考虑块体内耦合作用及锚杆塑性效应的非连续变形分析方法
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摘要
随着大型水利水电工程以及深部资源开发工程的飞速发展,岩石非连续大变形问题的理论与计算成为学术界研究的焦点。块体系统非连续变形分析(DDA)是近三十年来才发展起来的一种新的数值计算方法,它在满足弹性理论基本方程的条件下能够反映出岩体变形的不连续性,既具有离散元法可计算块体大位移的特点,又具有有限元理论基础的严密性,具有广泛的应用前景,是目前岩土工程分析中的研究热点之一。非连续变形分析方法由于发展的较晚,在工程应用方面有诸多的局限性。本文对非连续变形分析方法进行了改进,考虑了位移收敛准则和锚杆的塑性变形。然后建立了非连续变形分析方法与有限元方法的耦合程序,讨论了并行算法。最后结合四川巴底水电站项目对该方法进行了深入研究,主要研究了等效力学参数的确定和动态施工过程等。本文的主要工作概括如下：
1.对非连续变形分析方法进行了改进,加入了位移收敛判断准则。然后采用非连续变形分析方法对双裂隙岩块进行单轴和双轴压缩模拟试验,研究了裂隙角度和侧向应力大小对岩块特性的影响,得到了裂隙岩块在这两种加载试验中的破坏过程和应力—应变曲线,同时也得到了岩块中裂隙的起裂应力和岩块的峰值强度。在双轴压缩模拟试验中绘制了裂隙角度为45。岩块在不同侧向压力下的强度包络线,并根据包络线方程式确定参数的c、φ的取值,同时根据等效连续介质分析方法分析了某地下洞室的稳定性。随后,在程序中加入了锚杆的塑性变形力学模型,并采用改进后的程序模拟了劈裂试验中含裂隙试块的锚固效果,得到锚杆的塑性力学特性可以更好的描述锚杆的受力,更贴近工程实际情况。
2.应用有限元参数化设计语言APDL,开发了非连续变形分析方法程序与有限元程序图形用户界面的接口程序ANSYS2DDARF,可以生成BLAC文件,使前处理更加直观方便。同时,在线性位移模式下,推导了非连续变形分析程序和有限元程序耦合方法的总体平衡方程,并且详细推导了相应的的弹性子矩阵、惯性子矩阵、荷载子矩阵和接触子矩阵等。非连续变形分析方法与有限元方法耦合后,每个块体的自由度由网格节点的数量所确定,更加准确的描述了块体的变形。最后采用耦合分析方法分析了某地下洞室围岩的位移影响因素,得到侧压力系数、围岩破碎面粘聚力、内摩擦角、抗拉强度对围岩的位移影响较大,同时顶拱为支护的关键位置,为工程提供了参考。
3.考虑了非连续变形分析方法基于OpenMP的并行算法。首先提出了刚度矩阵并行组装策略,对非连续变形分析的刚度矩阵进行了并行化处理。然后对非连续变形分析的方程组计算采用改进的SSOR-PCG方法。最后通过算例表明改进后的并行算法可以使程序具有良好的加速比,明显的提高了模型的计算速度。
4.在非连续变形分析方法的实际工程应用中,以四川巴底水电站地下洞室群为研究背景,首先数值模拟中的力学参数考虑了岩体中节理的随机性和岩体力学参数的不确定性,通过现场实测数据和数值模拟的方法进行等效确定。然后研究了动态施工方法,突出了对开挖顺序、分步开挖、分步支护过程进行模拟计算分析,并给出相应的解决方法,使程序可以更加真实的反映实际施工过程。
5.将非连续变形分析方法与有限元方法的耦合问题,动态施工过程,基于OpenMP并行问题,锚杆的塑性变形力学模型和位移收敛准则使用C++语言在VC++平台中编制到计算程序中,使程序同时具备较好的分析块体变形的功能和工程应用的功能。
With the surging development of economic construction and large-scale water conservancy and hydropower engineering in China, large discontinuous deformation theory and computing of rock has become the focus of academic research. The discontinuous deformation analysis of block systems (DDA), as a new numerical method developed in the past thirty years, is able to mirror the discontinuity of rock mass deformation while satisfying the fundamental equations of the elastic theory. The DDA method has promising prospects in engineering application, thus being one of the research hotspots in geotechnical engineering. However, the DDA method still has some limitations in engineering applications. In this thesis, the discontinuous deformation analysis method is improved by taking into account the displacement convergence criterion and the plastic deformation of bolts. Besides, the coupling of DDA method and finite element method is established and parallel algorithm of DDA is also discussed. Eventually, the DDA method is applied in the project of Sichuan Badi Hydropower Station, in which the determination of equivalent mechanical parameters and the dynamic construction process are mainly studied. The main contents of this thesis are listed as following:
1. Adopting the discontinuous deformation analysis method, the uniaxial and biaxial compression experiments of double-fractured rock mass were numerically simulated. Influences of different fracture angles and lateral stresses on the behavior of rock mass under compression tests were studied and the corresponding stress-strain curves, together with the crack initiation stress and the peak strength of specimens were obtained. In the biaxial compression experiments of double-fractured rock mass considering different lateral pressures, the strength envelope diagram of45°fractured specimen were obtained. The parameters obtained from the biaxial compression experiments were used in a practical engineering example and the different damage states of intact rock and fractured rock were analyzed after excavation of underground caverns by means of the equivalent continuum method. Nevertheless, the plastic deformation mechanical model of anchor was added in the program of DDA. With this improvement in program, the axial load-displacement curves and the crack propagation process of different anchored-fractured specimens were obtained, which means it could simulate the anchorage effect on fractured rock. The simulation results and the previous splitting tests under similar conditions agree well with each other. At this point, the improved program showed its ability to provide better description of the anchor bolt stress.
