Two-dimensional Discontinuous Deformation Analysis Research Articles

Dynamic Coupled Hydromechanical Approach for Fractured Rock Mass Seepage Using Two-Dimensional Discontinuous Deformation Analysis

Dynamic Coupled Hydromechanical Approach for Fractured Rock Mass Seepage Using Two-Dimensional Discontinuous Deformation Analysis

Investigating the Stability of the Candi Kelir using DDA

Candi Kelir, which is a candi in Prambanan, is a historical masonry structures threatened by high potency of earthquake in Indonesia. Investigating the stability of Candi Prambanan is essential for determining the capability to withstand earthquake loads. Discontinuous Deformation Analysis (DDA) has been extensively applied in the disciplines of rock mechanics and rock engineering. Two-dimensional DDA is chosen to simulate the behaviour of Candi Kelir towards earthquake load. Geometry of each block of Candi Kelir is obtained by Close Range Photogrammetry (CRP) method. Simulation of Candi Kelir is conducted using the seismic excitation from the destructive 2006 Yogyakarta Earthquake. The result of the simulation shows the capability of DDA to simulate the behaviour of masonry structure which allows fully detachment of the blocks. During the earthquake, most of the top structures are failing, thus DDA can simulate and generate the result. Wider application of DDA into the historical masonry structure will be helpful to prevent more damage due to earthquakes.

Contact detection algorithm for arbitrarily shaped blocks based on contact theory in 2D-DDA

Contact theory proposed by Shi expresses the contact problem mathematically by establishing an entrance block and reference point, which greatly reduces the complexity of the contact problem. In this paper, a contact detection algorithm based on contact theory for blocks of arbitrary shapes is proposed and integrated into two-dimensional discontinuous deformation analysis (2D-DDA). First, a new vertex-to-edge contact cover detection algorithm that considers contact transfer information is proposed. Second, a filtering algorithm is designed to preserve contact covers based on contact transfer information. Third, an efficient algorithm is proposed to combine contact patterns based on contact covers. The proposed algorithm is verified by using classic examples, and the results are compared with the results of classic 2D-DDA. The findings confirm that the proposed algorithm is feasible and efficient.

MICROSCOPIC DISCONTINUITY DEFORMATION ANALYSIS OF CAPILLARY IN UNSATURATED SOIL

Capillary action is one of significant sources of matric suction in the unsaturated soil. So we propose a new method based on two-dimensional Discontinuous Deformation Analysis(DDA)to simulate the distribution of capillary water and to calculate soil water characteristic curve(SWCC)under different saturation. Firstly,the radius of capillary water meniscus is calculated with iterative algorithm method,and circle center trajectory intersection method is used to determine capillary water distribution in this algorithm. Then,the matric suction,calculated with Young-Laplace equation,is taken into account in the control equation of the original DDA method with the surface tension. Moreover,in order to verify the accuracy of the algorithm,an ideal loess structure model is established. In this model,the soil particles used are mainly coarse particles with high content of loess. The particle size distribution and shape accord with the actual values. And then,the model is used to simulate the distribution of capillary water and to calculate soil water characteristic curve(SWCC). The results show that simulated SWCC contains boundary effect stage,transition stage and residual stage. The distribution of capillary water is simulated at each stage. In addition,the result comparison between the numerical simulation and the experimental data shows the simulation results agree well with experimental data,which suggest that this method is available for simulating capillary action in unsaturated soil.

Improvement of vertex-to-vertex contact processing in two-dimensional DDA

This paper proposes a new critical concept for contact processing in the original two-dimensional discontinuous deformation analysis (DDA). A new critical concept that is inside or outside the reference line is proposed to enhance contact processing in the original DDA. When the vertex P is inside of one reference line, the reference line is shifted to the other edge so that P is now outside. The original rules are applicable only when both vertices are outside or inside of both the possible edges. The new critical concept is a stricter algorithm that remedies the indeterminacy of detecting the candidate reference line for vertex-to-vertex contact in the original DDA. The accuracy and effectiveness of the contact-improved DDA were studied using various numerical examples. The simulation results showed that the proposed method is more accurate and useful compared to original method after contact improvement and can be better applied to models with arbitrary vertex-to-vertex contact states.

