On the calibration and verification of Voronoi-based discontinuous deformation analysis for modeling rock fracture

Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to rock fracture simulation.However,parameter calibration,a fundamental issue in discontinuum methods,has not received enough attention in DDA.In this study,the parameter calibration of DDA for intact rock is carefully studied.To this end,a subblock DDA with Voronoi tessellation is presented first.Then,a modified contact constitutive law is introduced,in which the tensile and shear meso-strengths are modified to be independent of the bond lengths.This improvement can prevent the unjustified preferential failure of short edges.A method for imposing confining pressure is also introduced.Thereafter,sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock.Based on the sensitivity analysis,a unified calibration procedure is suggested for both cases with and without confining pressure.Finally,the calibration procedure is applied to two examples,including a biaxial compression test.The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.

FORMULATIONS OF THE THREE-DIMENSIONAL DISCONTINUOUS DEFORMATION ANALYSIS METHOD

This paper extends the original 2D discontinuous deformation analysis(DDA)method proposed by Shi to 3D cases,and presents the formulations of the 3D DDA.The formulations maintain the characteristics of the original 2D DDA approach.Contacts between the blocks are detected by using Common-Plane (C-P) approach and the non-smooth contact,such as of vertex-to-vertex,vertex- to-edge and edge-to-edge types,can be handled easily based on the C-P method.The matrices of equilibrium equations have been given in detail for programming purposes.The C program codes for the 3D DDA are developed.The ability and accuracy of the formulations and the program are verified by the analytical solutions of several dynamic examples.The robustness and versatility of the algorithms presented in this paper are demonstrated with the aid of an example of scattering of densely packed cubes.Finally,implications and future extensions are discussed.

Simulation of failure process of jointed rock

A modified discontinuous deformation analysis (DDA) algorithm was proposed to simulate the failure behavior of jointed rock. In the proposed algorithm, by using the Monte-Carlo technique, random joint network was generated in the domain of interest. Based on the joint network, the triangular DDA block system was automatically generated by adopting the advanced front method. In the process of generating blocks, numerous artificial joints came into being, and once the stress states at some artificial joints satisfy the failure criterion given beforehand, artificial joints will turn into real joints. In this way, the whole fragmentation process of rock mass can be replicated. The algorithm logic was described in detail, and several numerical examples were carried out to obtain some insight into the failure behavior of rock mass containing random joints. From the numerical results, it can be found that the crack initiates from the crack tip, the growth direction of the crack depends upon the loading and constraint conditions, and the proposed method can reproduce some complicated phenomena in the whole process of rock failure.

Static and dynamic stability analysis using 3D-DDA with incision body scheme

Discontinuous deformation analysis （DDA） provides a powerful numerical tool for the analysis of discontinuous media. This method has been widely applied to the 2D analysis of discontinuous deformation. However, it is hindered from analyzing 3D rock engineering problems mainly due to the lack of reliable 3D contact detection algorithms for polyhedra. Contact detection is a key in 3-D DDA analysis. The limitations and advantages of existing contact detection schemes are discussed in this paper, and a new approach, called the incision body （IB）, is proposed, taking into account the advantages of the existing methods. A computer code 3DIB, which uses the IB scheme as a 3D contact detection algorithm, was programmed with Visual C^＋＋. Static and dynamic stability analysis for three realistic engineering problems has been carried out. Furthermore, the focus is on studying the stability of a gravity dam on jointed rock foundation and dynamic stability of a fractured gravity dam subject to earthquake shaking. The simulation results show that the program 3DIB and incision body scheme are capable of detecting 3D block contacts correctly and hence simulating the open-close and slide process of jointed block masses. In addition, the code 3DIB could provide an effective tool for evaluating the safety of 3D dam structures, which is quite important for engineering problems.

Simulation of blast induced crater in jointed rock mass by discontinuous deformation analysis method

Rock blasting is a dynamic process accom panied with the propagations of shock waves and the dispersion of the explosion gas.This paper adopts the discontinuous deformation analysis(DDA)method to simulate the rock blasting process.A dynamic parameter adjustment and the non-reflecting boundary condition are implemented in the DDA method.The sub-block DDA method to simulate fracture problems is used.The blasting process in jointed rock mass is simulated by application of the explosion gas pressure on the expanding borehole walls and induced connected fracture surfaces around the boreholes.The blast craters with different overburdens are derived.The whole process including the explosion gas dispersion,borehole expansion,rock mass failure and cast,and the formation of the final blasting piles in rock blasting are well reproduced numerically.Parametric study for different overburdens is carried out,and the results are analyzed and discussed.

