Application of modified discontinuous deformation analysis to dynamic modelling of the Baige landslide in the Jinsha River

Accurate dynamic modeling of landslides could help understand the movement mechanisms and guide disaster mitigation and prevention.Discontinuous deformation analysis(DDA)is an effective approach for investigating landslides.However,DDA fails to accurately capture the degradation in shear strength of rock joints commonly observed in high-speed landslides.In this study,DDA is modified by incorporating simplified joint shear strength degradation.Based on the modified DDA,the kinematics of the Baige landslide that occurred along the Jinsha River in China on 10 October 2018 are reproduced.The violent starting velocity of the landslide is considered explicitly.Three cases with different violent starting velocities are investigated to show their effect on the landslide movement process.Subsequently,the landslide movement process and the final accumulation characteristics are analyzed from multiple perspectives.The results show that the violent starting velocity affects the landslide motion characteristics,which is found to be about 4 m/s in the Baige landslide.The movement process of the Baige landslide involves four stages:initiation,high-speed sliding,impact-climbing,low-speed motion and accumulation.The accumulation states of sliding masses in different zones are different,which essentially corresponds to reality.The research results suggest that the modified DDA is applicable to similar high-level rock landslides.

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

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.

Dynamic process analysis of the Niumiangou landslide triggered by the Wenchuan earthquake using the finite difference method and a modified discontinuous deformation analysis

The Niumiangou landslide was the largest landslide triggered by the 2008 Wenchuan earthquake,which was significantly affected by the amplification effect of seismic acceleration.The ringshear experiments indicated that the materials in the source area of the Niumiangou landslide were subjected to friction degradation under a big shear displacement,which may result in rapid movement of the landslide.In order to better understand the landslide movement and study the effect of the friction degradation on movement mechanisms,the dynamic process of Niumiangou landslide was simulated with a new numerical method,which combines the finite difference method(FDM)and the discontinuous deformation analysis(DDA).First,the FDM was used to study the initiation time,amplification effect and velocity of the landslide.Afterwards,these initiation velocities were applied to the blocks in the DDA model by corresponding coordination in the FDM model.A displacementdependent friction model of the sliding surface was incorporated into DDA code to further understand the kinetic behavior of the landslide.The results show that the displacement-dependent friction strongly decreases the friction coefficient of sliding surface under a big displacement,which can obviously promote the run-out and velocity of landslide.The model output well matches the topographic map formed by the landslide.This implies that the proposed model can be applied to the simulation of earthquake-induced landslides with amplification effect,and the friction degradation model is important to clarify the movement mechanism of high-speed and long-distance landslides.

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.

Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block de- formation. In this paper, 3D DDA is coupled with tetrahe- dron finite elements to tackle these two problems. Tetrahe- dron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topol- ogy shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Valida- tion is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demon- strates the robustness and versatility of the coupled method.

天体运动的三维DDA模拟

不连续变形分析(DDA)方法广泛应用于岩土工程领域,其中三维球颗粒DDA(3D-SDDA)理论能够对球形物体模型的运动进行数值模拟。本研究将不连续变形分析方法应用于太阳系天体运行模拟,将各天体看作球状物体,仅考虑天体间的引力和其自身惯性力,通过建立系统总体平衡方程式,推导载荷矩阵方程,求解总体方程,编写Matlab计算程序,从而得到各天体的运动参数,对天体运动进行数值模拟。结果表明,利用3D-SDDA理论能够模拟日-地二体系统和日-地-月三体系统在宇宙空间中的运行状态,获取任意时刻天体的空间位置和速度信息。分别将日-地二体系统的数值计算结果与开普勒计算方法所得结果对比,日-地-月三体系统的结果与虚拟天文馆软件Stellarium高精度数据对比,结果吻合良好。同时输入月全食发生的限制条件,能够正确预测出月全食发生时刻。

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.

