Investigation of Liquefaction Mechanism in Double Sand Lenses
M.Sc., Department of civil Eng.
Amirkabir University of Technology, Iran
and
Associate Professor, Department of Civil Eng.
Amirkabir University of Technology, Iran
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Investigation of Liquefaction Mechanism in Double Sand Lenses
M.Sc., Department of civil Eng. and Associate Professor, Department of Civil Eng. |
ABSTRACT
In many cases of heavy earthquakes, liquefaction has resulted in serious damages. Existing anisotropy in soil layers results in some difficulties to realize the reason for these phenomena. Loose sand lenses buried in fine soils are one of the cases which may result in these problems and as a weak point during the earthquake can cause this phenomenon. In this paper, using FLAC 2D software, double sand lenses liquefaction mechanism and soil deformation due to applying cyclic loading has been studied and investigated. The FLAC software that has been used for analyzing is capable of modeling progressed models of soil and loading under different conditions.
Keywords: Keywords: Liquefaction; Ground Failure; Cyclic Loading; Double sand lenses; Deformation
INTRODUCTION
On many occasions, liquefaction occurs during earthquakes. For soils, especially those consisting of loose saturated cohesionless material in seismically active areas, if drainage is unable to occur during the period of the loading sequence, then the tendency for volume reduction in each cycle of loading results in a corresponding progressive increase in pore water pressure. If the effective stress becomes zero and the sand having lost its strength it maybe said to have liquefied, although this maybe only a temporary state.
Ground failure in the form of sand boils, lateral spreads and settlement is the common effect of liquefaction in soil deposits. However, in many regions with proper soil specifications, the large deformation has been observed in the ground surface. These areas that have been placed near the seas contain some sedimentary layers of loose and comparatively uniform fine sand surrounded by clayey or silty soils. The deformation of these areas after earthquake is related to liquefaction of these sand layers-named sand lenses.
In current study, by making use of previous studies results, the behavior of double sand lenses subjected to dynamic loading has been studied. So, the sand lenses and surrounding fine soils have been modeled by FLAC software. FLAC is a two-dimensional explicit finite difference program for engineering mechanics computation. This program simulates the behavior of structures built of soil, rock or other materials that may undergo plastic flow when their yield limits are reached. The dynamic feature in this software can be coupled to the ground water flow model; this permits analyses involving time-dependent pore pressure change associated with liquefaction.
MODEL GENERATION
To generate the model, a mesh has been used with 100m length and 20m height. Then, double sand lenses with 8m length and 4m free space were placed in the mentioned model. As it was shown in Figures 1 and 2, the ellipse geometry has been chosen for sand lenses shape and the water table is in ground surface elevation. So, sand lenses and surrounding fine soils are completely saturated.
Figure 1. The mesh has been used for modeling
Figure 2. The sand lenses and surrounding fine soil materials
As it was shown in Figure 3, the Mohr-Coulomb model has been used to model the behavior of surrounding clayey soil. This constitutive model is the conventional model used to represent stress-strain behavior and corresponding shear failure in soils and rocks. The strength-deformation characteristics related to surrounding fine soil are set to clay with medium plasticity and are shown in Table 1.
Figure 3. Geometric parameters of sand lenses and surrounding soil
(L=2a=8m; D=2b=2.66m; d=4m; Zo=8m; Zmin=6.66m)
Table 1. Clayey soil specifications
used for analysis
Considering Finn model (active in dynamic mode) the behavior of loose and saturated sand lenses during dynamic loading is simulated. This model captures the basic mechanisms that can lead to liquefaction in sand. The maximum shear and bulk modulus in sand soil have been computed based on Seed and Idriss method. These values associated with other soil parameters have been shown in Table 2.
Table 2. Sand soil parameters
used for analysis
STATIC ANALYSIS
In this stage, initial stress and pore water pressure in the model should be computed. Therefore, the model subjected to its weight is analyzed statically. The results obtained from this analysis have been shown in Figures 4 to 6 as stress and pore pressure contours.