Discontinuous deformation and displacement analysis: From continuous to discontinuous

A discontinuous deformation and displacement(DDD) analysis method is proposed for modelling the rock failure process. This method combines the rock failure process analysis(RFPA) method(based on finite element method) and discontinuous deformation analysis(DDA) method. RFPA is used to simulate crack initiation, propagation and coalescence processes of rock during the small deformation state. The DDA method is used to simulate the movement of blocks created by the multiple cracks modelled by the RFPA. The newly developed DDD method is particularly suitable for modelling both crack propagation and block movement during the rock failure process because of the natural and convenient coupling of continuous and discontinuous deformation analyses. The proposed method has been used to simulate crack initiation, propagation and coalescence within a slope as well as the block movement during the landslide process. Numerical modelling results indicate that the proposed DDD method can automatically simulate crack propagation and block movement during the rock failure process without degrading accuracy.

A Coupling Model of the Discontinuous Deformation Analysis Method and the Finite Element Method

Neither the finite element method nor the discontinuous deformation analysis method can solve problems very well in rock mechanics and engineering due to their extreme complexities. A coupling method combining both of them should have wider applicability. Such a model coupling the discontinuous deforma- tion analysis method and the finite element method is proposed in this paper. In the model, so-called line blocks are introduced to deal with the interaction via the common interfacial boundary of the discontinuous deformation analysis domain with the finite element domain. The interfacial conditions during the incre- mental iteration process are satisfied by means of the line blocks. The requirement of gradual small dis- placements in each incremental step of this coupling method is met through a displacement control proce- dure. The model is simple in concept and is easy in numerical implementation. A numerical example is given. The displacement obtained by the coupling method agrees well with those obtained by the finite ele- ment method, which shows the rationality of this model and the validity of the implementation scheme.

深埋矿井沿空留巷切顶卸压底板变形控制

目前有关巷道底鼓的研究与实践主要探讨巷道底板的变形机理及控制技术,对沿空留巷切顶卸压前后底板力学分析不全面。针对该问题,基于煤体分区破坏特征构建了切顶前后巷道围岩和底板力学模型,分析实体煤、巷旁支护及采空区对底板的作用,获得切顶前后巷道底鼓解析解,得出巷旁煤帮弹塑性区、巷道支护体及顶板下沉区底板所受载荷共同影响巷道底鼓量大小。采用数值模拟验证切顶卸压前后沿空留巷围岩破坏特征、应力分布及底鼓量变化,结果表明:切顶卸压技术可有效缩小巷道实体煤侧面及顶部的破坏区域,维持巷道围岩结构稳定;巷道底板最大应力、巷旁支护阻力、巷道底鼓量均下降,平均降幅分别为25.78%,56.14%,54.07%。现场应用结果表明,厚硬顶板沿空留巷底鼓量由709.3451 mm降至320.9658 mm,切顶卸压技术可以优化巷道围岩应力结构,抑制巷道底鼓,有效改善底板破坏情况。

An improved three-dimensional spherical DDA model for simulating rock failure

In this paper, a discontinuous numerical model, namely SDDARF3D(three-dimensional spherical discontinuous deformation analysis for rock failure), is proposed for simulating the whole process of rock failure. Firstly, within the framework of the classical discontinuous deformation analysis(DDA) method, the formulation of three-dimensional spherical DDA(3D SDDA) is deduced; secondly, a bonding and cracking algorithm is constructed and the SDDARF3 D model is proposed; thirdly, corresponding VC++ calculation code is developed and some verification examples are calculated. The simulated results can intuitively reproduce the failure phenomena of rock mass, indicating that the proposed SDDARF3 D numerical model is correct and effective.

三维DDA方法的验证及其在隧道围岩垮塌控制中的应用

为准确模拟隧道围岩垮塌灾害演化过程与锚杆加固处置,通过嵌入锚杆支护算法实现了三维非连续变形分析方法(DDA)中的锚杆支护模拟.首先,介绍了三维DDA方法模拟块体运动的基本原理,提出了三维DDA方法中锚杆支护算法;其次,针对隧道围岩垮塌灾害中的不同运动模式,采用三维DDA方法模拟了块体滑移、转动以及碰撞过程,验证了三维DDA方法模拟块体运动的准确性;最后,采用三维DDA方法模拟了工程尺度的节理岩体隧道围岩垮塌过程.结果表明:无支护条件下隧道洞周块体垮塌高度为3.9 m,洞周块体位移呈现出明显的各向异性特征;有支护条件下隧道洞周块体保持稳定状态,隧道左拱肩部位锚杆轴力较大,实际施工过程中可增加该区域锚杆长度.

