断续节理岩体破坏过程的数值分析方法研究
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摘要
众所周知,岩体的断裂破坏与内部裂纹的萌生、扩展及贯通有关,但现有的数值计算方法难以模拟裂纹萌生、开叉、汇交等问题,本文提出了一种断续节理岩体断裂破坏分析方法DDARF(Discontinuous Deformation Analysis for Rock Failure),亦即用改进的不连续变形分析方法来模拟岩体的断裂破坏过程。
首先,采用Monte-Carlo方法在计算区域内生成随机节理网络。然后,在节理网络上采用计算网格自动生成技术—行波法,将计算区域离散为细密的三角形块体系统,块体的力学参数采用Weibull分布,以模拟岩体的不均匀性。然后,采用粘结算法,对块体剖分过程中产生的虚拟节理,即连续区的块体边界,进行粘结处理,将虚拟节理两边的块体粘结起来,以模拟连续区特性,而虚拟节理的粘结强弱可以直接通过粘结力来反映,其动态变化将决定裂纹沿块体边界的扩展,并加入块体内部的开裂算法,用以模拟裂纹穿过块体的扩展,这样,裂纹扩展就可以通过粘结失效和块体开裂而模拟出来。针对本文的算法,编制了相应的C++程序模块,并加入到石根华教授的DDA程序中,形成了岩体裂纹扩展、破坏分析计算程序DDARF。采用DDARF程序计算了大量的算例,分别模拟了单轴压缩、巴西圆盘、单轴拉伸、粱三点弯曲试验,研究了不同试件中的裂纹扩展情况,并分析了不同应力状态下的裂纹扩展规律。DDARF计算结果与相关试验结果、其它数值方法模拟结果的吻合,验证了本文算法的正确性。最后,将DDARF方法应用到实际工程中,研究了复杂情况下的裂纹扩展情况及岩体破坏过程。DDARF方法适用于岩体连续、断续、完全离散的情形,可以模拟出裂纹萌生、扩展、贯通、直至岩体崩塌破坏的全过程。
此外,为了研究爆炸产生的应力波在节理岩体中的传播问题,在DDA中加入了一种新的边界条件—无反射边界,并研究了节理面对爆炸波传播的影响,以及爆炸波在节理岩体中的传播及衰减规律,为DDARF方法在岩体动力学领域的应用奠定了基础。
The failure of rock mass is related to the generation, propagation and coalescence of interior cracks, so the study on the law of crack propagation is very necessary for uncovering the mechanism of rock failure and estimating the safety of rock structures. Owing to the mechanical and geometrical complexity of crack propagation, numerical simulation is the most effective tool among the available investigation approaches. However, the commonly-employed numerical methods can not simulate some phenomena in rock failure, such as new crack generation, crack branching, multi crack interaction etc. Against this background, based on the discontinuous deformation analysis (DDA) method, DDARF (discontinuous deformation analysis for rock failure) is proposed in this thesis.
In the proposed method, the random joint network is produced in the area of interest by using Monte-Carlo technique. On the basis of the joint network, the triangular DDA block system is automatically generated by adopting the FE adaptive mesh generation technique—the advanced front method. To simulate the heterogeneity of rock mass, the randomly distributed mechanical parameters statistically satisfying Weibull’s law are assigned to these blocks. In the process of generating blocks, numerous artificial joints come into being, and they provide the potential paths along which the cracks generate and propagate. The blocks between artificial joint are glued together by adhesive algorithm, and if the glue is invalid, the artificial joint will break and become real crack. In order to eliminate the effect of block boundary on crack propagation path, the fracturing algorithm within one block is established. In this way, the rock failure process can be simulated. Based on the proposed algorithms, the corresponding C++ program module is developed and incorporated into the original DDA code, i.e. the DDARF grogram. For verification, a series of numerical examples are computed to simulate the propagation and coalescence of the closed joints in different rock samples under different loading conditions. The simulated results agree well with the existing experimental and numerical results, indicating that the proposed algorithms are correct and valid. Finally, the rock failure process under more complex condition of some concrete rock engineerings is modeled. With the introduction of the artificial joint concept into the discontinuum-based DDA, DDARF can be applied to simulate the cases of continuum, semicontiuum, as well as discontinuum, without any mathematic difficulty. Moreover, it can easily simulate the generation, propagation and coalescence of rock crack, and the whole process of rock failure is thereafter reproduced.
In addition, for modeling dynamic problems by DDA method, a new boundary condition, namely non-reflecting boundary or viscous boundary, is presented in this thesis. The approach is to attach the independent dashpots along the normal and shear directions of specific boundaries, in this way, the energy of stress waves can be absorbed efficiently when the stress waves reach those boundaries, and non-reflecting condition is achieved. The proposed viscous boundary condition is incorporated into the DDA code. To verify the effect of absorbing stress wave of viscous boundary, some examples are calculated, and the numerical results are compared with the test data. This work provides the fundamental for DDARF to simulate the dynamic failure of rock mass.
