非均质弹脆塑性煤岩材料破坏的SPH程序实现及数值模拟研究
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摘要
岩石材料是一种典型的非均质材料,具有诸如弹性、脆性、塑性、粘性以及上述性质的组合形式等等,这构成了岩石材料的复杂性。在岩石力学计算方法发展较快的今天,引入新的计算方法来考察岩石的各种特性,具有较好的理论意义和应用价值。
本文首次引入了光滑粒子流体动力学(SPH)方法来计算非均质煤岩材料的受力变形规律,利用Fortran语言开发了SPH求解固体力学问题的程序,进行弹性材料加载数值试验及非均质弹脆塑性岩石力学数值试验。主要完成了以下内容：
(1)利用SPH方法进行了静态压缩试验的稳定性和可靠性研究。论文研究了SPH方法求解静态压缩问题的收敛性,提出了程序收敛的步长公式及考察指标。通过与弹性解析解对比,SPH方法应用于静态加载问题的时候稳定性和可靠性较好；提出了加快SPH方法弹性阶段计算速度的方法,即在弹性阶段小变形情况下不重复进行粒子搜索,计算速度得到了显著提高,同时计算结果与不采用加快计算速度方法一样。
(2)进行了SPH框架下提高边界精度的设置方法的研究。改进的边界条件设置方法在固体力学静态加载数值试验中效果优于基本边界条件(Essential Boundary Conditions)和传统型边界条件(Traditional Boundary Conditions)。
(3)基于SPH方法的非均质弹脆塑性岩石类材料数值模型及其破坏的模拟研究。本文对屈服强度非均质满足Weibull分布的材料受压情况下的破坏规律进行了研究,展现了单向加载情况下岩石从细观破坏、塑性区沿近似45°方向进行扩展以及塑性区域的贯通等过程；平面应变问题的岩石试件破坏一般具有共轭剪切破坏形式、主破坏带形式及加载面“V”型破坏形式等；试件破坏过程中,破坏带尖端应力具有奇异性,而其两边应力发生回弹；随着均质程度的降低,岩石试件峰值应力逐渐变小,声发射由主震型向群震型发展。
Rock material is a typical heterogeneity material, which has properties of elasticity, brittleness, plasticity, viscosity or their combinations. With rapid development of numerical calculation methods today, the applications of new numerical methods to rock mechanics research have good theoretical and practical value.
Firstly in this paper, Smooth Particle Hydrodynamics (short for SPH) method is used to calculate the stress and deformation law of heterogeneity rock. With the help of Fortran compiler, the SPH procedure for solving the problem of solid mechanics is created. Main achievements of the paper are described as the following:
(1) The research of stability and reliability in solving quasi-static compression tests with SPH numerical method is studied. A step length formula and an indicator of program convergence are proposed. Compared with elastic analytical solution, SPH method has excellent stability and reliability when it applied to solve the static load problem. And the program ignores the repeat search algorithm in the stage of small elastic deformation, and then the calculation is significantly faster than before with the results same as before.
(2) The improvement research on boundary conditions setting. The setting of improved boundary conditions in compression simulation is better than that of essential boundary conditions and traditional boundary conditions.
(3) The research and simulation of heterogeneous elastic-brittle-plastic rock material failure based on SPH method. A series of studies is taken on heterogeneity model with random Weibull distribution of material strength. The rock failure starts from micro-mechanical failure and then plastic region spreads or transfixes along angle of about 45 degrees until the rock is completely failure. The rock failure has tree forms-conjugate shear failure, main failure and V-type failure. And the simulation results show that stress singularity in failure region tips and stress rebound along the failure sides. With the heterogeneity degree reducing, peak pressure is decreased and the head pattern of acoustic emission is gradually turned into agminated pattern.
本文首次引入了光滑粒子流体动力学(SPH)方法来计算非均质煤岩材料的受力变形规律,利用Fortran语言开发了SPH求解固体力学问题的程序,进行弹性材料加载数值试验及非均质弹脆塑性岩石力学数值试验。主要完成了以下内容：
(1)利用SPH方法进行了静态压缩试验的稳定性和可靠性研究。论文研究了SPH方法求解静态压缩问题的收敛性,提出了程序收敛的步长公式及考察指标。通过与弹性解析解对比,SPH方法应用于静态加载问题的时候稳定性和可靠性较好；提出了加快SPH方法弹性阶段计算速度的方法,即在弹性阶段小变形情况下不重复进行粒子搜索,计算速度得到了显著提高,同时计算结果与不采用加快计算速度方法一样。
(2)进行了SPH框架下提高边界精度的设置方法的研究。改进的边界条件设置方法在固体力学静态加载数值试验中效果优于基本边界条件(Essential Boundary Conditions)和传统型边界条件(Traditional Boundary Conditions)。
(3)基于SPH方法的非均质弹脆塑性岩石类材料数值模型及其破坏的模拟研究。本文对屈服强度非均质满足Weibull分布的材料受压情况下的破坏规律进行了研究,展现了单向加载情况下岩石从细观破坏、塑性区沿近似45°方向进行扩展以及塑性区域的贯通等过程；平面应变问题的岩石试件破坏一般具有共轭剪切破坏形式、主破坏带形式及加载面“V”型破坏形式等；试件破坏过程中,破坏带尖端应力具有奇异性,而其两边应力发生回弹；随着均质程度的降低,岩石试件峰值应力逐渐变小,声发射由主震型向群震型发展。
Rock material is a typical heterogeneity material, which has properties of elasticity, brittleness, plasticity, viscosity or their combinations. With rapid development of numerical calculation methods today, the applications of new numerical methods to rock mechanics research have good theoretical and practical value.