焦家金矿破碎岩体变形破坏规律研究

焦家金矿-570~630 m中段矿(岩)体节理裂隙发育,易出现楔形不稳定结构,进而发生岩体冒落。对岩体进行了地质钻孔、结构面条件调查等得出,焦家金矿岩体较为破碎,节理发育,节理产状分布范围广。对开采扰动下巷道收敛变形规律进行研究与总结,并通过雷达测试分析焦家金矿巷道破坏深度,损伤深度基本保持在2 m,存在较多的结构弱面,需及时采取加固措施。此研究对该处矿体的支护等做出合理规划,进一步指导采场结构参数的合理选取,以确保该矿段的安全生产。对类似矿山破碎矿体的治理条件有一定的借鉴意义。

深埋软岩隧道围岩稳定性分析与防护措施研究

深埋软岩隧道初支大变形问题是隧道建设常见难题之一。针对西南地区某在建铁路隧道出现初支开裂变形及拱顶坍塌等问题,进行围岩内部位移监测及初支变形监测,并结合隧祉区情况对隧道灾害成因进行分析。研究结果表明:根据围岩深部位移曲线斜率,判断出围岩松动圈范围处于6.0~7.0 m;围岩前期变形速率快,水平收敛值明显大于拱顶沉降值,最大变形在上台阶收敛处,为93.2 mm,其主要原因是区域构造应力作用影响;初始在前期释放迅速,初支-围岩接触压力在空间上分布各不相同,围岩压力大小并不直接影响围岩变形情况;对已发生大变形区域采用径向注浆加固,对未开挖段落将超前小导管支护改为T76超前管棚注浆支护,有效控制了大变形持续发展,可为深埋软岩隧道断层破碎带处开挖前后大变形防护提供参考。

DDA方法在复杂地质条件下地下厂房围岩变形与破坏特征分析中的应用研究

以清江水布垭水电工程地下厂房为例,应用非连续变形分析方法对复杂地质条件下地下厂房围岩的变形与破坏特征开展了研究,重点分析了厂房区域地应力水平、锚固、岩体结构条件及结构面强度参数等对洞室围岩变形的影响。分析结果表明,当水平初始应力增加时,洞室围岩位移量相应增加,由于洞室边墙分布有多条层间剪切带且围岩具有软硬相间的层状岩体结构特点,使得边墙变形存在错动现象。锚固后洞室边墙围岩的变形明显减小,且围岩应力状态得到显著改善。对于高边墙地下洞室,陡倾角结构面在边墙上的出露对围岩的稳定十分不利,在一定的岩体结构条件下,围岩的破坏可表现为因局部块体的崩落所引起的整个洞室围岩的破坏。在相同岩体结构条件下,降低结构面强度参数,洞室围岩可以从变形稳定状态发展到不稳定状态,围岩的失稳主要表现为因围岩大变形引起的失稳。

用非连续变形分析方法模拟岩石裂纹扩展

提出一种用非连续变形分析方法模拟岩石裂纹扩展的方法。将计算区域自动剖分成三角形块体单元,块体边界分为真实的节理边界和虚拟节理边界。裂纹扩展沿虚拟节理进行,按照界面破裂准则进行裂纹扩展分析。该方法可以模拟裂纹萌生、扩展、贯通和岩体破碎全过程,适用于完整岩石、断续岩体乃至完全不连续岩体等任意情形。由于该方法基于离散颗粒数值模型,其计算过程不会遇到数学上的困难。根据所提算法,编制VC++程序模块,并计算几个算例。模拟结果与已有的物理、数值试验结果吻合得较好,表明所提算法是有效的。

非连续变形岩石断裂分析中的一种全长剪切锚杆

锚杆从锚固方式上可划分两种:端部锚固方式和全长锚固方式。全长锚固锚杆作为工程支护中的一种重要锚杆类型,具有广泛的应用前景。非连续变形分析(DDA)以及在此基础上发展的非连续变形的岩石断裂分析(DDARF)方法中锚杆为端锚形式,且只考虑了锚杆的轴向作用,而忽略了锚杆作用力对锚固岩体的侧向限制。为了更好地理解锚杆的支护机制,考虑锚杆的剪切作用,提出了DDARF中一种新的锚固形式——全长剪切锚杆支护形式。用改进的全长剪切锚杆支护方法对一公路隧道稳定性进行了分析,并与端锚支护形式进行了对比,结果表明,提出的全长剪切锚杆支护方法是有效的,锚固效果比端锚支护更好。

