MODELING OF DEFORMATION-CRACKING PROCESSES OF GEOMATERIALS BASED ON A CONTINUUM-DISCONTINUUM METHOD: A CASE STUDY OF COMPACT TENSION TEST
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摘要: 地质体材料易发生拉裂，为了有效模拟地质体材料的变形-拉裂过程，自主研发了一种连续-非连续方法。该方法实质是拉格朗日元法与虚拟裂缝模型的耦合，既能较准确模拟应力应变场，又能较准确模拟连续介质向非连续介质转化的复杂过程。以岩样紧凑拉伸试验为例开展变形-拉裂过程研究，得到以下结果。紧凑拉伸岩样的变形-拉裂过程：在岩样的Ⅴ形缺口尖端附近出现最大主应力集中现象；节点发生分离，虚拟或真实裂缝扩展，最大主应力始终集中于虚拟裂缝的尖端位置；岩样被拉裂成两部分。最大不平衡力发生1次突增对应着1个节点的分离。在峰值之前，岩样的载荷-位移曲线表现出了硬化现象；随着岩样尺寸的增加，应力-应变曲线的峰值有所下降，这与Bazǎnt的尺度律相一致，且峰后应力-应变曲线的陡峭程度增大。目前针对紧凑拉伸试验的模拟结果是合理的，由此在一定程度上说明了提出的连续-非连续方法在连续介质向非连续介质转化模拟方面的突出能力。Abstract: Geomaterials are easily subject to tensile cracking. To model effectively deformation-cracking processes of geomaterials, a continuum-discontinuum method is developed, which is a combination of the Lagrangian element method and the fictitious crack method. This method can be used to more accurately model the stress and strain fields and the complex transition process from the continuum medium to the discontinuum medium. To demonstrate the ability of this method, deformation-cracking processes of rock specimens under compact tension are modeled. The following results are found. Deformation-cracking processes of rock specimens under compact tension are as follows:firstly, the concentrated maximum principal stress is observed at the tip of the Ⅴ-shaped notch; secondly, nodes get separated, fictitious or real cracks extend, and the concentrated maximum principal stress is at the tip of the Ⅴ-shaped notch all the time; finally, the rock specimen is split to two parts. A rapid increase in the maximum unbalanced force corresponds to a nodal separation. Load-displacement curves exhibit strain-hardening phenomena at pre-peak. The peak of stress-strain curve decreases with an increase of the size of the rock specimen, which is consistent with the scaling law of Bazǎnt. Moreover, the post-peak stress-strain curve becomes steep with an increase of the size of the rock specimen. The present numerical results of rock specimens under compact tension are reasonable, indicating the apparent ability of the present continuum-discontinuum method to model the transition process from the continuum medium to the discontinuum medium.
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图 1 虚拟裂缝面上节点处法向的确定
①-④为虚拟裂缝面附近的单元；a-f为虚拟裂缝面上的节点；n1-n4为虚拟裂缝面的外法向；nc和nd分别为虚拟裂缝面上节点c和d的外法向
Figure 1. Determination of normal directions of nodes on fictitious cracking faces
图 2 岩样变形—开裂过程中σ3的时空分布规律(方案1)
Figure 2. Spatiotemporal distribution of σ3 during the deformation-cracking process (scheme 1)
图 4 岩样变形—开裂过程中σ3的时空分布规律(方案2)
Figure 4. Spatiotemporal distribution of σ3 during the deformation-cracking process (scheme 2)
图 6 岩样变形—开裂过程中σ3的时空分布规律(方案3)
Figure 6. Spatiotemporal distribution of σ3 during the deformation-cracking process (scheme 3)
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