基于DDA方法的排碴井筒堵塞概率分析

依托某公路隧道的超大直径通风竖井工程,针对通风竖井施工中心小直径井筒排碴存在极大堵塞风险、严重影响建设工期的问题,考虑到井筒落石属于非连续变形动力学过程,因此,采用非连续变形分析(DDA)方法,通过对井筒落石进行数值建模,以球体作为基本块体单元,基于捆绑算法将球颗粒捆绑成相应形状块体,模拟块体运动过程中的碰撞、摩擦等,开展了针对性的小直径井筒落石堵塞概率分析。数值模拟结果表明,为避免小直径排碴井筒发生堵塞现象,应严格控制抛入排碴井筒的岩块尺寸与块度;钻爆法施工的小直径排碴井筒超欠挖现象越严重,井筒堵塞概率越大。模拟结果较为真实地反映了排碴井工况的工程实际。

Discontinuous deformation analysis for subsidence of fractured formations under seepage: A case study

With the growing prominence of recycling projects of groundwater,the attention towards subsidence concerns in geological formations is intensifying.However,due to the long evolutionary time and complex underground discontinuities,the deformation field and subsidence mechanism are difficult to obtain.To this concern,this study implemented the Hydro-Mechanical Coupled Discontinuous Deformation Analysis(HM-DDA)in a groundwater recycling project located at a goaf mining site.The method for establishing numerical stratigraphic models and determining the required numerical parameters is introduced.This contributes to the comprehensive reconstruction of changes in in-situ stress within the goaf area,encompassing the initial stress equilibrium state,as well as the processes of water pumping and injection.The results indicated that the water injection process mitigated stress concentrations at both ends of the goaf area.Specifically,a 30-m rise in water head resulted in a corresponding elevation of the ground surface by 3.94 cm.

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.

A 3-D DDA damage analysis of brick masonry buildings under the impact of boulders in mountainous areas

In mountainous areas, geological disasters carrying large boulders can cause severe damage to the widely used masonry buildings due to the high impact forces. To better understand the damage of brick masonry buildings under the impact of boulders, a "block-joint" model is developed using threedimensional discontinuous deformation analysis(3-D DDA) to simulate the behaviour of the "brick-mortar" structure. The "block-joint" model is used to capture not only the large displacement and deformation of individual bricks but also the large-scale sliding and opening along the mortar between the bricks. The linear elastic constitutive model is applied to account for the non-plastic deformation behaviour of brick materials. Furthermore, the mechanical characteristics of the mortar are represented using the Mohr-Coulomb and Drucker-Prager criteria. To propose safe structural design schemes and effective reinforcement for brick masonry buildings, seven construction techniques are considered, includingdifferent grades of brick and mortar, effective shear areas and reinforced members. The proposed 3-D DDA model is used to analyse the velocity distribution and the key point displacements of the brick masonry building under the impact of boulders. The results show that upgrading the brick and mortar, increasing the wall thickness, making full use of the wall thickness, and adding a circular beam and structural column are very effective approaches for improving the impact resistance of brick masonry buildings.

岩石圆盘径向压缩破坏的Voronoi子块体单元DDA方法模拟

非连续变形分析(DDA)方法是计算离散可变形块体系统力学行为的数值计算方法,可通过子块体单元DDA方法模拟岩石的开裂破坏。考虑到Voronoi多边形颗粒与细观尺度下岩石矿物晶粒形态的相似性,提出一种基于随机圆的Voronoi颗粒单元模型生成方法;并通过完整及带预制裂纹岩石圆盘径向压缩破坏的模拟,验证岩石破裂问题Voronoi子块体单元DDA模拟方法的适用性。结果表明,当子块体单元数较小时,圆盘表现出更高的整体强度;随着子块体单元数的增大,起裂处位置更接近真实,开裂破坏路径更清晰;子块体单元数较大时不同倾角预制裂纹圆盘破坏的模拟结果与实验结果高度吻合,并能有效反映圆盘中心加工小孔对开裂破坏路径的影响。使用Voronoi子块体单元DDA方法能够有效模拟岩石的开裂破坏过程,为进一步开展基于Voronoi颗粒单元模型的岩石开裂破坏模拟创造了条件。