Numerical Analyses on the Rockbolt Behaviour in Rock Wedges Reinforcement Using 2D-DDA

One major concern in the design and construction of caverns in jointed rock mass is the potential failure of rock wedges falling from the roof or sliding out from the sidewalls. The rockbolts are commonly used to improve the stability and to prevent failure in the caverns. In this paper, the two-dimensional discontinuous deformation analysis (2D-DDA) method was used to analyse the stability of the rock wedge supported by rockbolts on the cavern roof. The joint relaxation method was adopted to represent a deformable rock joint under stresses. Parametric studies were conducted to investigate the effects of the confining pressure, the spacing and the angle between rockbolt and direction of wedge falling on the stability of the rock wedge. The numerical simulation results indicate that the wedge is self-supporting after stress redistribution if the confining pressure is larger than the critical confining pressure and the semi-apical angle of the wedge is less than the friction angle of rock joint. The force in rockbolt slightly decreases with reduced rockbolts spacing but increase when the rockbolt is not along the falling direction of rock wedge.

A robust contact detection algorithm based on the Contact Theory in the three-dimensional discontinuous deformation analysis

The two-dimensional discontinuous deformation analysis (DDA), as a discrete numerical method, has been successfully used to simulate many rock mechanics and rock engineering problems. However, for the development of the three-dimensional DDA (3D-DDA), the contact detection between polyhedral blocks has long been one of the key difficulties awaited to be solved. A universal Contact Theory was proposed by Shi in 2015, in which the complicated contact relationship of two any-shaped blocks is represented by a simple relationship between a reference point and an entrance block, along with a concept of the contact cover. In the present study, a robust contact detection algorithm in the 3D-DDA for convex polyhedral blocks based on the Contact Theory is proposed. In this algorithm, all the six basic contact types of polyhedral blocks are functionally treated as two contact types, namely, the vertex-to-face contact and the non-parallel edge-to-edge contact; meanwhile, the vertex-to-vertex and vertex-to-edge contacts are specially handled to guarantee the effectiveness and efficiency of the algorithm. Two special contact cases with the parallel edge-to-edge contact and the vertex-to-vertex contact, respectively, and two multi-block cases, in which various contact types and the transition between them are involved, are simulated to verify the effectiveness and robustness of the proposed contact detection algorithm. Moreover, failure simulations of sliding and toppling slopes with massive rock blocks are conducted and in the sliding case the effect of a retaining wall is also simulated. Results indicate that, the proposed algorithm can handle the contact detections of convex polyhedral blocks effectively under critical and complex conditions, which builds a good precondition for the successful development and practical application of the 3D-DDA method.

OpenMP-Based Parallel Two-Dimensional Discontinuous Deformation Analysis for Large-Scale Simulation

Abstract Discontinuous deformation analysis (DDA) has gained wide acceptance in geotechnical engineering. The simulation of large-scale engineering problems using DDA is computationally expensive. ...

Distributed-Spring Edge-to-Edge Contact Model for Two-Dimensional Discontinuous Deformation Analysis

Edge-to-edge contact is a fundamental contact type in blocky systems. In two-dimensional discontinuous deformation analysis (2D DDA, and hereinafter DDA for short), an edge-to-edge contact is transformed into two separated vertex-to-edge contacts by applying two pairs of concentrated springs. Although this simplification facilitates the DDA algorithm, it is not always sufficiently accurate and can even yield irregular results. To solve this problem, a distributed-spring contact model (DSCM) that exerts distributed instead of concentrated forces on contact edges is proposed in this paper for the edge-to-edge contact in DDA. Submatrices for the force matrix and stiffness matrix are obtained by minimizing the potential energy of the distributed contact forces and are incorporated into an improved DDA (I-DDA) code. Four examples are evaluated to illustrate the validations and advantages of the I-DDA. The first example is a single square impacting on a base block. Deformation of the contact area is evaluated by comparison with the theoretical deformation solution, and the results calculated by the I-DDA show better agreement with the analytical solution than the original DDA (O-DDA). The second example is an impact validation, proving that the I-DDA is more adaptable to discrete systems containing blocks of different sizes. Then an example and an experiment about block rebounding are provided, demonstrating that the errors in rotation and rebounding exhibited in the O-DDA results are avoided when using the I-DDA, indicating that the I-DDA provides more realistic solutions. The results of this study suggest that the proposed I-DDA incorporating the DSCM is quite accurate and capable of improving calculation accuracy compared to the O-DDA.

