Mathematical Description and Complete Solution of the Critical State in the Shear Band of Granular Soil
-
摘要: 为正确模拟土体涉及剪切带演化的后失效力学响应，需采用包含细观特征长度的高阶连续介质力学模型. 笔者利用前期所建立的微极亚塑性模型，对颗粒土中剪切带的发展过程进行了分析推导，得到了剪切带临界状态条件下关键变量所满足的非线性微分方程. 该文展示了上述非线性微分方程的简要推导，重点讨论了该非线性微分方程的主要性质、主要参数变化范围和求解途径；通过对剪切带进一步的力学分析补充建立了一个能量方程，使问题具有确定解. 在此基础上，应用数值积分求出了剪切带厚度因子和剪切内应力、变形率分布及剪切速度分布的完全解. 其中剪切带厚度因子对于微极亚塑性模型细观参数的确定具有重要作用.Abstract: High-order continuum models are needed for properly capturing the post-failure mechanical responses of soils involving shear bands. Through analysis on the evolution of shear band in granular soils based on a previously proposed micropolar hypoplastic model, a governing equation for the shear band in the critical state was obtained, which is a special nonlinear ordinary differential equation satisfied by the Cosserat angular velocity. A concise derivation of the governing equation was conducted. The properties of the governing equation, the range of the chief parameter and the approach to the solution were mainly discussed. An energy balance equation was formulated as a complementary condition for the determinant of the problem through analysis on the mechanical properties of the shear band. Then, the complete solutions, including the shear-band thickness factor, the stress distribution, the strain rate components, and the shear velocity, were obtained through numerical integration. The shear band thickness factor is particularly useful in determination of the micro-strength parameter of the constitutive model.
-
图 1 剪切带脱离体及受力示意图及坐标系选取
Figure 1. Schematic diagram for the shear band with applied forces and coordinates
图 2 平面应变条件下Cosserat介质质点自由度
Figure 2. Degrees of freedom of a Cosserat continuum particle in the plane strain condition
图 6 半带厚内$\hat{\theta}(\xi), \hat{\theta}^{\prime}(\xi)$和$\hat{R}(\xi)$
Figure 6. Variations of $\hat{\theta}(\xi), \hat{\theta}^{\prime}(\xi)$ and z(ξ) in the half shear band
图 7 剪切带内正则化应力、偶应力分布
Figure 7. Distributions of the normalized stress and the couple stress components in the shear band
-
[1] ROSCOE K H, SCHOFILD A N, THURAIRAJAH A. Yielding of clays in states wetter than critical[J]. Géotechnique, 1963, 13(3): 211-240. doi: 10.1680/geot.1963.13.3.211 [2] WOOD D M. Soil Behaviour and Critical State Soil Mechanics[M]. Cambridge: Cambridge University Press, 1990. [3] ROSCOE K H. The influence of strains in soil mechanics[J]. Géotechnique, 1970, 20(2): 129-170. doi: 10.1680/geot.1970.20.2.129 [4] VARDOULAKIS I, GRAF B. Calibration of constitutive models for granular materials using data from biaxial experiments[J]. Géotechnique, 1985, 35(3): 299-317. doi: 10.1680/geot.1985.35.3.299 [5] RUDNICKI J W, RICE J. Conditions for the localization of deformation in pressure sensitive dilatant materials[J]. Journal of Mechanics and Physics for Solids, 1975, 23(6): 371-394. doi: 10.1016/0022-5096(75)90001-0 [6] CHAMBON R, CROCHEPEYER S, DESRUES J. Localization criteria for non-linear constitutive equations of geomaterials[J]. Mechanics of Cohesive-Frictional Materials, 2000, 5(1): 61-82. doi: 10.1002/(SICI)1099-1484(200001)5:1<61::AID-CFM83>3.0.CO;2-M [7] ERINGEN A C. Mechanics of micromorphic continua[C]//IUTAM Symposia. Berlin: Springer-Verlag, 1968: 18-35. [8] AIFANTIS E C. On the microstructural original of certain inelastic models[J]. Journal of Engineering Materials and Technology, 1984, 106(4): 326-330. doi: 10.1115/1.3225725 [9] MVHLHAUS H B, VARDOULAKIS I. The thickness of shear band in granular materials[J]. Géotechnique, 1987, 37(3): 271-283. doi: 10.1680/geot.1987.37.3.271 [10] ODA M. Micro-fabric and couple stress in shear bands of granular materials[C]//THORNTON C, ed. Powders and Grains. 1993. [11] HUANG W, NVBEL K, BAUER E. Polar extension of a hpoplastic model for granular materials with shear localization[J]. Mechanics of Materials, 2002, 34(9): 563-576. doi: 10.1016/S0167-6636(02)00163-1 [12] GUDEHUS G. A comprehensive constitutive equation for granular materials[J]. Soil and Foundations, 1996, 36(1): 1-12. doi: 10.3208/sandf.36.1 [13] BAUER E. Calibration of a comprehensive hypoplastic model for granular materials[J]. Soils and Foundations, 1996, 36(1): 13-26. doi: 10.3208/sandf.36.13 [14] NVBEL K, HUANG W. A study of localized deformation pattern in granular media[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(27/29): 2719-2743. [15] HUANG W, SLOAN S W, SHENG D. Analysis of plane Couette shear test of granular media in a Cosserat continuum approach[J]. Mechanics of Materials, 2014, 69(1): 106-115. doi: 10.1016/j.mechmat.2013.09.008 -
下载:
点击查看大图
计量
- 文章访问数: 89
- HTML全文浏览量: 33
- PDF下载量: 27
- 被引次数: 0
