Time Integration in Discontinuous Deformation Analysis

Doolin, David M.; Sitar, Nicholas

doi:10.1061/(asce)0733-9399(2004)130:3(249)

Cited by 86 publications

(59 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Statistical analyses of existing data from earthquakes can provide suggested attenuation relationships for the regions at hand, on the basis of recorded data (see [1]). In some regions, however, recorded data are very scarce due to lack of instrumentation and seismic network infrastructure, and in all regions 465 provided by a time integration formulation similar to Newmark direct integration method with parameters = 0.5 and = 1.0, into the general equation of motion [18,19]. The result is a system of equations for solving the dynamic problem which, after collecting terms on both sides, typically expressed as:K D =F, where K i j is a 6×6 coefficient sub-matrix , D i is a 6×1 deformation matrix of block i and F i is a 6×1 loading matrix of block i. Sub-matrices [K ii ] depend on the material properties of block i and sub-matrices [Kij] are defined by the contacts between blocks i and j.…”

Section: Introductionmentioning

confidence: 99%

Constraining paleo PGA values by numerical analysis of overturned columns

Yagoda-Biran

Hatzor

2009

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

SUMMARYThe estimated peak ground acceleration (PGA) for a specific region cannot always be determined reliably from compilation and statistical analyses of instrumental data acquired because of the relatively short time window available for such an approach, typically up to 100 years of instrumentation. We propose a complimentary approach for estimating PGA in a specific region, through back analysis of seismically driven column collapse in historic monuments, using the numerical discrete element discontinuous deformation analysis (DDA) method. Preliminary threshold 'paleo PGA' values thus obtained constrain the lower bound of PGA estimates using information from a much broader time window, in the case study presented here of approximately 1200 years.

show abstract

Section: Introductionmentioning

confidence: 99%

Constraining paleo PGA values by numerical analysis of overturned columns

Yagoda-Biran

Hatzor

2009

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

show abstract

“…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%

“…Doolin and Sitar [16] studied the time integration of DDA and noted that the algorithmic damping may be important considering the penalty formulation. Bao et al [17] obtained an equivalent damping ratio from the algorithmic damping in DDA using the cantilever beam model.…”

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

View full text Add to dashboard Cite

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.

show abstract

“…It is worth highlighting that an implicit time integration algorithm, i.e., the Newmark- method with two parameters =0.5 and r=1.0 is used in the traditional DDA [32] The numerical damping is essential for the DDA analysis, as it allows the oscillations caused by contact forces to dissipate rapidly, resulting in a stable state, which ultimately allows the open-close iteration to converge rapidly. The amount of numerical damping is also proportional to the time step size.…”

Section: Discontinuous Deformation Analysis (Dda)mentioning

confidence: 99%

Comparisons between centrifuge and numerical modeling results for slope toppling failure

Chen

Gong

et al. 2015

Sci. China Technol. Sci.

View full text Add to dashboard Cite

This paper presents series studies on the toppling mechanism by centrifuge tests and numerical simulations. Two different discrete element methods, i.e., the continuum-based discrete element method (CDEM) and the discontinuous deformation analysis (DDA), are adopted. The modeling results show that both the methods can accurately capture the failure modes of the centrifuge tests, including three distinct zones and two failure surfaces. Comparisons are made between the physical test and numerical simulation results. The critical inclination angle of the tilting table where the slope models are fixed on can be moderately predicted by the two methods, with different degrees of precision. The error between the test results and the simulated results is within 1% for the slope models without rock-bridges by both CDEM and DDA. However, it is amplified for the staggered-joint models that simulate the rock-bridges. With DDA, the average error is about 5%, and the maximum error is up to 17%. While with CDEM, the errors for the aligned-joint models are ranged from 1% to 6%, and it is from 10% to 29% for the staggered-joint models. The two numerical methods show the capability in simulating toppling failure of blocky rock mass with and without rock-bridges. The model with rock-bridges which provides a certain bending resistance is more stable than the one without any rock-bridge. In addition, the two failure surfaces were observed, which is different from the common understanding that only one failure surface appears. rock slope model, toppling failure, rock-bridge, centrifuge test, continuum based discrete element method, discontinuous deformation analysis Citation:Chen Z Y, Gong W J, Ma G W, et al. Comparisons between centrifuge and numerical modeling results for slope toppling failure.

show abstract

Time Integration in Discontinuous Deformation Analysis

Cited by 86 publications

References 4 publications

Constraining paleo PGA values by numerical analysis of overturned columns

Constraining paleo PGA values by numerical analysis of overturned columns

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

Comparisons between centrifuge and numerical modeling results for slope toppling failure

Contact Info

Product

Resources

About