A nonlinear cyclic constitutive model for soils considering pore-water-soil-skeleton coupling effects and its numerical realization in 3D stress space
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摘要: 波浪作用导致海床土体产生复杂的流固耦合效应，即土体受到正应力差和剪应力的三维耦合剪切作用，瞬态超孔隙水压力呈振荡与累积两种增长模式且引起土体循环软化。现有Masing型非线性动力本构模型未能完全考虑该流固耦合效应。现将Davidenkov骨架曲线拓展至三维应力空间，采用“扩展Masing”法则构造土体应力–应变滞回曲线，基于Biot动力固结理论，将Byrne提出的剪切-体积应变耦合模型引入体积相容方程作为累积超孔压增长的源项，建立了一个可描述流固耦合效应的土体非线性动力本构模型。基于FLAC3D计算平台实现了该本构模型的二次开发，通过与模型理论值对比保证了程序的计算精度，与土单元循环扭剪试验对比验证了该本构模拟土体动力流固耦合效应的可行性与合理性，为利用FLAC3D进行海洋岩土工程的研究提供了有效手段。Abstract: Wave action leads to complex pore-water-soil-skeleton coupling effects of seabed soils, that is, the soils are subjected to three-dimensional coupled shear action of normal stress difference and shear stress, and the transient excess pore water pressure increases in two modes of oscillation and accumulation, resulting in cyclic softening of soils. Most of the already-established Masing nonlinear dynamic constitutive models have failed to fully consider the growth mode of the excess pore water pressure and the cyclic softening effects of the soil skeleton. In this study, the Davidenkov skeleton curve is extended to the three-dimensional stress space, and the stress-strain hysteresis curve of soils is constructed by the "extended Masing" rule. Based on the Biot dynamic consolidation theory, the shear volume strain coupling model proposed by Byrne is introduced into the fluid continuity equation as the source term of the growth of the cumulative excess pore pressure, and a nonlinear dynamic constitutive model for soils is established to describe the pore-water-soil-skeleton coupling effects. Based on the FLAC3D platform, the secondary development of the constitutive model is realized. The calculation accuracy of the program is validated by comparing with the theoretical solution of the model. The feasibility and the rationality of the proposed nonlinear dynamic constitutive model to deal with such problems are verified by comparing with the soil element cyclic torsional shear tests. It provides an effective means for the study on marine geotechnical engineering using the FLAC3D.
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图 2 DavByrne模型描述的应力-应变关系曲线示意图
Figure 2. Shear stress-strain curves described by DavByrne model
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图 3 考虑流固耦合效应的非线性动力模型程序流程图
Figure 3. Program flowchart of nonlinear dynamic constitutive model considering pore-water-soil-skeleton coupling effects
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图 7 计算与理论的应力-应变关系曲线对比
Figure 7. Comparison of stress-strain relationship curvess between calculation and theory
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图 10 波浪荷载作用下试验与DavByrne模型和Finn模型的超孔压结果对比
Figure 10. Comparison of results among tests, DavByrne model and Finn model under wave loading
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图 11 地震作用下试验与DavByrne模型的超孔压比结果对比
Figure 11. Comparison of excess pore pressure ratios between tests and DavByrne model under seismic loading
表 1 模拟循环剪切试验模型参数
Table 1 Model parameters of simulated cyclic shear tests
剪切模量G/MPa Davidenkov模型 Byrne模型 A B γ0/10-4 σ′ref/kPa C1 C2 γth/% 50 1.02 0.35 4 100 0.43 0.93 0.02 
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表 2 模拟循环三轴试验模型参数
Table 2 Model parameters of simulated cyclic triaxial tests
剪切模量G/MPa Davidenkov模型 Byrne模型 A B γ0/10-4 σ′ref/kPa C1 C2 γth/% 53 1.02 0.43 4.1 100 0.55 1.38 0.02
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