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完整岩石拉压应力状态下的张裂破坏准则

EXTENSION FAILURE CRITERION FOR INTACT ROCK UNDER TENSION AND COMPRESSION STRESS

  • 摘要: 一点的应力状态可由3个主应力\sigma_1, \sigma_2, \sigma_3来表示, 当规定主应力以压为正时, 沿最大主应力\sigma_1方向将产生收缩变形, 若中间主应力\sigma_2和最小主应力\sigma_3都远小于\sigma_1, 则沿\sigma_2和\sigma_3方向会产生横向扩张变形, 当横向扩张变形达到一定极限时, 将会在平行于\sigma _1的方向产生张裂破坏. 如何建立这种张裂破坏的强度准则目前尚缺乏研究, 最大拉应变理论(第二强度理论)有时被用来解释张裂破坏, 但最大拉应变理论难以应用于三向受力状态. 本文分别用\varepsilon_1, \varepsilon_2表示最大张应变和次大张应变, 则最大拉应变理论认为当\varepsilon_1达到单向拉伸屈服应变时, 材料将产生破坏. 而本文将根据\varepsilon_1+\varepsilon_2之和达到极限值\varepsilon_u来建立张裂破坏准则. 可以证明\varepsilon_1 +\varepsilon_2所表示的是\sigma_1主平面的面积增长率. 当\sigma_3<\sigma_2 \ll \sigma_1时, 大部分岩石都具有脆性破坏的特点, 所以可将破坏前的岩石视为满足广义胡克定律的线弹性材料, 这样用\varepsilon_1, \varepsilon_2表示的强度准则可通过\sigma_1, \sigma_2, \sigma_3来表示. 在这个过程中还可考虑岩石在拉伸和压缩时具有不同弹性参数和强度的特点, 并可通过单向拉伸和单向压缩的破坏状态来确定\varepsilon_u. 不管\sigma_1, \sigma_2, \sigma_3是压应力, 还是拉应力, 或者\sigma_1, \sigma_2, \sigma_3中有拉有压的情形, 基于\varepsilon_1 +\varepsilon_2 =\varepsilon_u都可建立相应的强度准则. 所建立的准则可以反映中间应力\sigma_2对强度的影响规律, 通过建立的强度准则还可以证明: 静水拉力能引起屈服, 而静水压力不能产生屈服; 压缩破坏能使塑性体积增大, 其结果比Mohr-Coulomb准则更能反映实际情形. 并通过拉压应力状态下的试验数据验证了所建立的强度准则, 所得理论计算结果和已有的试验数据吻合得很好. 通过提出的强度准则和圆盘劈裂的试验结果, 可获得更为可靠的岩石单轴抗拉强度.

     

    Abstract: The stress state at a point in the material can be represented by three principal stresses \sigma_1, \sigma_2, \sigma_3. When it is specified that the principal stress is positive in pressure, the shrinkage deformation occurs along the direction of the maximum principal stress \sigma_1. If both the intermediate principal stress \sigma_2 and the minimum principal stress \sigma _3 are far less than \sigma_1, the lateral extending deformation will occur along the direction of \sigma_2 and \sigma_3. When the lateral extending deformation reaches a certain limit, the extending tension failure will occur in the direction parallel to \sigma_1. There is still a lack of research on how to establish the strength criterion of this kind of extending tension failure, the maximum tensile strain theory (the second strength theory) is sometimes used to explain the extending tension failure, but it is difficult to apply it to the triaxial stress state. In this paper, \varepsilon_1, \varepsilon_2 are used to represent the maximum tensile strain and the intermediate tensile strain respectively. Based on the maximum strain theory, the failure will occur if \varepsilon_1 reaches the uniaxial tensile yield strain. The extension failure criterion will be established herein when the sum of \varepsilon _1 +\varepsilon_2 reaches the critical value \varepsilon_u and it can be proved that \varepsilon_1 +\varepsilon_2 actually denotes the extension rate of the \sigma_1-plane. When \sigma_3 <\sigma_2 \ll \sigma_1, most rocks have the characteristics of brittle failure, so the rock material in prefailure stage can be assumed as linear elastic that satisfies the generalized Hooke's law. Thus, the strength criterion expressed by \varepsilon_1 and \varepsilon_2 can be expressed by \sigma_1, \sigma_2, \sigma_3. In this process, the rock's characteristics of different elastic parameters and strength under tension and compression can also be considered, and the failure state of uniaxial tension and uniaxial compression can be used to determine \varepsilon_u. Regardless of whether \sigma_1, \sigma_2, \sigma_3 are compressive stress or tensile stress, or there is tension and compression in \sigma_1, \sigma_2, \sigma_3, corresponding strength criteria can be established based on \varepsilon_1 +\varepsilon_2 =\varepsilon_u. The established criterion can reflect the effect of intermediate principal stress \sigma_2 on the strength. It can also be proved that: like yielding which will happen under the hydrostatic tension but not under the hydrostatic compression; compression failure can increase the plastic volume, and the results can better reflect the actual situation than Mohr-Coulomb criterion. The established strength criterion is verified by experimental data under tension-compression stress state and the theoretical calculation results are in good agreement with the existing test data. Through the proposed strength criterion and the test results of disc splitting, a more reliable uniaxial tensile strength of rock can be obtained.

     

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