Bond-slip modeling of a CMC rockbolt element using 2D-DDA method

The bonding condition at the rock and rockbolt interface is one of the most important factors to determine the load transfer mechanism of a CMC rockbolt element. The two-dimensional Discontinuous Deformation Analysis (2D-DDA) method is used in this paper to investigate the pullout performance of the CMC rockbolt element which is modeled as three components, i.e. the rock, the rockbolt and the mortar. The material properties used in the numerical models are calibrated against the experiments results. The simulated results show that a bond stress versus slip displacement curve of the CMC rockbolt element is exhibiting three stages which could be represented by a trilinear bond-slip model. Parametric studies have been carried out to investigate the effects of the confining pressure and those of the geometry configuration of the rockbolt ribs on the bond stress versus slip displacement curves and the crack propagations in the mortar. It is found that the maximum bond strength and the residual bond strength increase with the increase of confining pressure. Under lower confining pressure, the rib face angle controls the dilation of rock blocks. The obtained key parameters of the trilinear bond – slip models can be used to simulate the bond behavior between the rockbolt and rock interface in pullout test. The nodal axial forces and nodal bond force distributions along the rockbolt could be curve fitted using exponential models. The obtained parameters of the exponential models can be used for engineering practice under similar conditions.

Simulating the failure process of the Xinmo landslide using discontinuous deformation analysis

The Xinmo landslide slope in Sichuan, China, was stable during the intensive Wenchuan Earthquake in 2008 but failed on June 24, 2017. Landslide debris buried Xinmo Village and blocked the Songpinggou River at the slope toe. This study aims to clarify the post-failure behavior of the landslide using two-dimensional discontinuous deformation analysis (2D DDA). The simulation results provide comprehensive information on the initiation and the evolution of the landslide. The failure process determined by the DDA correlates well with the seismic signal analysis results. In addition, the location of the calculated rock deposit is similar to that shown by the topographic map after the landslide. The maximum rock velocity in the landslide is 65.4 m/s. Therefore, the impacts of the high-velocity blocks and the buildings in Xinmo Village must be considered to simulate the burial of Xinmo Village by rocks and the transport of additional rocks across the Songpinggou River. This Xinmo landslide study demonstrates that the DDA accurately simulates the post-failure behavior and determines the impact area of a landslide with complicated failure processes and topography.

Development of a Unified Rock Bolt Model in Discontinuous Deformation Analysis

In this paper, a unified rock bolt model is proposed and incorporated into the two-dimensional discontinuous deformation analysis. In the model, the bolt shank is discretized into a finite number of (modified) Euler–Bernoulli beam elements with the degrees of freedom represented at the end nodes, while the face plate is treated as solid blocks. The rock mass and the bolt shank deform independently, but interact with each other through a few anchored points. The interactions between the rock mass and the face plate are handled via general contact algorithm. Different types of rock bolts (e.g., Expansion Shell, fully grouted rebar, Split Set, cone bolt, Roofex, Garford and D-bolt) can be realized by specifying the corresponding constitutive model for the tangential behavior of the anchored points. Four failure modes, namely tensile failure and shear failure of the bolt shank, debonding along the bolt/rock interface and loss of the face plate, are available in the analysis procedure. The performance of a typical conventional rock bolt (fully grouted rebar) and a typical energy-absorbing rock bolt (D-bolt) under the scenarios of suspending loosened blocks and rock dilation is investigated using the proposed model. The reliability of the proposed model is verified by comparing the simulation results with theoretical predictions and experimental observations. The proposed model could be used to reveal the mechanism of each type of rock bolt in realistic scenarios and to provide a numerical way for presenting the detailed profile about the behavior of bolts, in particular at intermediate loading stages.