DDA数值方法在岩质边坡倾倒破坏分析中的应用

倾倒是岩质边坡失稳的典型破坏形式之一,而常规的滑动极限平衡分析方法不适宜用于这类边坡的稳定分析。长期以来,Hoek和Bray著《岩石边坡工程》中介绍的Goodman和Bray提出的基于极限平衡原理的分析方法(以下简称G-B法),一直是研究这类问题的主要手段之一,但对其合理性仍有待验证。采用当前国际上发展的一种最新数值分析方法——非连续变形分析(DDA),结合一典型算例对该方法进行验证,对倾倒破坏的失稳变形机理进行分析研究,指出了采用G-B法可能出现的问题。

岩石破坏非连续变形分析弹脆性本构模型的二次开发

岩石非连续变形分析方法DDARF成功实现了模拟岩体裂纹萌生、扩展、贯通、破碎的全过程,但算法只考虑了岩体的线弹性本构模型,没有分析岩体的非线性应力-应变关系。为更符合真实岩体工程,同时扩展岩石非线性本构模型的应用范围,分别采用摩尔-库仑强度准则和最大拉应力强度准则对岩体进行剪切和拉伸破坏判断;对理想弹脆性本构模型进行算法分析,并在VC++平台下程序实现;对"自定义"的岩体非连续变形分析方法弹脆性本构模型与室内单轴压缩试验进行比较分析;将岩体非连续变形分析方法弹脆性本构模型应用于大型地下洞室开挖,并与线弹性本构模型进行对比。结果表明,非连续变形分析方法中自定义岩体弹脆性本构模型是可行的,它能够反映岩体变形的非线性特征,与室内试验吻合度较好;非连续变形分析方法弹脆性本构模型应用于大型地下工程,能更安全且真实地分析洞室围岩的稳定性,进而更好地指导地下洞室的防护措施。

深埋巷道破裂围岩位移分析

针对深埋巷道围岩普遍处于破裂状态的特点,采用非连续变形分析(DDA)软件对巷道围岩松动圈非连续体位移影响因素的变化规律进行了模拟研究.分析了用锚杆、锚索和注浆加固以增加围岩破裂面的黏结力、抗拉强度和内摩擦角的数值来减少位移量的机理,提出了非连续体巷道失稳破坏的判断标准,并对埋深1 159 m的大松动圈围岩巷道的非连续体位移进行了定量计算和实地观测.实测结果与DDA软件计算值比较吻合,说明对于深埋巷道破裂围岩采用DDA方法进行位移计算和支护参数设计是可行的.

DDA方法块体稳定性验证及其在岩质边坡稳定性分析中的应用

首先,介绍DDA方法中关于块体接触力的计算过程,提出计算沿潜在滑动面稳定性安全系数的计算方法;然后,在此基础上以沿折坡单块体滑动问题为实例,利用DDA方法分别计算仅考虑滑动面摩擦角?和同时考虑摩擦角?和黏聚力c条件下块体的运动稳定性和安全系数大小,并与理论值进行比较与验证;最后,针对乌江银盘水电工程右坝肩边坡开挖后因软弱断层控制引起的稳定性及处理措施选取问题,利用已有的极限平衡分析条块系统,将DDA方法应用于该边坡稳定性分析,对边坡的实际稳定状态及锚固效果进行对比分析与评价。研究结果表明,利用DDA方法在计算滑面上条块系统沿滑面稳定安全系数时,因其条块间接触力是建立在严格的力学平衡方程基础上,允许块体系统非连续变形,并且勿需条块界面强度等比例调用的假定,其结果对反映实际岩质边坡的稳定性应该更具合理性。另外,DDA方法关于边坡锚固模拟计算,充分反映和验证了锚杆在边坡稳定性加固处理中的效果。

节理岩质边坡变形的DDA模拟

对原非连续变形分析方法(DDA方法)中边界约束方法进行了推广,将其应用于节理岩质边坡变形规律的数值模拟,并利用模型实验结果验证了推广方法的正确性。