Showing papers on "Discontinuous Deformation Analysis published in 2022"

Parametric research on the time step and spring stiffness in three‐dimensional discontinuous deformation analysis method

Abstract: Three‐dimensional discontinuous deformation analysis method (3D.DDA) is a dynamic calculation method based on the implicit solution. Inertial force is introduced in the solution process to ensure that the time variable is the real time variable, and springs are applied at the block boundary to avoid mutual intrusion between blocks. Therefore, the value of time step and contact spring stiffness directly affect the accuracy of 3D.DDA calculation results. Firstly, we analyzed the effects of the time step and contact spring stiffness on the numerical calculation results of the 3D.DDA method based on the theoretical formula derivation. Secondly, we studied the influence mechanism of time step on the simulation results of the 3D.DDA method individually based on the double block free falling model. And we determined the reasonable value area of time step. Then, considering the contacts between blocks, we studied the joint influence mechanism of time step and contact spring stiffness on the 3D.DDA simulation results based on the double block sliding model. And we analyzed the error between the 3D.DDA simulation value and the theoretical value under the conditions of different time step and contact spring stiffness. Based on that, we divided the combined value area of time step and contact spring stiffness into four regions (Q1, Q2, Q3, and Q4) and determined the optimal value area of time step and contact spring stiffness. At last, we carried out the slope rockfall model experiment and numerical simulation, and the trajectory of the falling rock in the numerical simulation was basically consistent with the experiment results, which verified the effectiveness of the optimal value area of time step and contact spring stiffness. The research results can provide a reference for the choice of the value of time step and contact spring stiffness in the numerical simulation based on the 3D.DDA method.

A continuous-discontinuous deformation analysis method for simulating the progressive failure process of riverbanks

Abstract: River scouring is the primary cause of impulsive riverbank failure. Its direct effect is to cause catastrophic changes in the structure of the riverbank slope, which then leads to riverbank collapse. However, its internal evolution mechanism is unclear. To solve this problem, a continuous-discontinuous deformation analysis method that can reveal the evolution mechanism has been developed based on the Discontinuous Deformation Analysis (DDA) method. It discretizes the soil into Voronoi-shaped sub-blocks, forces the displacement coordination of the continuous medium through the defined bar element between the sub-blocks, and simulates the evolution from continuum to discontinuum through the bar element failure. At the same time, the open-close iteration algorithm is still used to deal with the contact between the real block boundaries and there is no need to judge the contact between sub-blocks. Then, for the first time, a generalized model of riverbank collapse caused by flow erosion is built, the entire failure process is simulated, and the effects of different soil strengths and slope ratios on the failure mode are discussed. The results indicate that it is insufficient to explain the mechanism of riverbank collapse only by using the concept of circular slip failure of a traditional soil slope.

Investigating the Role of Earthquakes on the Stability of Dangerous Rock Masses and Rockfall Dynamics

Abstract: In recent years, earthquake rockfalls have occurred frequently all over the world, resulting in heavy casualties and property losses. Unfortunately, research on rockfall dynamics upon earthquake events is still rare due to limited field and experimental data, and restricted to numerical simulations of only two dimensions. In order to primarily reveal the role of earthquakes on rockfall, this study focused on the stability of rock blocks on an inclined slope, and following rockfall dynamics by three-dimensional discontinuous deformation analysis (3-D DDA). First, earthquake input methods were discussed and implemented for the triangulated regular network (TRN) in 3-D DDA. The effectiveness was verified by comparison with analytical solution results of a single block on the inclined slope under seismic loads. Further, by discussing the variations of the boundary chart of failure modes, it indicated that the block was more prone to slide even with a large friction angle, became instability under seismic conditions. Moreover, a regular dodecahedron rock block was released on a stochastic roughness slope with two platforms through parallel realizations. The indices of the movement characteristics of the block, such as runout distance, lateral displacement range, and resting position, were investigated. The results showed that the maximum runout distance was not sensitive to seismic load, but the lateral displacement range was significantly sensitive to seismic load and increased appreciably. Through the 3D-DDA numerical simulations, both rock stability and rockfall behaviors under earthquake conditions could be better understood. Furthermore, it will be helpful to by analyzing trajectories and kinetic energies predict earthquake rockfall disasters and design reasonable protective countermeasures under earthquake scenarios.

