Cyclic liquefaction behavior of silty sand considering initial static shear effect: a DEM investigation
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摘要: 为研究含细粒砂土液化行为的微观机理，采用颗粒流程序PFC3D模拟了砂土在不排水循环荷载下液化特性，将含有少量细粒的砂土试样与净砂在相同初始状态参数下的循环响应进行了对比，研究了初始静剪和细粒含量对砂土动力液化特性的影响。模拟结果显示，不同静剪应力条件下，含细粒砂土呈现出两种典型的液化破坏模式：循环流动和残余变形累积。当试样表现为循环流动型响应时，配位数逐渐减小至4；而当土体破坏由残余变形累积导致时，配位数变化较小且组构模量始终大于0。相同初始状态和应力条件下，含细粒砂土在循环加载过程中的配位数变化量较净砂大，其抗液化能力也相应较大。此外，随着静剪应力增加，试样的配位数变化量逐渐增大，其抗液化动强度也随之增大。Abstract: To gain more insights into the microscopic mechanism of the liquefaction behavior, the particle flow program PFC3D is used to simulate the liquefaction process of silty sands under undrained cyclic loading. The effects of the initial static shear stress and fines content on the cyclic liquefaction behavior of sand are investigated. The simulation responses of silty sand containing a small amount of fines are compared with those of clean sand under the same initial state parameters. The simulated results show that regardless of the fines content, different initial static shear stress conditions can result in two liquefaction failure patterns: cyclic mobility and residual deformation accumulation. Generally, the samples exhibit cyclic mobility accompanied by a decrease in the coordination number. The coordination number of samples under residual deformation accumulation changes slightly, while the fabric norm F is always greater than zero as the cyclic shearing proceeds. Under the identical initial state and stress conditions, the coordination number variation of fine-grained sand during cyclic loading is larger than that of clean sand, and its liquefaction resistance is also larger. Furthermore, a higher initial static shear level leads to a larger change in the coordination number and also an increase in the cyclic liquefaction resistance.
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图 5 qmax或qmin相等时应力条件示意图
Figure 5. Diagram of stress conditions under equal qmax or qmin
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图 6 等向固结下净砂循环液化响应
Figure 6. Cyclic liquefaction response of clean sand under isotropic consolidation
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图 7 等向固结下含细粒砂土循环液化响应（fc = 5%）
Figure 7. Cyclic liquefaction responses of silty sand under isotropic consolidation (fc = 5%)
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图 8 等向固结下含细粒砂土循环液化响应（fc = 10%）
Figure 8. Cyclic liquefaction responses of silty sand under isotropic consolidation (fc = 10%)
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图 9 不同初始静剪下5%含细粒砂土的应力应变曲线
Figure 9. Stress-strain curves of sand with fc = 5% under various initial static shear stresses
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图 10 不同初始静剪下10%含细粒砂土的应力应变曲线
Figure 10. Stress-strain curves of sand with fc = 10% under various initial static shear stresses
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图 11 不同SSR下的破坏振次Nf（CSR = 0.25）
Figure 11. Number of cycles for failure (Nf) under various SSRs (CSR = 0.25)
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图 12 净砂在3种加载模式下的应力应变曲线（qmax = 350 kPa）
Figure 12. Stress-strain curves of clean sand under different loading modes (qmax = 350 kPa)
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图 13 10%含细粒砂在不同加载模式下的应力应变曲线（qmin = -350 kPa）
Figure 13. Stress-strain curves of sand with fc = 10% under different loading modes (qmin = -350 kPa)
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图 14 10%含细粒砂在不同加载模式下的配位数演化
Figure 14. Evolution of coordination number of sand with fc = 10% under various loading modes
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图 16 不同应力条件下的∆Zm及循环响应类型总结
Figure 16. Summary of cyclic behavior types and ∆Zm under various stress conditions
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图 17 qmax相同时净砂在不同加载模式下组构模量演化
Figure 17. Evolution of fabric norm of clean sand under different loading modes and same qmax
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图 18 不同应力条件下的Ff及循环响应类型总结
Figure 18. Summary of cyclic behavior types and Ff under various stress conditions
表 1 数值模拟参数
Table 1 Parameters for numerical simulation
颗粒密度ρ /(kg·m-3) 法向刚度kn/(N·m-1) 切向刚度ks/(N·m-1) 颗粒间摩擦系数μ 阻尼比
β2600 105 105 0.5 0.7 
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表 2 极孔隙比与临界孔隙比汇总
Table 2 Limit void ratios and critical void ratios of samples
fc/% emax emin ec Dr/% 0 0.872 0.557 0.744 48.6 5 0.826 0.479 0.700 43.5 10 0.734 0.373 0.610 41.3
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表 3 不排水循环三轴模拟方案
Table 3 Schemes of undrained cyclic triaxial simulation
qs/
kPaqcyc/
kPaSSR CSR Nf_0 Nf_5 Nf_10 加载模式 0 250 0 0.25 12 19 31 SR 50 250 0.05 0.25 13 26 41 SR 100 250 0.1 0.25 10 30 53 SR -50 250 -0.05 0.25 8 21 29 SR -100 250 -0.1 0.25 6 16 17 SR 0 350 0 0.35 2 5 2 SR 50 300 0.05 0.3 4 14 15 SR 175 175 0.175 0.175 35 93 201 IR 200 150 0.2 0.15 57 172 — NR -50 300 -0.05 0.3 3 9 10 SR -175 175 -0.175 0.175 13 — 42 IR -200 150 -0.2 0.15 20 — 84 NR 注：Nf_0、Nf_5和Nf_10分别对应细粒含量为0、5%和10%试样的破坏振次；SR为应力翻转模式；IR为中间应力翻转模式；NR为无应力翻转模式。
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