Latest advances in discontinuous deformation analysis method
Jiao Y Y, Zhao Q, Zheng F, et al. Latest advances in discontinuous deformation analysis method. Sci China Tech Sci
Latest advances in discontinuous deformation analysis method
JIAO YuYong 0 1
ZHAO Qiang 0
ZHENG Fei 0
WANG Long 0
0 State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences , Wuhan 430071 , China
1 Faculty of Engineering, China University of Geosciences , Wuhan 430074 , China
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Discontinuous deformation analysis (DDA) method,
proposed firstly by Shi [1] in 1988, is a novel numerical approach
to simulate the discontinuous deformation behaviors of
blocky rock structures. In DDA, the domain of interest is
represented as an assemblage of discrete blocks and the joints
are treated as interfaces between blocks. The governing
equations of DDA are derived from Newton’s Second Law
of Motion and the Principle of Minimum Potential Energy.
In the calculation, the large displacement solution of a block
is obtained through the procedure of time-step integration,
and accordingly, the collapse process of a block system can
be reproduced dynamically. As no compatibility condition
is needed to form the global equilibrium equations and each
individual block moves independently, the calculation does
not encounter mathematical problems even solving any large
displacement.
As a theoretically rigorous numerical method, DDA has
been one of the focuses in the discontinuous computing field
since its birth. So far, the two-dimensional programs and
related engineering applications are becoming mature.
However, when the DDA method is extended from 2D to 3D, and
when it is used to solve large scale engineering problems,
several major difficulties appear. These difficulties lie in three
aspects, i.e., there is no accurate and robust contact theory
to tackle 3D problems; the computational efficiency is low
and the computational scale is relatively small; refining DDA
simulation needs further improvements in basic theory and
hybrid algorithms. Fortunately, aiming at the problems
mentioned above, significant progresses have been made recently.
The most important advance in DDA study is the
appearing of a novel approach for contact calculation. In 2015, Shi
[2] proposed a general contact theory for 2D and 3D
discontinuous computation, including a new definition for
operating the point sets named as the entrance block. The boundary
of an entrance block is a contact cover system. Each contact
cover defines a contact point and all closed-contact points
define the movements, rotations and deformations of all blocks
as in real cases. Given a reference point, the concept of
entrance block can simplify the contact computation greatly by
determining the shortest distance between two blocks in a
straightforward way, by defining the contact points through
the first entrance, and by obtaining the shortest path of exit
easily. As a robust method, the proposed new contact theory
can help us in eliminating the biggest obstacle in 3D DDA
programming.
There are also major improvements in basic DDA theory
these years. To avoid the introduction of virtual springs that
are commonly used in the classical DDA, Zheng et al. [3]
proposed the dual form DDA in which the contact forces are
utilized as the basic variables instead of the block displacements.
Based on the projection-contraction algorithm, they designed
the compatibility iteration for the quasi-variational inequality.
The main advantage of this method is that the computational
accuracy, robustness and efficiency can be guaranteed with
removal of the virtual springs. In order to improve the
accuracy of the disk-based DDA, Amir Reza Beyabanaki and
Bagtzoglou [4] presented the new formulations of stiffness
and force matrices for non-rigid disks using a new efficient
contact model. In their model, disk-disk and
disk-boundary contacts are transformed into the form of point-to-line
contacts and normal spring, shear spring and frictional force
sub-matrices are derived by vector analysis. The augmented
Lagrangian method is used as the penalty function, and the
reference line can be obtained directly by using only
coordinates of disk centers and their radii. By introducing a viscous
damping component to absorb discrete blocks’ kinetic energy,
Jiang et al. [5] established the global equations of the discrete
block system that take damping effects into account, and
defined the convergence criteria for DDA solutions, which
provided more objective standards for the DDA application in
geotechnical engineering.
Recent efforts in coupling DDA with other numerical
methods are also noteworthy. Combining the FE-based rock
failure process analysis (RFPA) method with the DDA method,
Tang et al. [6] proposed a discontinuous deformation and
displacement (DDD) analysis method for modeling the rock
failure process. In the proposed model, RFPA is used to
simulate crack initiation, propagation and coalescence processes
of rock, while D (...truncated)