Investigation on Deformation Mechanism and Treatment Effect of a Scattered Slope Based on Continuum–Discontinuum Element Method and Finite Difference Method

Abstract: Slope deformation and failure is an inevitable engineering problem in highway construction and operation in mountainous areas. Its essence is a continuous–discontinuous gradual failure process of slope under the action of unbalanced force. Slope deformation and failure mechanism is the basis and key content of its emergency treatment and comprehensive treatment. In this study, the continuous–discontinuous element method (CDEM) and finite difference method are used to analyze the deformation mechanism and support the effect of a scattered slope in the Biwei Expressway. The results showed that the change in the local geological environment caused by roadbed excavation leads to slope slippage along the surface and then pulls the upper rock mass gradually to produce slippage failure, resulting in the stability gradually decreasing. The mechanism is traction sliding–tensile cracking. The continuous–discontinuous element method can effectively simulate the formation process of the main and sub sliding planes during excavation and can better display the phenomenon of slope failure and gradual disintegration. The emergency disposal of the gravity anti-sliding retaining wall in front of the slope can effectively control further deformation and ensure temporary stability. In comprehensive treatment, step-type slope excavation, gravity anti-sliding retaining wall, and anchor frame beam are adopted to control the deformation and failure of slope and ensure long-term stability. The numerical simulation results are consistent with the actual results, which effectively explains the rationality of this study. The research results of this study can provide some reference for the emergency treatment and comprehensive treatment of slopes in mountainous areas and for the construction and operation of highways and other infrastructure in mountainous areas.

DEM-Based Numerical Investigation of Seismic Stability of Rock Slope in Terms of Rigid Block Displacement

Abstract: For the seismic behavior of a rock slope or more specifically a rock wedge, the limit equilibrium method is frequently utilized to determine the static and pseudo-static safety factor, and the Newmark method is usually applied to estimate the permanent dynamic displacement. However, the two methods are relatively complex, which negatively affects their usage in engineering practice. A new idea to analyze the static and dynamic stability of a complex rock slope was provided in this paper by combing the rigid discrete element method (DEM), shear strength reduction (SSR) method, and Newmark method. The research results show that (1) by setting the joint contact stiffness to a very large magnitude, the joint displacement caused by the reduction of joint contact stiffness during the SSR calculation process can be considered ignorable, making the contact behavior between the respective two joints approximately satisfy the rigid-plastic assumption. In this manner, it is feasible to calculate the static and pseudo-static safety factor (SF) and the permanent dynamic displacement of a rock wedge with the rigid DEM. (2) The SF and sliding forces of wedges can be directly calculated by this new method without any auxiliary assumption of motion direction or sliding type. Additionally, the new method is suitable for complex wedges, which is important to practical design. (3) The rigid DEM can be realized in 3DEC, which is testified in this paper by 5 classic static examples and 3 typical dynamic examples. (4) The effect of some important parameters, such as the excitation acceleration amplitude and dip of intersection line between two joints, on the dynamic displacement and SF under dynamic excitation was analyzed. The parameter analysis revealed that evaluating the seismic performance of a rock slope only with the pseudo-static SF would potentially underestimate the seismic displacement, under some special conditions. (5) An example case was presented in this paper that the seismic stability assessment of a block was performed with the proposed approach in terms of seismic displacement. And the slope reinforcement scheme was suggested with respect to exceedance probability. It is noted that the reinforcement scheme obtained from the rigid DEM has a better cost-saving benefit under the same SF. Overall, the knowledge gained in this paper may offer a new idea for the static and dynamic analysis to the rock slope stability.

Dynamic behavior and stability of model slopes with hexagonal jointing, Part 6: Prediction by improved discontinuous deformation analysis

Abstract: In this study, to investigate the performance and the issues of the seismic stability evaluation of discontinuous rock slopes, predictive analysis of shaking table experiments of rock slope models was conducted using an improved discontinuous deformation analysis (DDA) incorporating implicit updating algorithm of friction law. In order to clarify the meanings and determination methods of the input parameters, the list and determination method of all material and numerical parameters used in the analysis are explained. The simulated results with the improved DDA was discussed in terms of the acceleration level inducing slope failure, the mode and extent of the failure by comparing with the experimental results.