Firstly in this paper, Smooth Particle Hydrodynamics (short for SPH) method is used to calculate the stress and deformation law of heterogeneity rock. With the help of Fortran compiler, the SPH procedure for solving the problem of solid mechanics is created. Main achievements of the paper are described as the following:
(1) The research of stability and reliability in solving quasi-static compression tests with SPH numerical method is studied. A step length formula and an indicator of program convergence are proposed. Compared with elastic analytical solution, SPH method has excellent stability and reliability when it applied to solve the static load problem. And the program ignores the repeat search algorithm in the stage of small elastic deformation, and then the calculation is significantly faster than before with the results same as before.
(2) The improvement research on boundary conditions setting. The setting of improved boundary conditions in compression simulation is better than that of essential boundary conditions and traditional boundary conditions.
(3) The research and simulation of heterogeneous elastic-brittle-plastic rock material failure based on SPH method. A series of studies is taken on heterogeneity model with random Weibull distribution of material strength. The rock failure starts from micro-mechanical failure and then plastic region spreads or transfixes along angle of about 45 degrees until the rock is completely failure. The rock failure has tree forms-conjugate shear failure, main failure and V-type failure. And the simulation results show that stress singularity in failure region tips and stress rebound along the failure sides. With the heterogeneity degree reducing, peak pressure is decreased and the head pattern of acoustic emission is gradually turned into agminated pattern.
引文
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4.孙秀山,岑章志,刘应华.固体力学计算方法的发展[C].北京：第二届全国力学史与方法论学术研讨会,2005,100-107.
5.李嗣贵,邓金根,李明志.节理破碎地层井壁稳定性的离散元分析[J].岩石力学与工程学报,2002,21(增刊)：2139-2143.
6.楼芬,邓建.无网格法及其在岩石力学与工程中的应用[J].地下空间与工程学报,2007,3(6)：1014-1017.
7.李九红,程玉民.无网格方法的研究进展与展望[J].力学季刊,2006,27(1)：113-149.
8. Luca Massidda. ARMANDO, A SPH Code for CERN-Some Theory, a Short Tutorial, the Code Description and Some Examples[R]. European Organization for Nuclear Research,2008.
9. J. K. Chen, J. E. Beraun, C. J. Jih. Completeness of corrective smoothed particle method for linear electrodynamics [J]. Computational Mechanics,1999,24 (4):273-285.
10. G. R. Liu, M. B. Liu. Smoothed particle hydrodynamics—a meshfree particle method [M]. New Jersey:World Scientific Publishing Company,2003.
11. Rodriguez-paz. M, Bonet. J. A corrected smooth particle hydrodynamics formulation of the shallow-water equations [J]. Computers & Structures,2005,83(17/18):1396-1410.
12. B(?)rve S, Omang M, Trulsen J. Regularized smoothed particle hydrodynamics with improved multi-resolution handling [J]. Journal of Computational Physics,2005,208(1): 345-367.
13. Wang Kam Liu, Sukky Jun, Shaofan Li, Jonathan Adee, Ted Belytschko. Reproducing kernel particle methods for structural dynamics [J]. International Journal for Numerical Methods in Engineering,1995,38(10):1655-1679.
14. Crespo, A.J.C., M. Gomez-Gesteira, and R.A. Dalrymple. Modeling Dam Break Behavior over a Wet Bed by a SPH Technique [J]. Journal of Waterway, Port, Coastal, and Ocean Engineering,2008,134(6):313-320.
15. Khayyer, A. and H. Gotoh. On particle-based simulation of a dam break over a wet bed [J]. Journal of Hydraulic Research,2010,48(2):238-249.
16. Colagrossi A, Landrini M. Numerical simulation of interfacial flows by smoothed particle hydrodynamics [J]. Journal of Computational Physics,2003,191(2):448-475.
17. Shao S D, Lo E Y M. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface [J]. Advances in Water Resources,2003,26(7): 787-800.
18. B. D. Rogers, R. A. Dalrymple and P. K. Stansby. Simulation of caisson breakwater movement using 2-D SPH [J]. Journal of Hydraulic Research,2010,48(Extra Issue): 135-141.
19. Narayanaswamy, M., A.J.C. Crespo, Gomez-Gesteira, M., and R.A. Dalrymple. SPHysics-Funwave hybrid model for coastal wave propagation [J]. Journal of Hydraulic Research,2010,48(Extra Issue):85-93.
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