【作者】 张小强；

【导师】 周小平；

【作者基本信息】 重庆大学 ， 土木工程， 2018， 博士

【摘要】 为了更好研究非连续问题,克服传统数值方法存在的缺点,例如离散元法依赖单元(或粒子)直径大小;有限元法存在网格扭曲等不足之处。本文提出一种无网格粒子数值模拟计算方法-广义粒子动力学(General particle dynamics(GPD))法。应用GPD法研究岩土体损伤局部损和渐进破坏,研究内容以及结论:(1)应用GPD法,研究岩石试样在单轴和三轴压缩条件下局部损伤及破坏过程。当粒子受力满足Hoke-Brown强度准则时,认为此粒子破坏,不对周围其他粒子产生影响,我们称作“死亡粒子”。当荷载继续增加时,“死亡粒子”数量逐渐增加,这些粒子标记出了岩样损伤区域。通过和单轴压缩试验结果进行对比,得到以下结论:GPD法可以有效的模拟脆性材料损伤局部化和渐进破坏。在此基础上,模拟了岩样三轴压缩试验,分析了中间主应力对岩样局部损伤区域影响、岩石峰值强度影响和岩石最终破坏模式影响。(2)利用GPD模拟土质边坡渐进破坏。土体边坡荷载为自重,模型左右边界通过鬼粒子方法设置成为自由滑移边界,其边界粒子切向速度与实体粒子相同,而法向速度相反。底部通过虚粒子设置成为固定边界,其速度设置为零。模拟结果得出:土体边坡内部塑性等效应变由局部应变发展成为应变局部化带,并且贯通整个边坡体,形成临界滑移面。通过有限元软件对比模拟研究,得出以下结论:证明GPD法研究土体边坡变形问题是一个很好的工具,同时克服了有限元软件的网格畸变缺陷。(3)为了更进一步优化GPD算法,节约计算时间,防止计算结果出现应力不稳定现象,造成实体粒子成团等缺陷。提出虚拟键模型的广义粒子动力学法(VB-GPD)。采用Drucker-Prager强度准则判断键上应力是否满足强度准则,当键上应力满足Drucker-Prager准则,那么键处于塑性状态。随着应力增加,塑性键数量也随之增加,通过非关联流动法则判断塑性区,从而确定产生塑性变形的区域。通过模拟粘土体单轴压缩试验,得出土体试样首先出现塑性应变局部化,其逐渐发展成为应变局部化带,最终导致土体试样破坏。分析单轴压缩下土体变形-受力关系,验证了VB-GPD法研究塑性变形的可行性,最终应用到模拟均匀土质边坡。对比VB-GPD和GPD模拟结果,可以得出以下结论:VB-GPD在计算效率方面比GPD有所提高。建立同样的有限元模型,对比临界滑裂面、安全系数和最终破坏形态可知,VB-GPD可以有效的模拟塑性变形破坏。(4)为了更好的分析裂隙和节理对岩质边坡稳定性的影响,本文最后应用VB-GPD模型分析含预制裂纹的岩质边坡稳定性。建立六种不同裂纹排布的数值模型,采用重力叠加法施加外部荷载作用。模拟结果分析了边坡内部裂隙起始、发展和贯通的过程,得出多种裂纹连接模式。由于强度折减法在粒子法中不能应用,因为对于粒子法而言,每一个折减系数都不存在不收敛的解。因此,本文将重力叠加法引入VB-GPD算法中,求得含裂隙的岩质边坡安全系数。结果可知,VB-GPD在分析脆性材料变形和破坏是可行的,为研究岩质边坡提供了一种新的、更深入的方法。更多还原

【Abstract】 In order to study the non-continuous problems and overcome the shortcomings of traditional numerical methods,such as discrete element method dependences on the size of the unit(or particle)diameter and finite element method is of mesh distortion.Therefore,a meshless numerical method is proposed in this paper,which is named as general particle dynamics method(GDP),and is applied to study local damage and gradual failure of rock-soil mass.The main research contents and conclusions are conclued as followings:(1)The GPD method is used to study the local damage and failure process of rock samples with uniaxial and triaxial compression.When the particle meets the Hoke-Brown strength criterion,it is considered as the dead particle,which is considered as failure and without affect on surrounding particles.When the load continues to increase and the number of dead particles increases,the macroscopic damage area of the rock sample are marked by these particles.Compared with the experimental results obtained by uniaxial compressive,the conclusion is obtained as follows: the GPD algorithm can effectively study the failure process of brittle materials.Meanwhile,the triaxial compression test of rock sample is simulated,and the influence of intermediate principal stress on local damage area,rock peak strength and rock ultimate failure mode is analyzed by using the GPD method.(2)The GPD is adopted to study the stability of soil slope with self-weight loading.The left-right boundary is set as the free-slip boundary through the ghost particles,the bottom is set as the fixed boundary through the virtual particles.If the influence domain of any particle is intersection with the boundary wall particles,the boundary particle is generated as a ghost particles boundary particles at the same position which corresponding to the any particle,the variables are the same as the corresponding real particles except of speed.That is to say,the tangential velocity of ghost is same with the real particles and the normal velocity of ghost is the opposite of the real particle.The fixed boundary of the bottom is fixed with three rows of virtual particles,whose velocity is set as zero.The simulation results show that the plastic equivalent strain of the soil slope is developed by the local strain and becomes the strain localization zone through the whole slope,then a critical slip surface is formed.It is proved that GPD method is a good tool to study the deformation of soil slope through the comparison of the finite element simulation results.(3)In order to further optimize the GPD algorithm and save calculation time.The virtual bond model is proposed and introduced into the GPD method,which is called as the virtual bond general particle dynamic method(VB-GPD).It is assumed that the interaction between particles are connected by the bond,namely virtual bonds,the Drucker-Prager strength criterion is choosed to determine whether the stress on a bond meet the strength criterion.When the stress on bond meets the Drucker-Prager criterion,the bond is in state of plastic.With the increase of stress,the number of plastic bond increases,and the plastic zone is determined by the non-associative flow rule.The clay is simulated by VB-GPD method under uniaxial compression,it is concluded that soil sample plastic strain localization develops and becomes the strain localization band until versed in the soil sample,the failure of soil sample is formed and the bearing capacity is lost.The strain-stress relationship of soil sample under the uniaxial compression is analyzed,it is verified that the VB-GDP method can well study the plastic deformation.Finally,the VB-GPD is applied to the simulation of homogeneous soil slope and analyzed its stability.The formation process of the critical sliding surface and safety factor of soil slope are obtained by the numerical simulation.The same finite element model is established to compare the critical sliding surface,the safety factor and the ultimate failure mode,we can conclude that the VB-GPD can effectively simulate the plastic deformation failure.(4)In order to analyze the impact of the cracks and joints on the stability of rock slope,this paper analyzes the stability of rock slope with prefabricated flaws by using the VB-GDP model.Some numerical models are established with different cracks arraies.The simulation results analyze the process of crack initiation,development and coalesces,and variety types of crack connection modes are obtained.Because the strength reduction method cannot be applied in the particle method,as for the particle method,there is no non-convergent solution for particle method.Therefore,a method of calculation method of safety factor is proposed in this paper which is based on gravity increase method.The results show that VB-GPD is feasible to analyze the deformation and failure of brittle materials,and provides a new and deeper method for studying the flawed rock slope.更多还原