Investigation of 2D Seismic DDA Method for Numerical Simulation of Shaking Table Test of Rock Mass Engineering

Abstract: Since the basic theory of the discontinue deformation analysis (DDA) method was proposed, the DDA open source has gone through a long development process. At present, different kinds of programs have been widely applied in rock mass engineering such as slope, dam, and tunnel. This paper introduces the solution principle of DDA motion equations in detail, as well as the development status of the 2D open-source program. Numerical simulation of shaking table test of rock mass engineering using 2D DDA program is highlighted, and investigations of seismic wave pre-processing and seismic input method are carried out. First, based on the Newmark integration scheme, the integration algorithms of synthetic or measured seismic wave time history, correction function of seismic wave, and DDA simulation are unified. Then, three seismic input methods are implanted in the DDA program, and the applicability of various seismic input methods is discussed. On this basis, using the improved seismic 2D DDA program, a shaking table test of typical rock mass engineering is simulated. Through the comparison between the theoretical/test data and simulation results, the reliability of the improved DDA program in seismic response analysis is verified; the large mass method and the large stiffness method are more suitable for rigid foundation, such as shaking table test; the propagation of the seismic wave presents a significant amplification effect due to the reflection, refraction, and diffraction in the tunnel. The research results provide DDA theory and an open-source program for analyzing the seismic response of rock mass engineering.

Comparison of Material Point Method and Finite Element Method for Post-Failure Large Deformation Geotechnical Analysis

Abstract: Finite Element Method (FEM) has been the state-of-the-art method in geotechnical analysis since it first formulated in the 40s. It capable to handle Multiphysics simulation, soil-structure and soil-water interaction, and time history analysis. Though powerful, the standard Lagrangian FEM suffers mesh distortion when handling large strain deformation problem. This mesh entanglement problem makes post-failure analysis is considerably challenging to model if not impossible to do using FEM. The Material Point Method (MPM) then later introduced to solve these large strain deformation problems. Adapted from the Particle in Cell (PIC) method, MPM is a hybrid method that combines Eularian and Lagrangian approach by utilizing moving material points which are moving over spatially fixed computational mesh. This approach enables MPM to calculate not only fluid mechanics such in PIC but also solid mechanics and its intermediatory states. To demonstrate the capability of MPM and its consistency with FEM in geotechnical analysis, this article presents a comparison of FEM and MPM analysis on a hypothetical slope using Mohr-Coulomb constitutive model. The simulation shows that both FEM and MPM analyses are consistent to each other especially in small strain scheme. However, in large strain deformation, MPM is still able to get convergent result while FEM is not. The MPM simulation is also able to animate post failure behavior clearly, calculate post-failure strains and stresses distribution, and present final geometry of the model.

Consideration of countermeasures using rockfall simulation by discontinuous deformation analysis

Abstract: In order to rationally design rockfall countermeasures, it is necessary to predict detailed rockfall behavior by numerical simulation according to the conditions of slopes and rockfalls. In this study, we try rockfall simulation using Discontinuous Deformation Analysis. This method is a method to analyze the motion between blocks composed of polygons of arbitrary elastic bodies, and as a feature, the energy conservation law and the uniqueness/convergence of the solution are guaranteed for the entire analysis target. On the other hand, in this method, the shape of the rockfall is reproduced in detail, so parameters such as the shape index that quantitatively expresses the shape and the velocity energy ratio that indicates the decay of energy at the time of collision of the rockfall have a large effect on the rockfall behavior. In this study, we modeled the actual slope shape and rockfall from the data measured by the airborne laser, and quantitatively evaluated the effect by performing simulations by changing the shape index and velocity energy ratio. In this paper, we consider how to use the simulation for the design of rockfall countermeasures based on the results such as the change in the amount of jumping due to the difference in slope shape, geology, and rockfall shape.

Order two superconvergence of the cdg method for the stokes equations on triangle/tetrahedron

Abstract: A new conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the Stokes equations. The CDG method gets its name by combining good features of both conforming finite element method and discontinuous finite element method. It has the flexibility of using discontinuous approximation and simplicity in formulation of the conforming finite element method. This new CDG method is not only stabilizer free but also has two order higher convergence rate than the optimal order. This CDG method uses discontinuous $ P_k $ element for velocity and continuous $ P_{k+1} $ element for pressure. Order two superconvergence is derived for velocity in an energy norm and the $ L^2 $ norm. The superconvergent $ P_k $ solution is lifted elementwise to a $ P_{k+2} $ velocity which converges at the optimal order. The numerical experiments confirm the theories.