Figure 4. Initial total stress contours in the model
Figure 5. Initial effective stress contours in the model
Figure 6. Initial pore pressure contours in the model
DYNAMIC ANALYSIS
Numerical methods relying on the discretization of a finite region of space require the appropriate conditions be enforced at the artificial numerical boundaries. In static analyses, fixed or elastic boundaries can be realistically placed at some distance from the region of interest. But in dynamic problems, however, such boundary conditions cause the reflection of upward propagating waves back into the model and do not allow the necessary energy radiation. So, by making use of FLAC software abilities, the boundary conditions were converted from simple to free-field boundaries. These conditions cause absorbing most of the energy in the wave reflected from side boundaries and preventing disorder of propagating waves. Also, dynamic input was applied to the base of the model as a sine acceleration wave in x-direction corresponding to the xy-axes for the model. Considering the amplitude of this wave, amax = 0.2g, the frequency, f = 5 Hz, and duration, td = 10 sec, the mechanism of sand lenses liquefaction and soil deformation due to this event were studied.
As it was shown in Figure 7, the effective stress in sand lenses tends to zero after 12 cycles of loading (t = 2.4 sec) and liquefaction occurs in sand soils. Also, the pore water pressure changes prior to loading has been presented in Figure 8. It can be seen that the pore water pressure in sand lenses increases during cyclic loading and after a maximum magnitude at t =2.4 sec of loading, obtains a relatively constant level to end of the loading.
Figure 7. Vertical effective stress in sand lenses during cyclic loading
Figure 8. Pore water pressure in sand lenses during cyclic loading
The residual pore water pressure at the end of each cycle increases progressively with increasing number of cycles. The rate of pore water pressure development accelerates as liquefaction is approached; at which point strain amplitudes rapidly increase (Figure 9).
Figure 9. Shear strain increase in sand lenses elements during loading
Figures 10 and 11 represent vertical effective stress and pore water pressure contours at the end of loading, respectively.
Figure 10. The effective stress contours at the end of loading
Figure 11. The pore pressure contours at the end of loading
To model the stress-strain behavior of sand soils during dynamic loading, a program was prepared in C++. So, the hysteresis loops were modeled prior to increase in shear strain in sand lenses as shown in figure 12. It can be seen that shear modulus decreases with increasing shear strain and at the end of loading the shear modulus magnitude decreases to 5 percent of initial value.
Figure 12. The hysteresis loops in sand lenses during cyclic loading
The soil vertical displacement after liquefaction of sand lenses is shown as contours in figure 13. It can be observed that occurring liquefaction in double sand lenses and settlement formation in sand soils, a bowled settled media in the middle of double sand lenses is established. Also, the maximum magnitude of soil settlement occurs near the liquefied lenses while this deformation decreases with increasing distance of lenses horizontally and vertically. So, in a distance of approximately 3 to 4 times of lenses length, the settlements are negligible.
Figure 13. Soil vertical deformation contours due to liquefaction of double sand lenses
POST-LIQUEFACTION ANALYSIS
At the end of dynamic loading, the soil surrounded by lenses is completely liquefied and the effective stress in sand lenses approaches approximately zero. In this occasion, with beginning of sand soil consolidation and excess pore pressure dissipation the effective stresses increase gradually. So, a post-liquefaction analysis has been performed to illustrate the mechanism of excess pore pressure dissipation. The excess pore water pressure dissipation after 1, 10, 30 and 60 minutes of loading are shown in figures 14 to 17. It can be seen that the pore pressure decrease has a high rate at first and then its rate becomes lower, so that, huge time is needed for complete pore pressure dissipation.
Figure 14. The excess pore water pressure dissipation after 1 minute of loading
Figure 15. The excess pore water pressure dissipation after 10 minutes of loading
Figure 16. The excess pore water pressure dissipation after 30 minutes of loading
Figure 17. The excess pore water pressure dissipation after 60 minutes of loading
Figures 18 through 21 show increasing soil vertical deformation after 1, 10, 30 and 60 minutes of loading. Considering theses figures, increase in soil layers deformation after loading occurs very slowly, so that, just 4 mm of settlement is added to existing deformation after 60 minutes of loading.
Figure 18. The maximum soil vertical deformation after 1 minute of loading
Figure 19. The maximum soil vertical deformation after 10 minutes of loading
Figure 20. The maximum soil vertical deformation after 30 minutes of loading
Figure 21. The maximum soil vertical deformation after 60 minutes of loading
SUMMARY AND CONCLUSIONS
In this paper, the mechanism of double sand lenses liquefaction and soil deformation are studied. So, effective stress decrease, pore pressure increase and upper soil layers settlement are simulated by FDM. Also, based on the analyses performed by FLAC software presented in this paper, the following conclusions are reached:
REFERENCES
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