2. Parametric design language APDL was applied in the interface program development of discontinuous deformation analysis and ANSYS calculation program, which greatly facilitates the pretreatment process. In the meantime, the general balance equations of the method that couples the DDA and ANS YS were deduced in the linear displacement mode, and the corresponding elastic matrixes, inertia matrixes, load matrixes and contact matrixes were also deduced in details. After coupling the two methods, the freedom degrees of each block are determined by the number of nodes, thus being able to more accurately describe the deformation of blocks. Finally, factors that impact on the displacements of an underground cavern were analyzed employing the coupling method, from which it was concluded that the lateral pressure coefficient, rock crushing surface cohesion, internal friction angle and tensile strength have larger effects on the stability of the surrounding rock mass. In addition, the top arch of the cavern was the key position for supporting arrangement in this project, providing reference for the engineering.
3. The parallel algorithm based on OpenMP method was considered in the DDA program and the parallel assembly strategy of stiffness matrix was put forward. The calculation of the DDA equations was conducted with the modified SSOR-PCG method in order to improve the calculation efficiency. Finally, it was proved by calculating numerical examples that the modified parallel algorithm can significantly enhance the rate of calculation.
4. In the practical application of engineering, the Badi Hydropower Station, mechanical parameters of the DDA were determined through field test data and numerical simulation, considering the randomness of rock joints and the uncertainty of rock mechanical parameters. Dynamic construction process is studied in this engineering while excavation sequence, step-by-step excavation and supporting process were specifically analyzed.
5. The coupling problem of the discontinuous deformation analysis method and the finite element method, the dynamic construction process of excavation and the step-by-step support problem were tackled through numerical simulation carried out based on OpenMP parallel algorithm. The plastic deformation model of anchor bolts and the displacement convergence criterion were added to the DDA source program, through compiling calculation program in VC++platform with C++language. Last but not least, this program could potentially provide a better analysis of block deformation and engineering application.
1.对非连续变形分析方法进行了改进,加入了位移收敛判断准则。然后采用非连续变形分析方法对双裂隙岩块进行单轴和双轴压缩模拟试验,研究了裂隙角度和侧向应力大小对岩块特性的影响,得到了裂隙岩块在这两种加载试验中的破坏过程和应力—应变曲线,同时也得到了岩块中裂隙的起裂应力和岩块的峰值强度。在双轴压缩模拟试验中绘制了裂隙角度为45。岩块在不同侧向压力下的强度包络线,并根据包络线方程式确定参数的c、φ的取值,同时根据等效连续介质分析方法分析了某地下洞室的稳定性。随后,在程序中加入了锚杆的塑性变形力学模型,并采用改进后的程序模拟了劈裂试验中含裂隙试块的锚固效果,得到锚杆的塑性力学特性可以更好的描述锚杆的受力,更贴近工程实际情况。
2.应用有限元参数化设计语言APDL,开发了非连续变形分析方法程序与有限元程序图形用户界面的接口程序ANSYS2DDARF,可以生成BLAC文件,使前处理更加直观方便。同时,在线性位移模式下,推导了非连续变形分析程序和有限元程序耦合方法的总体平衡方程,并且详细推导了相应的的弹性子矩阵、惯性子矩阵、荷载子矩阵和接触子矩阵等。非连续变形分析方法与有限元方法耦合后,每个块体的自由度由网格节点的数量所确定,更加准确的描述了块体的变形。最后采用耦合分析方法分析了某地下洞室围岩的位移影响因素,得到侧压力系数、围岩破碎面粘聚力、内摩擦角、抗拉强度对围岩的位移影响较大,同时顶拱为支护的关键位置,为工程提供了参考。
3.考虑了非连续变形分析方法基于OpenMP的并行算法。首先提出了刚度矩阵并行组装策略,对非连续变形分析的刚度矩阵进行了并行化处理。然后对非连续变形分析的方程组计算采用改进的SSOR-PCG方法。最后通过算例表明改进后的并行算法可以使程序具有良好的加速比,明显的提高了模型的计算速度。
4.在非连续变形分析方法的实际工程应用中,以四川巴底水电站地下洞室群为研究背景,首先数值模拟中的力学参数考虑了岩体中节理的随机性和岩体力学参数的不确定性,通过现场实测数据和数值模拟的方法进行等效确定。然后研究了动态施工方法,突出了对开挖顺序、分步开挖、分步支护过程进行模拟计算分析,并给出相应的解决方法,使程序可以更加真实的反映实际施工过程。
5.将非连续变形分析方法与有限元方法的耦合问题,动态施工过程,基于OpenMP并行问题,锚杆的塑性变形力学模型和位移收敛准则使用C++语言在VC++平台中编制到计算程序中,使程序同时具备较好的分析块体变形的功能和工程应用的功能。
With the surging development of economic construction and large-scale water conservancy and hydropower engineering in China, large discontinuous deformation theory and computing of rock has become the focus of academic research. The discontinuous deformation analysis of block systems (DDA), as a new numerical method developed in the past thirty years, is able to mirror the discontinuity of rock mass deformation while satisfying the fundamental equations of the elastic theory. The DDA method has promising prospects in engineering application, thus being one of the research hotspots in geotechnical engineering. However, the DDA method still has some limitations in engineering applications. In this thesis, the discontinuous deformation analysis method is improved by taking into account the displacement convergence criterion and the plastic deformation of bolts. Besides, the coupling of DDA method and finite element method is established and parallel algorithm of DDA is also discussed. Eventually, the DDA method is applied in the project of Sichuan Badi Hydropower Station, in which the determination of equivalent mechanical parameters and the dynamic construction process are mainly studied. The main contents of this thesis are listed as following:
1. Adopting the discontinuous deformation analysis method, the uniaxial and biaxial compression experiments of double-fractured rock mass were numerically simulated. Influences of different fracture angles and lateral stresses on the behavior of rock mass under compression tests were studied and the corresponding stress-strain curves, together with the crack initiation stress and the peak strength of specimens were obtained. In the biaxial compression experiments of double-fractured rock mass considering different lateral pressures, the strength envelope diagram of45°fractured specimen were obtained. The parameters obtained from the biaxial compression experiments were used in a practical engineering example and the different damage states of intact rock and fractured rock were analyzed after excavation of underground caverns by means of the equivalent continuum method. Nevertheless, the plastic deformation mechanical model of anchor was added in the program of DDA. With this improvement in program, the axial load-displacement curves and the crack propagation process of different anchored-fractured specimens were obtained, which means it could simulate the anchorage effect on fractured rock. The simulation results and the previous splitting tests under similar conditions agree well with each other. At this point, the improved program showed its ability to provide better description of the anchor bolt stress.
2. Parametric design language APDL was applied in the interface program development of discontinuous deformation analysis and ANSYS calculation program, which greatly facilitates the pretreatment process. In the meantime, the general balance equations of the method that couples the DDA and ANS YS were deduced in the linear displacement mode, and the corresponding elastic matrixes, inertia matrixes, load matrixes and contact matrixes were also deduced in details. After coupling the two methods, the freedom degrees of each block are determined by the number of nodes, thus being able to more accurately describe the deformation of blocks. Finally, factors that impact on the displacements of an underground cavern were analyzed employing the coupling method, from which it was concluded that the lateral pressure coefficient, rock crushing surface cohesion, internal friction angle and tensile strength have larger effects on the stability of the surrounding rock mass. In addition, the top arch of the cavern was the key position for supporting arrangement in this project, providing reference for the engineering.
3. The parallel algorithm based on OpenMP method was considered in the DDA program and the parallel assembly strategy of stiffness matrix was put forward. The calculation of the DDA equations was conducted with the modified SSOR-PCG method in order to improve the calculation efficiency. Finally, it was proved by calculating numerical examples that the modified parallel algorithm can significantly enhance the rate of calculation.
4. In the practical application of engineering, the Badi Hydropower Station, mechanical parameters of the DDA were determined through field test data and numerical simulation, considering the randomness of rock joints and the uncertainty of rock mechanical parameters. Dynamic construction process is studied in this engineering while excavation sequence, step-by-step excavation and supporting process were specifically analyzed.
5. The coupling problem of the discontinuous deformation analysis method and the finite element method, the dynamic construction process of excavation and the step-by-step support problem were tackled through numerical simulation carried out based on OpenMP parallel algorithm. The plastic deformation model of anchor bolts and the displacement convergence criterion were added to the DDA source program, through compiling calculation program in VC++platform with C++language. Last but not least, this program could potentially provide a better analysis of block deformation and engineering application.
引文
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