Peridynamics for Moisture Diffusion and Crack Propagation in Unsaturated Soil Desiccation
edited-by
edited-by
(Contributed by ZHANG Qing, M.AMM Editorial Board)-
摘要: 非饱和土失水收缩变形是一种水力耦合现象，其诱发的开裂问题严重削弱了土体的水力和力学特性，造成各种潜在的自然灾害. 相对于饱和土体，非饱和土的失水收缩机制更为复杂，受到广泛关注. 为此，提出了一种考虑水-力耦合作用效应的键型近场动力学(PD)模型，探究由于水分变化引起的非饱和土体变形开裂特征. 在该模型中，非饱和土扩散方程由近场动力学微分算子进行重构，键型近场动力学运动方程采用改进的微弹性模量. 然后提出了一种显-隐式混合算法，扩散方程采用显式差分格式求解，运动方程采用隐式整体格式求解，有效避免了两类方程在同一显式格式下时间步不协调的问题. 通过非饱和土块干燥收缩变形和三维土盘干燥开裂的算例分析，验证了模型和算法的有效性. 研究结果表明，所建立的模型和算法能较好地捕捉非饱和土失水收缩开裂的过程.Abstract: Unsaturated soil desiccation cracking is a coupled hydro-mechanical problem. It seriously weakens the hydraulic and mechanical characteristics of soil, causing various natural disasters potentially. For the unsaturated soil, the mechanism of moisture diffusion and deformation is more complicated compared with saturated soil, attracting wide attention. Thus, a coupled hydro-mechanical bond-based peridynamic (BB PD) model was proposed to explore the moisture diffusion and crack propagation in unsaturated soil. Specifically, the moisture diffusion equation for unsaturated soil was recast with the peridynamic differential operator, and an improved micro-modulus was adopted to revise the bond force density in the BB PD. In addition, a hybrid algorithm combining the explicit difference scheme for solving the diffusion equation and the implicit scheme for solving the motion equation was adopted, to avoid the incongruity of time steps for two types equations under the same explicit scheme. The validity of the proposed model and algorithm was verified by the examples on the desiccation of an unsaturated soil block and the desiccation cracking of a 3D unsaturated soil plate. The results show the potential of peridynamics in capturing desiccation cracks of unsaturated soil.
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Key words:
- unsaturated soil /
- hydro-mechanical coupling /
- desiccation cracking /
- peridynamics
edited-byedited-by1) (我刊编委章青来稿) -
图 2 土块的几何模型和边界条件
Figure 2. The geometric model and boundary conditions of the soil block
图 3 水分含量和竖向位移云图
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 3. Contours of the moisture content and the vertical displacement
图 4 a，b和c点水分含量和垂直方向位移近场动力学解与有限差分解
Figure 4. Results comparison between the peridynamics and the finite difference method at points a, b and c
图 5 土盘几何模型与边界条件
Figure 5. The geometrical model and boundary conditions of the soil plate
图 7 H=4 mm截面含水量随时间变化
Figure 7. Moisture content changes with time at the section of H=4 mm
图 8 不同时刻水分含量随深度变化
Figure 8. Moisture content changes with the depth at different moments
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