首先,采用Monte-Carlo方法在计算区域内生成随机节理网络。然后,在节理网络上采用计算网格自动生成技术—行波法,将计算区域离散为细密的三角形块体系统,块体的力学参数采用Weibull分布,以模拟岩体的不均匀性。然后,采用粘结算法,对块体剖分过程中产生的虚拟节理,即连续区的块体边界,进行粘结处理,将虚拟节理两边的块体粘结起来,以模拟连续区特性,而虚拟节理的粘结强弱可以直接通过粘结力来反映,其动态变化将决定裂纹沿块体边界的扩展,并加入块体内部的开裂算法,用以模拟裂纹穿过块体的扩展,这样,裂纹扩展就可以通过粘结失效和块体开裂而模拟出来。针对本文的算法,编制了相应的C++程序模块,并加入到石根华教授的DDA程序中,形成了岩体裂纹扩展、破坏分析计算程序DDARF。采用DDARF程序计算了大量的算例,分别模拟了单轴压缩、巴西圆盘、单轴拉伸、粱三点弯曲试验,研究了不同试件中的裂纹扩展情况,并分析了不同应力状态下的裂纹扩展规律。DDARF计算结果与相关试验结果、其它数值方法模拟结果的吻合,验证了本文算法的正确性。最后,将DDARF方法应用到实际工程中,研究了复杂情况下的裂纹扩展情况及岩体破坏过程。DDARF方法适用于岩体连续、断续、完全离散的情形,可以模拟出裂纹萌生、扩展、贯通、直至岩体崩塌破坏的全过程。
此外,为了研究爆炸产生的应力波在节理岩体中的传播问题,在DDA中加入了一种新的边界条件—无反射边界,并研究了节理面对爆炸波传播的影响,以及爆炸波在节理岩体中的传播及衰减规律,为DDARF方法在岩体动力学领域的应用奠定了基础。
The failure of rock mass is related to the generation, propagation and coalescence of interior cracks, so the study on the law of crack propagation is very necessary for uncovering the mechanism of rock failure and estimating the safety of rock structures. Owing to the mechanical and geometrical complexity of crack propagation, numerical simulation is the most effective tool among the available investigation approaches. However, the commonly-employed numerical methods can not simulate some phenomena in rock failure, such as new crack generation, crack branching, multi crack interaction etc. Against this background, based on the discontinuous deformation analysis (DDA) method, DDARF (discontinuous deformation analysis for rock failure) is proposed in this thesis.
In the proposed method, the random joint network is produced in the area of interest by using Monte-Carlo technique. On the basis of the joint network, the triangular DDA block system is automatically generated by adopting the FE adaptive mesh generation technique—the advanced front method. To simulate the heterogeneity of rock mass, the randomly distributed mechanical parameters statistically satisfying Weibull’s law are assigned to these blocks. In the process of generating blocks, numerous artificial joints come into being, and they provide the potential paths along which the cracks generate and propagate. The blocks between artificial joint are glued together by adhesive algorithm, and if the glue is invalid, the artificial joint will break and become real crack. In order to eliminate the effect of block boundary on crack propagation path, the fracturing algorithm within one block is established. In this way, the rock failure process can be simulated. Based on the proposed algorithms, the corresponding C++ program module is developed and incorporated into the original DDA code, i.e. the DDARF grogram. For verification, a series of numerical examples are computed to simulate the propagation and coalescence of the closed joints in different rock samples under different loading conditions. The simulated results agree well with the existing experimental and numerical results, indicating that the proposed algorithms are correct and valid. Finally, the rock failure process under more complex condition of some concrete rock engineerings is modeled. With the introduction of the artificial joint concept into the discontinuum-based DDA, DDARF can be applied to simulate the cases of continuum, semicontiuum, as well as discontinuum, without any mathematic difficulty. Moreover, it can easily simulate the generation, propagation and coalescence of rock crack, and the whole process of rock failure is thereafter reproduced.
In addition, for modeling dynamic problems by DDA method, a new boundary condition, namely non-reflecting boundary or viscous boundary, is presented in this thesis. The approach is to attach the independent dashpots along the normal and shear directions of specific boundaries, in this way, the energy of stress waves can be absorbed efficiently when the stress waves reach those boundaries, and non-reflecting condition is achieved. The proposed viscous boundary condition is incorporated into the DDA code. To verify the effect of absorbing stress wave of viscous boundary, some examples are calculated, and the numerical results are compared with the test data. This work provides the fundamental for DDARF to simulate the dynamic failure of rock mass.
引文
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