Modeling of Rock Joints Under Cyclic Loading Conditions Using Discontinuous Deformation Analysis

The shear strength of rock joints is an important factor to be considered when analyzing the stability of jointed rock mass. Rock joints tend to have smaller shear resistances in the reverse shearing than that of the forward shearing. A conceptual model describing the general shear behavior of rock joints under cyclic loading and the Barton–Bandis joint model considering the surface roughness degradation are implemented into the two-dimensional discontinuous deformation analysis (DDA) model. The modified DDA model is empirically validated by cyclic shear tests on two types of rock joints. Numerical simulations agree well with the experimental results, indicating that the DDA model is capable of describing the varying shear behaviors of rock joints subjected to cyclic loading conditions.

Advances in Two-Dimensional Discontinuous Deformation Analysis for Rock-Mass Dynamics

AbstractThis paper contains a summary of the developments and applications of the two-dimensional discontinuous deformation analysis (DDA2D) method regarding the modeling of rock-mass dynamics problems. Reviews on the control parameter value selections in DDA2D calculations and the developments and applications of the DDA2D regarding the analysis of rock slope failures, landslides, rockfall, some earthquake-related problems, and so forth, are performed. Research on the DDA2D for three basic rock-mass dynamics problems, such as block dynamic sliding, stress wave propagation, and dynamic fracturing, are specially stated. The modeling of rock blasting, a typical exact rock dynamics problem, is selected as a representative application example of the DDA method to be presented. Generally, the DDA2D has shown to be a powerful numerical method for the modeling of rock-mass dynamics. However, one should pay enough attention to the value selections of those important user-supplied control parameters, as well as to...

An Angle-Based Method Dealing with Vertex–Vertex Contact in the Two-Dimensional Discontinuous Deformation Analysis (DDA)

Due to the discontinuity of the direction of a normal vector at the corner, vertex-vertex contact is indeterminate in numerical modelling. Two classes are indeterminate in two-dimensional discontinuous deformation analysis (DDA), designated as "genuine indeterminacy" and "pseudo indeterminacy". While examining these indeterminacies, it is necessary to pre-process quasi-vertex-vertex contact and determine contact or entrance edges. On one hand, improper pre-processing not only changes the equilibrium equations of the system, but also increases the burden on open-close iteration. On the other hand, there are two kinds of quasi-contact edges, i.e. the same and different block quasi-contact edges. Certain previous distance-based methods, which are used to seek the correct entrance edge, lead to some forced contacts, including vertex-vertex or vertex-edge. New pre-processing and angle-based methods for determining entrance edges are developed in this study. Additionally, the new concept of strengthening the movement trend of blocks is presented in DDA. The new pretreatment method combining the angle-based method and a strategy for strengthening the movement trend of blocks are intended to reduce forced contacts, maintain the movement trend of blocks, and speed up open-close iterations to a certain extent. Furthermore, the new method only depends on the orientation of quasi-contact edges and the movement trend of convex corners. The effectiveness of these improvements is verified by translational motion, rotation trend, and time-step size effect tests.

Numerical studies on rockbolts mechanism using 2D discontinuous deformation analysis

To understand the response of rockbolts under various loads is an important part in the design of rock reinforcement. In this paper, the rockbolt models are developed within the frame work of the two-dimensional discontinuous deformation analysis (DDA). The rockbolt material is modeled by the elastic, linear strain-hardening behavior. To simulate the anchored system employed in various rockbolts, different bond stiffness are used for the interface between the rock and the rockbolt. The rockbolt models for the expansion shell anchored bolt, the split set, the fully grouted rebar and the D-bolt are considered in the simulations of the pullout tests. Extreme pull-out loadings were also applied to examine the bearing capability and deformation capability of the rockbolt system. In addition, two kinds of popular permanent rockbolts, the fully grouted rebar and D-bolt were further studied in the simulation of drop tests. The effects of impact amplitude and duration on the rockbolt behaviors were studied by single drops to demonstrate the advantage of D-bolt in energy dissipation. The results showed that the proposed rockbolt models can realistically predict the bonding forces and axial loading along the length of rockbolt.

