Application of the discontinuous deformation analysis method to stress wave propagation through a one-dimensional rock mass

Fu, Xiaodong; Sheng, Qian; Zhang, Yonghui; Chen, Jian

doi:10.1016/j.ijrmms.2015.09.017

Cited by 49 publications

(14 citation statements)

References 38 publications

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“…It is thus obvious that [13,14,16,18] both the average acceleration method ( = 1/4, = 1/2) and the constant acceleration method ( = 1/2, = 1) meet the unconditionally stable condition, while the linear acceleration method ( = 1/6, = 1/2) and the central difference method ( = 0, = 1/2) are the conditionally stable method. In general, the accuracy of Newmark method depends on the time interval, the physical parameters of the system, and the loading condition.…”

Section: Algorithmic Damping Of the Newmark Methodmentioning

confidence: 99%

“…Hatzor et al [11] and Tsesarsky et al [5] obtained that 2% kinetic damping was the correct number for the dynamic analysis of a single block on an inclined subjected to dynamic loading. However, the significance of the kinetic damping is still not clear, and the value of initial velocity discounted is hard to choose; therefore, some researchers have introduced self-adaptive damping [12] and viscous damping [13,14] to address these problems. Lin and Xie [15] also analyzed the performance of Newmark time integration with kinetic damping.…”

Section: Introductionmentioning

confidence: 99%

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Study on the Damping of the Discontinuous Deformation Analysis Based on Two‐Block Model

Feng

Jiang

et al. 2017

Mathematical Problems in Engineering

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The deformation and failure of rock mass is a process of energy dissipation; the damping of DDA is a very important and basic problem. The correctness and effectiveness of DDA rely on the appropriate values of the numeric controlling parameters like time interval, spring stiffness, and assumed maximum displacement ratio 2 , and the contact using the penalty method is the core content of DDA. A mechanical model of two contact blocks loaded with the normal force acting along one side of block boundary is established to study the DDA damping problem, which involves the contact and eliminates the influence of some numeric control parameters (e.g., 2 ). Based on the Newmark method and the theory of DDA, the motion equations of two-block system can be established, and then the relationship of some numeric control parameters and the influence of damping can be obtained. The algorithmic damping increases with the increasing of time interval. Given a very small time interval, the spring stiffness may have no obvious effect on the algorithmic damping. The numerical results reveal that the essence of time interval influencing the openclose iteration is the fact that the algorithmic damping is mainly controlled by time interval.

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Section: Algorithmic Damping Of the Newmark Methodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Study on the Damping of the Discontinuous Deformation Analysis Based on Two‐Block Model

Feng

Jiang

et al. 2017

Mathematical Problems in Engineering

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“…Regarding the artificial damping, a simple viscous damping term as shown in Equation is used in the CA, NPC, and MNPC approaches. For SDOF system, the viscous damping ratio ξ viscous related with damping coefficient gg in Equation can be represented in the following format,

ξ_{viscous} = \frac{{((), 1 - italicgg)}^{2}}{4 normalΩ} .

The parameter gg in Equation can be set to a value ranging from 0 to 1. For quasi‐static analysis, it is usually set to 0 to dissipate the kinetic energy of the system.…”

Section: Properties Of the New Approachmentioning

confidence: 99%

“…For quasi‐static analysis, it is usually set to 0 to dissipate the kinetic energy of the system. For dynamic analysis, the coupling effects of damping by the time integration approach and viscous terms in CA approach are similar to that of Rayleigh damping . In the CD approach, the local damping and global damping are used for quasi‐static simulation, while the Rayleigh damping are commonly applied for dynamic problems…”

Section: Properties Of the New Approachmentioning

confidence: 99%

“…2 As an implicit and displacement-based method, DDA have been successfully implemented on both static and dynamic problems in rock engineering. 3 In the past decades, many improvements have been made on the discontinuous computation framework for the analyses of rock slides, 4-7 tunnels, 8,9 seismic site response, 10,11 rock fragmentation, [12][13][14] rock dynamics, [15][16][17][18] hydraulic fracturing, [19][20][21][22][23] and thermo-hydro-mechanical problems. [24][25][26] Meanwhile, the implementation of three-dimensional DDA has gained popularity in various rock engineering problems.…”

Section: Introductionmentioning

confidence: 99%

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Modified predictor‐corrector solution approach for efficient discontinuous deformation analysis of jointed rock masses

Zheng

Leung

Zhu

et al. 2018

Num Anal Meth Geomechanics

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Summary The high computational costs associated with the implicit formulation of discontinuous deformation analysis (DDA) have been one of the major obstacles for its implementation to engineering problems involving jointed rock masses with large numbers of blocks. In this paper, the Newmark‐based predictor‐corrector solution (NPC) approach was modified to improve the performance of the original DDA solution module in modeling discontinuous problems. The equation of motion for a discrete block system is first established with emphasis on the consideration of contact constraints. A family of modified Newmark‐based predictor‐corrector integration (MNPC) scheme is then proposed and implemented into a unified analysis framework. Comparisons are made between the proposed approach and the widely used constant acceleration (CA) integration approach and central difference (CD) approach, regarding the stability and numerical damping features for a single‐degree‐of‐freedom model, where the implications of the proposed approach on open‐close iteration are also discussed. The validity of the proposed approach is verified by several benchmarking examples, and it is then applied to two typical problems with different numbers of blocks. The results show that the original CA approach in DDA is efficient for the simulation of quasi‐static deformation of jointed rock masses, while the proposed MNPC approach leads to improved computational efficiency for dynamic analysis of large‐scale jointed rock masses. The MNPC approach therefore provides an additional option for efficient DDA of jointed rock masses.

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Impact of soft minerals on crack propagation in crystalline rocks under uniaxial compression: A grain‐based numerical investigation

Zhou,

Lv,

et al. 2024

Num Anal Meth Geomechanics

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Varying external conditions in the metallogenetic process of crystalline rocks contribute to the complex mineral and textural characteristics, rendering the mechanical properties highly heterogeneous at the mineral scale. This research focused on the influences of minerals with relatively low strength and stiffness (soft minerals) in crystalline rocks on their cracking behavior. A particle‐based discrete element method (DEM) was first employed to establish random grain‐based models (GBM) of crystalline rocks containing soft minerals with different contents, strengths, and stiffnesses. On this basis, responses of the mechanical properties and crack propagation to these parameters were systematically investigated and an optimized micro‐parameter calibration method for real CT (computed‐tomography) ‐based GBM was then proposed considering the characteristics of soft minerals. The results demonstrate that with the decrease of the strength of soft mica, the intragranular cracks are prone to initiate and propagate inside the soft minerals and lead to the final crack coalescence. The decrease in the stiffness of soft minerals enhances their controlling effects on the cracking propagation. Based on the CT‐based granite model, it was found that a heterogeneous stress field is produced due to the spatial distribution of the soft (mica) and hard (quartz and feldspar) minerals, and the mica minerals tend to terminate cracks or force cracks to deflect or bypass individual grains during crack propagation. This study sheds light on the damage and failure processes of crystalline rocks with contrast mineral components.

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Application of the discontinuous deformation analysis method to stress wave propagation through a one-dimensional rock mass

Cited by 49 publications

References 38 publications

Study on the Damping of the Discontinuous Deformation Analysis Based on Two‐Block Model

Study on the Damping of the Discontinuous Deformation Analysis Based on Two‐Block Model

Modified predictor‐corrector solution approach for efficient discontinuous deformation analysis of jointed rock masses

Impact of soft minerals on crack propagation in crystalline rocks under uniaxial compression: A grain‐based numerical investigation

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