界面元法的开裂和损伤梯度模型及其工程应用
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摘要
拱坝—地基系统稳定分析中对坝肩破坏的研究至关重要,而目前广泛采用的有限元法不能够有效地模拟岩石基础中断层、节理等薄弱面的不连续特性。基于此,本文引入界面元数值方法,以模拟岩基中的不连续界面,并对坝肩稳定及岩体的开裂扩展加以研究。主要内容包括:
1.为了模拟岩石类材料在复杂受力条件下的裂纹扩展,本文除了应用Mohr-Coulomb准则和最大拉应力准则外,还在模拟复合型裂纹特征方面提出以能量释放率准则作为开裂判据,并且根据界面元方法中开裂集中于界面的特点,提出了双材料界面开裂的处理方法,尝试对岩体中的断层等不连续面的材料特性和开裂特征进行模拟。
2.将损伤模型引入界面元方法中,模拟了材料屈服后实际承载力逐渐弱化的过程,并研究了岩石类材料中的破坏准则及分析方法。
3.讨论了非线性计算中界面元方法的网格依赖性问题,在损伤模型的基础上,引入了损伤梯度的方法,将非局部等效应变作为单元位移之外的另一未知量引入基本方程中,从而构造了损伤梯度模型的界面元迭代方法。通过对算例的计算分析,说明本文提出的方法能够有效地控制网格依赖性的出现。
4.利用界面元方法能够直接求得界面应力的特点,计算危险滑动面的抗滑稳定安全系数,结合工程实例校核了坝肩及基础中危险滑块的安全系数,并对最危险滑动面进行搜索。
5.对上述开裂模型和损伤梯度模型编制了计算程序,并将程序应用于小湾拱坝(1170高程的平面分析及锦屏拱坝的整体稳定分析中,模拟了坝肩沿断层、蚀变带及节理等滑动面的开裂、滑移现象以及损伤演化过程,并校核危险滑块的抗滑稳定安全系数。将计算结果与模型试验结果对比,展示了界面元方法在拱坝—地基系统稳定分析中的应用前景。
Study of abutment failure is important in stability analysis of arch dam-foundation systems. FEM cannot effectively simulate the faults and joints in rock foundations. Considering this, interface stress element method (ISEM) is presented to simulate discontinuous interfaces in rock foundations, and furthermore to study stability of dam abutment and crack propagation. The main contents of this paper are summarized as below:
Maximum energy release rate criterion is proposed to trace crack growth under various load-cases besides of Mohr-Coulomb criterion and maximum tensile stress criterion. Considering the characteristic of ISEM that the crack is concentrating on the interfaces, method of interfacial crack in bi-material is introduced in ISEM for the simulation of material characteristics and fracture behaviors.
The damage variable is introduced into the constitutive relation of ISEM to describe the decrease of loading capability after yield. Fracture criterion based on rock materials are researched as well as its analysis method.
The problem of mesh dependence in nonlinear calculation of ISEM is discussed and the gradient enhanced damage model is adopted on the basis of damage model. Nonlocal equivalent strain is introduced to the basic equations as another independent variable besides the displacements, thus iteration method of ISEM is constructed. Case studies are made, and through comparing numerical results with experimental results, the advantages of this method in avoiding mesh dependence are justified.
With the convenience of ISEM in obtaining interfacial stresses, stability safety factor of sliding surface is deduced. The safety factors of critical blocks in dam abutments and foundations are checked, and the riskiest sliding surfaces can be searched.
A program is developed and applied to 2D analysis of (1170 elevation of Xiaowan arch dam and 3D stability analysis of Jinping arch dam. Cracking and sliding in the riskiest sliding surfaces (e.g. faults, alteration zones, joints,
etc.) and damage evolution are simulated, and stability safety factors of blocks in rock foundation are checked. With the comparison between numerical results and experimental results, the applicability of ISEM in analyzing arch dam – foundation systems is revealed.
1.为了模拟岩石类材料在复杂受力条件下的裂纹扩展,本文除了应用Mohr-Coulomb准则和最大拉应力准则外,还在模拟复合型裂纹特征方面提出以能量释放率准则作为开裂判据,并且根据界面元方法中开裂集中于界面的特点,提出了双材料界面开裂的处理方法,尝试对岩体中的断层等不连续面的材料特性和开裂特征进行模拟。
2.将损伤模型引入界面元方法中,模拟了材料屈服后实际承载力逐渐弱化的过程,并研究了岩石类材料中的破坏准则及分析方法。
3.讨论了非线性计算中界面元方法的网格依赖性问题,在损伤模型的基础上,引入了损伤梯度的方法,将非局部等效应变作为单元位移之外的另一未知量引入基本方程中,从而构造了损伤梯度模型的界面元迭代方法。通过对算例的计算分析,说明本文提出的方法能够有效地控制网格依赖性的出现。
4.利用界面元方法能够直接求得界面应力的特点,计算危险滑动面的抗滑稳定安全系数,结合工程实例校核了坝肩及基础中危险滑块的安全系数,并对最危险滑动面进行搜索。
5.对上述开裂模型和损伤梯度模型编制了计算程序,并将程序应用于小湾拱坝(1170高程的平面分析及锦屏拱坝的整体稳定分析中,模拟了坝肩沿断层、蚀变带及节理等滑动面的开裂、滑移现象以及损伤演化过程,并校核危险滑块的抗滑稳定安全系数。将计算结果与模型试验结果对比,展示了界面元方法在拱坝—地基系统稳定分析中的应用前景。
Study of abutment failure is important in stability analysis of arch dam-foundation systems. FEM cannot effectively simulate the faults and joints in rock foundations. Considering this, interface stress element method (ISEM) is presented to simulate discontinuous interfaces in rock foundations, and furthermore to study stability of dam abutment and crack propagation. The main contents of this paper are summarized as below:
Maximum energy release rate criterion is proposed to trace crack growth under various load-cases besides of Mohr-Coulomb criterion and maximum tensile stress criterion. Considering the characteristic of ISEM that the crack is concentrating on the interfaces, method of interfacial crack in bi-material is introduced in ISEM for the simulation of material characteristics and fracture behaviors.
The damage variable is introduced into the constitutive relation of ISEM to describe the decrease of loading capability after yield. Fracture criterion based on rock materials are researched as well as its analysis method.
The problem of mesh dependence in nonlinear calculation of ISEM is discussed and the gradient enhanced damage model is adopted on the basis of damage model. Nonlocal equivalent strain is introduced to the basic equations as another independent variable besides the displacements, thus iteration method of ISEM is constructed. Case studies are made, and through comparing numerical results with experimental results, the advantages of this method in avoiding mesh dependence are justified.
With the convenience of ISEM in obtaining interfacial stresses, stability safety factor of sliding surface is deduced. The safety factors of critical blocks in dam abutments and foundations are checked, and the riskiest sliding surfaces can be searched.
A program is developed and applied to 2D analysis of (1170 elevation of Xiaowan arch dam and 3D stability analysis of Jinping arch dam. Cracking and sliding in the riskiest sliding surfaces (e.g. faults, alteration zones, joints,
etc.) and damage evolution are simulated, and stability safety factors of blocks in rock foundation are checked. With the comparison between numerical results and experimental results, the applicability of ISEM in analyzing arch dam – foundation systems is revealed.
引文
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