results pore pressure pore pressure effective stress effective stress time time Martin et al formula Byrne formula The curves show the results of shaking table simulations, using the two alternative relations (the actual values of the constants are provided in the FLAC manual). The total normal stress was constant in the simulations.

6 A third simple approach Roth et al have devised a scheme that uses a cyclic-strength curve directly, and generates increments of pore pressure in FLAC. Each cyclic stress excursion (normalized to effective vertical stress) is measured: CSR = τ / σ Then the number of cycles to liquefaction is determined from the cyclic strength curve, and used to compute a damage increment: cy i i D = 0.5/ N L Finally, the generated pore pressure increment is derived from the damage increment: i u = Dσ g v v

7 Roth approach (2) Roth & Dawson (2000) describe this approach, which was used in a full-scale simulation of Pleasant Valley Dam (Roth, Bureau & Brodt, 1991), to calculate the residual deformation that would accumulate during shaking. Although this approach generates pore pressures directly, it is conceptually similar to the previous two simple approaches, which generate volume-strain increments, and use FLAC s coupled logic to calculate the resulting pore pressure changes. The three schemes should give similar results when the fluid is considerably stiffer than the soil (for volumetric compression). The choice of method will probably depend on the ease by which standard test data can be used by the model.

8 Roth approach (3) The scheme has been applied to several cases of dam shaking. The following plot of excess pore pressures is reproduced from Roth, Inel, Davis & Brodt (1993).

9 Full, nonlinear approach In the previous schemes the volume-change calculation is not part of the constitutive law (in fact, a standard Mohr Coulomb law is used). An estimate of cyclic strain (or stress) is made by looking at successive peaks. With a full, nonlinear law, the volume strain evolves continuously as part of the formulation. In the BSHP model mean effective stress decreases with cycling, as shown: Thus, volume-changes, stress changes, pore-pressure changes, damping and plastic flow are integrated into one FLAC model. stress difference mean effective stress

10 Choice of method There seem to be three main approaches (if we restrict ourselves to FLAC as the nonlinear code of choice): 1. Equivalent-linear methods, using empirical schemes to estimate permanent displacements and pore pressure changes after the calculation is finished. 2. Time-marching simulation with FLAC, using simple schemes to represent damping and cyclic volume-changes (leading to pressure and effective stress changes). Deformations and pore pressures accumulate as the calculation proceeds. 3. Time-marching simulation with FLAC, using a comprehensive constitutive law, such as BSHP. There is no need for approximate damping and volume-change schemes.

11 Choice of method cont. The third approach is potentially the closest to reality. In one model, all the important mechanisms are present; e.g. Output from a simulation of New Exchequer Dam by Makdisi, Wang & Edwards (2000), using the BSHP model with FLAC (Fish version).

12 Choice of method cont. However, the simplified approach (#2) uses far fewer material parameters, and is conceptually much simpler (and therefore it s much easier to use common-sense checks on the results). In both FLAC approaches, the evolution of permanent damage, large strain, nonlinear wave effects and pore pressure build-up (& dissipation) are simulated. In contrast, the equivalent linear method takes drastic liberties with physics, although empirical rules and a long history of tuning up allow it to make good predictions. Engineers should at least start using the fully nonlinear approach in addition to the equivalent linear approach. Otherwise no experience will be accumulated.