基于DDA的岩质边坡稳定性评价方法

岩质边坡的稳定性主要受节理、裂隙等结构面控制,基于连续介质的边坡稳定性分析方法已不适用。为此,将节理岩体非连续变形分析(DDA)方法与强度折减法相结合,提出基于DDA的复杂岩质边坡稳定性分析方法,并给出强度折减策略和安全系数确定依据。通过单滑块直线滑面和多滑块圆弧滑面两个算例,并与理论解和条分法计算结果进行对比,验证该方法的准确性和有效性。以河南洛宁抽水蓄能电站场内公路岩质边坡为例,应用该方法分析不同折减系数下边坡的变形演化过程和位移演化规律,并确定边坡的安全系数。结果表明,在降雨及爆破开挖扰动影响下,边坡破坏首先发生在坡脚,然后逐渐发展到坡顶,与现场调查及监测结果较为吻合。该方法可为复杂岩质边坡稳定性评价提供一种新的研究途径。

浸入运动边界-格子Boltzmann方法4种固含率计算方法对比研究

为了达到流固耦合,格子Boltzmann方法(LBM)可采用浸入运动边界法(IMB)实现移动颗粒边界上的无滑移条件.该耦合方式(IMB-LBM)中固含率计算方法对流固耦合计算精度和效率有影响.对常用的固含率4种计算方法,即蒙特卡洛法(MCM)、单元分解法(UDM)、近似多边形法(APM)和闭合边界法(CBM),分别阐述其具体算法,对比了它们的计算精度和计算效率;最后通过圆盘颗粒非连续变形分析方法(DDDA)与IMB-LBM耦合模型下的一个多颗粒沉降流固耦合算例,对比分析了它们在流固耦合计算过程中的耗时.结果表明:1)CBM无误差,MCM和UDM在随机点数取1000,子单元数取100时误差稳定在1%以下,APM在颗粒直径大于格子长度10倍时,误差小于0.44%;2)MCM和UDM的计算精度及耗时分别与随机点数和子单元数相关,它们的计算耗时大于APM和CBM;3)计算效率上,APM>CBM>UDM>MCM,其中CBM计算耗时略微大于APM,APM和UDM计算耗时分别比MCM少2个和1个数量级.该结果可为IMB-LBM耦合模型中固含率计算方法优选提供借鉴.

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。

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。

强度折减DDA法及其在边坡稳定分析中的应用

在自行研制的非连续变形分析程序中实现自动强度折减法以模拟边坡的稳定性和安全系数。针对强度折减有限元法收敛标准的不确定性,通过分析滑块在边坡上的稳定性,提出以边坡滑移位移与强度折减系数曲线的最大曲率所对应的折减系数为边坡安全系数的判别标准,该判别标准克服了"位移突变准则"不准确的缺点;并基于该判别标准,分析水库岩体边坡的稳定性并得到岩体边坡安全系数随库水位变化的规律;最后对小湾某高边坡进行开挖模拟及开挖后边坡的稳定性进行计算分析。

基于Newmark积分方案的DDA方法

不连续变形分析(DDA)方法以离散的块体集合作为研究对象,引入动力学分析和时步积分技术模拟块体系统的不连续变形行为。对DDA采用的常加速度法进行拓展,给出求解块体系统运动方程的Newmark积分格式,并引入一种与块体不平衡力成正比的自适应阻尼使系统收敛到新的平衡状态,保证求解的稳定性。作为考核,将基于Newmark积分方案的DDA方法应用到隧洞开挖模拟,通过和UDEC软件的计算结果进行对比分析,论证改进后DDA方法的有效性和实用性,进一步拓展DDA解决实际工程问题的能力。