Development of Rock Bolt Elements in Two-Dimensional Discontinuous Deformation Analysis

Computer modeling can be used to explore and gain new insights into the impacts of rock bolt intersecting joints in rock masses, and to estimate the effectiveness of the rock reinforcement system. In order to achieve this goal, we couple a rock bolt element into the two-dimensional discontinuous deformation analysis (DDA2D) program. The coupling algorithm is based on the analytically-derived interface behavior between a rock bolt and the rock material for grouted rock bolts. The shear force generated by slippage along the interface is assumed to have a linear relationship with respect to the relative slipping distance between the rock bolt and the rock. The linear elastic criterion is applied to determine the material behavior of rock bolts before the axial stress reaches the yield value. The pullout tests are simulated to verify the coupling algorithm and the effects of the proposed rock bolt elements. Parametrical studies are also carried out to analyze the effectiveness of the rock bolts under various end conditions, joint locations and bond stiffness. In addition, the performance of the rock bolt during the interface debonding is analyzed using two types of constitutive laws, i.e., the friction law and the reduction law. The simulation results show that the proposed rock bolt models can predict the shear forces and axial loading along the rock bolts.

A New Viscous Boundary Condition in the Two-Dimensional Discontinuous Deformation Analysis Method for Wave Propagation Problems

Viscous boundaries are widely used in numerical simulations of wave propagation problems in rock mechanics and rock engineering. By using such boundaries, reflected waves from artificial boundaries can be eliminated; therefore, an infinite domain can be modeled as a finite domain more effectively and with a much greater accuracy. Little progress has been made, thus far, with the implementation and verification of a viscous boundary in the numerical, discrete element, discontinuous deformation analysis (DDA) method. We present in this paper a new viscous boundary condition for DDA with a higher absorbing efficiency in comparison to previously published solutions. The theoretical derivation of the new viscous boundary condition for DDA is presented in detail, starting from first principles. The accuracy of the new boundary condition is verified using a series of numerical benchmark tests. We show that the new viscous boundary condition works well with both P waves as well as S waves.

The vertex-to-vertex contact analysis in the two-dimensional discontinuous deformation analysis

In the two-dimensional discontinuous deformation analysis (DDA), contacts can be generalized into three types: vertex to edge, edge to edge, and vertex to vertex. In the vertex–edge contact, the contact reference edge is clearly and uniquely defined, while the contact reference edge for the vertex–vertex contact is not unique, which will lead to an indeterminate state. The indeterminacy of the vertex–vertex contact is a well-known problem in both the continuum-based methods and the discontinuum-based methods. The standard DDA employs the shortest path method to deal with the indeterminacy in the vertex–vertex contact, which is sensitive to the choice of analysis parameters, such as the time step size, the maximum displacement ratio and the contact spring stiffness. Two enhancements to the shortest path method are introduced in this paper. The first enhancement employs a temporary vertex–vertex contact spring to determine the moving tendency among two contact blocks. The second enhancement uses the trajectory of the vertex during a time step to find the entrance edge when the moving vertex invades into the target block. Examples show that these two enhancements to the standard DDA code work well.

An alternative scheme for the corner–corner contact in the two-dimensional Discontinuous Deformation Analysis

Formulated based on the discrete block system, the Discontinuous Deformation Analysis (DDA) requires an accurate contact analysis between discrete blocks. Among the various contacts, the modeling of the corner-corner contact is the most challenging one as the contact reference edges in the corner-corner contact are not unique, which may lead to an indeterminate state in the numerical analysis. The algorithm in the original DDA employs the penetration distance to determine the contact edge in the corner-corner contact, which may not work for cases where two corners are detected in contact but without a penetration. An enhanced algorithm for choosing the initial contact edge of the corner-corner contact in the DDA is presented in the paper, in which a special contact spring that works like a weak ''pin joint'' is added between the contact corners. The relative moving tendency is determined under the special contact spring, so that the program can automatically choose a reasonable contact reference edge for the corner-corner contact. Three numerical examples are used to illustrate the advantage of this alternative method over the original DDA code.