Key group analysis based on DDA method for rock slope stability analysis

Abstract: Inhomogeneity and discontinuities play a key role in resistance and behavior of rock masses. Today engineers have a wide range of methods to analyze the stability of rock slopes. Due to its simplicity and speed of evaluation, static analysis methods continue to play a special role in the stability assessment of jointed rock slopes. One of the most well-known static methods used in the stability analysis of rock slopes is the Key Block method (KBM), which is based on the key block finding and analyzing. In this method, if none of the key blocks are unstable, it implies that rock mass is stable. Occasionally, the combination of a number of stable blocks has led to formation a group of blocks that sometimes leads to instability. Therefore, the stability analysis of the jointed rock masses leads to study of groups of blocks that are potentially dangerous for the stability of a rock slope. The Key Group method (KGM), with its progressive approach, finds these critical groups and focuses the stability calculations on these groups. In order to increase the efficiency, accuracy and speed of this method and to develop it in three dimensions, it is decided to combine it with one of the numerical methods. The standard Discontinuous Deformation Analysis method (DDA) is an implicit method based on the finite element method. This is a sophisticated numerical method for modeling the quasi-static and dynamic behavior of rock block systems in discontinuous rock masses. The goal of this paper is to use of the potency of the numerical method of DDA to analyze the candidate key group. For this purpose, the DDA computer program was developed with Mathematica programming language and combined with the KGM software. The resulting package, after selecting the key group by the KGM method, proceeds to analyze it with the DDA method. Two examples solved illustrating the reasonable results and the efficiency of this developed method compared to that of the original KGM and SKGM. The results validated the proper accuracy and good performance of the procedure developed in this research.

Stability analysis of Xiluodu Hydropower Station right bank slope based on discontinuous deformation analysis method

Abstract: PurposeThe purpose of this study is to investigate the deformation characteristics and failure modes of the right bank slope of Xiluodu Hydropower Station after excavation.Design/methodology/approachMicro-seismic monitoring technology is applied to obtain the microfracture information and study the internal damage evolution law of the slope rock mass. A numerical model for discontinuous deformation analysis (DDA) is established to analyse the deformation characteristics and failure mode of the slope. Micro-seismic monitoring and DDA can verify and supplement each other's results in the investigation of slope failure.FindingsThe results show that the slope has a downhill displacement along the weathered zone under natural conditions; the maximum resultant displacement at the monitoring point is 380 mm. The micro-seismic events are concentrated in an area located 30–100 m horizontally away from the slope surface and at an elevation of 390–470 m. The distribution of these micro-seismic events is consistent with the location of the unloading and weathered zones; it is the same as the DDA simulation result.Originality/valueThe study is anticipated to be used as reference for the stability analysis of rock slopes. By combining the continuous (micro-seismic monitoring technology) and discontinuous (DDA) methods, the entire process starting from the gradual accumulation of internal rock micro-damage to the macroscopic discontinuous deformation and failure of the slope can be investigated.

Development of particle discontinuous deformation analysis method and its application in rock blasting

Abstract: Numerical methods based on continuity assumptions, such as finite element method, may be not sufficient or accurate enough to simulate the blasting failure process of rock materials due to its inherent small strain assumption and ignorance of rock block interactions. While the discontinuous deformation analysis method (DDA) has greater superiority in solving these dynamic problems of rock mass. By introducing the non-reflective boundary conditions in the block-DDA into self-developed software, the explosion processes of the spherical charge in the half-infinite domain are analyzed comprehensively. The real-time pressure which is converted by the volume of the blasting cavity is applied on the inner wall of the blast hole to perform the DDA simulation of rock blasting. Multiple sets of numerical examples are demonstrated, including the transmission of stress wave in a one-dimensional rod, the formation process of blasting funnel, etc. The simulation results match well with the existing physical and numerical test results in the literature. Reasonable numerical results indicate that, the proposed algorithm can be served a promising tool to predict blasting behaviour of rock.

Displacement behavior of tree intruded-fractures at a rock slope

Abstract: 岩盤の割れ目に樹木や樹木根が侵入する場合，その成長に伴って割れ目が徐々に拡大して不安定な岩塊が生まれ，やがてこれが落石となることがある．この割れ目の拡大がどのようなタイミングで生じるかを観察するため，北海道函館市内の岩盤斜面にてハリエンジュが侵入する割れ目の変位を3年6ヵ月にわたり計測した．データに含まれる変位計と岩盤の周期的な熱変形を補正した結果，樹木の成長期にあたる5月上旬から8月中旬にかけて明瞭な開口変位が確認できた．さらに，細かい変位に対して気候条件などとの比較を行った結果，温度の影響が強い樹木の肥大成長に加えて，地震，遮るものがない方向からの風，降雨の際に割れ目が僅かに開く傾向がみられた．これらは樹木の成長により不安定になったブロックから生じる浮石型落石の誘因となり得る．