The stability of crown pillar is critical during the transition from open pit to underground mining. Mining-induced fractures in the pillar form water seepage channels, which can cause potential ...water inrush hazards. A microseismicity-based method to establish seepage channel network and assess damage state of rock mass in the pillar is proposed. The formation processes of seepage channels and associated rock failure mechanism were analyzed. First, the spatiotemporal evolution of the microseismic (MS) events was presented, based on which the development process of the fractured zone was determined. Second, moment tensor inversion (MTI) was utilized to interpret the focal mechanism of the MS events. A 3D rose diagram was utilized to measure the fracture orientations and determine the main fracture surfaces, and a fracture network was subsequently established. Meanwhile, the distribution characteristics of the fracture radii and volumes were discussed. The results show that shear fractures were dominant in pillar and accounted for more than 90% of all MS events. The overall damage tensor of the pillar was subsequently assessed based on the MS-derived fractures, and the maximum damage direction was determined. Third, a fast chronological expansion method was proposed to iteratively build a connected network with a combination of MS event locations and the corresponding fracture orientations. The MS-derived connected network was used to estimate the distances of event-to-event seepage, from which the shortest seepage channel from each individual event to the network was determined in chronological order. Seepage channels between hydraulic recharge and discharge points were inferred. These results could be helpful for better characterization of seepage channel development and the implementation of pillar reinforcement.
The problem of computing (
α
,
β
)-core in a bipartite graph for given
α
and
β
is a fundamental problem in bipartite graph analysis and can be used in many applications such as online group ...recommendation and fraudsters detection Existing solution to computing (
α
,
β
)-core needs to traverse the entire bipartite graph once and ignore the fact that real-world graphs are often dynamic. Considering the real bipartite graph can be very large and dynamically updated, and the requests to compute (
α
,
β
)-core can be issued frequently in real applications, the existing solution is too expensive to compute the
(
α
,
β
)
-core. In this paper, we present an efficient algorithm for (
α
,
β
)-core computation based on a novel index such that the algorithm runs in linear time regarding the result size (thus, the algorithm is optimal since it needs at least linear time to output the result). We prove that the index only requires
O
(
m
) space where
m
is the number of edges in the bipartite graph. We also devise an efficient algorithm with time complexity
O
(
δ
·
m
)
for index construction where
δ
is bounded by
m
and is much smaller than
m
in practice. Moreover, we discuss efficient algorithms to maintain the index when the bipartite graph is dynamically updated. We show that we can decide whether a node in the index should be updated or not by visiting its neighbors. Based on this locality property, we propose an efficient index maintenance algorithm which only needs to visit a local subgraph near the inserted or removed edge. Finally, we show how to implement our index construction and maintenance algorithms in parallel. The experimental results on real and synthetic graphs (more than 1 billion edges) demonstrate that our algorithms achieve up to 5 orders of magnitude speedup for computing
(
α
,
β
)
-core, up to 3 orders of magnitude speedup for index construction and up to 4 orders of magnitude speedup for index maintenance, respectively, compared with existing techniques.
Graph is a ubiquitous structure representing entities and their relationships applied in many areas such as social networks, web graphs, and biological networks. One of the fundamental tasks in graph ...analytics is to investigate the relations between two vertices (e.g., users, items, and entities) such as how a vertex
A
influences another vertex
B
, or to what extent
A
and
B
are similar to each other, based on the graph topology structure. For this purpose, we study the problem of hop-constrained
s
-
t
simple path enumeration in this paper, which aims to list all simple paths from a source vertex
s
to a target vertex
t
with hop-constraint
k
. We first propose a polynomial delay algorithm, namely BC-DFS, based on a barrier-based pruning technique. Then, a join-oriented algorithm, namely JOIN, is designed to further enhance the query response time. On the theoretical side, BC-DFS is a polynomial delay algorithm with
O
(
km
) time per output where
m
is the number of edges in the graph. This time complexity is similar to the best known theoretical result for the polynomial delay algorithms of this problem. On the practical side, our comprehensive experiments on 15 real-life networks demonstrate the superior performance of the BC-DFS algorithm compared to the state-of-the-art techniques. It is also reported that the JOIN algorithm can further significantly enhance the query response time. In this paper, we also study the hop-constrained path enumeration problem with diversity constraint and propose a block-oriented algorithm, namely SCB. To further speed up the computation, hybrid lower bounds based on reverse shortest-path tree are also developed, namely SCB+. The experiments show our proposed methods significantly improve the query time and scalability comparing with baselines.
•A numerical model coupling joints, water and microseismicity is proposed to simulate rock mass damage.•An inversion model of rock damage based on microseismic moment tensor was proposed.•The ...integration of microseismic data is beneficial to the prediction of rock damage development.
The behaviour of rock mass is governed by the properties of the intact rock, the joints and the water conditions. Moreover, this behaviour is also influenced by the temporal and spatial damage evolution patterns of the rock. Thus, in this study, an approach that couples joints, water and microseismicity is proposed to model rock engineering problems. Joints are used to reduce the global properties of the rock mass, water is used to reduce the local properties of the rock mass, and microseismicity are used to reduce the point properties of the rock mass. Using data from the Shirengou iron mine, the effects of water and joints on the properties of rock masses were investigated, and a representative elementary volume of rock mass was determined. Then, a coupled fluid–solid numerical model was established to simulate the evolution of rock mass damage while considering the effects of joints and water. Finally, an inversion model of rock damage based on microseismic moment tensor was proposed. A numerical simulation of rock mass damage that couples joints, water and microseismicity was performed. The rock mass damage mechanism was then analysed. Joints and water were found to significantly affect the damage zones. The rock mass damage estimate would not be accurate without considering the effects of joints and water. Thus, water was the critical factor in the studied damage pattern. Further integration of microseismic data aided in modifying the numerical results and in predicting the damage development. The proposed approach can efficiently assess rock mass damage evolution and provide a basis for rock support.
Fourier-based generation method of rough discrete fracture network Zhou, Jingren; Liu, Feiyue; Fereshtenejad, Sayedalireza ...
International journal of rock mechanics and mining sciences (Oxford, England : 1997),
September 2023, 2023-09-00, Volume:
169
Journal Article
Peer reviewed
Natural fractures have been often generated with rough morphologies as a result of complex geological processes. Joint surface undulation/roughness degree dominantly affects mechanical ...characteristics of jointed rock masses, hence should be considered in geometrical modeling of fracture networks. Considering the intrinsic geometric characteristic of natural fractures, this paper proposes a method to generate rough discrete fracture networks (RDFN) for jointed rock mass. Fourier transform is employed to obtain statistical spectrum information of natural rough fractures and fractures in the RDFN model are individually reconstructed in spatial frequency domain based on the information. Besides, three scale-independent shape descriptors, namely Elongation, Regularity and Smoothness, are selected to characterize the geometric characteristics of fractures in different scales and to verify the rationality of the proposed method. A case study is further employed to demonstrate the accuracy of the proposed method, and its applicability to numerical realization is discussed. The proposed method is important for a wide range of applications when considering the discrete modelling of rough fractures.
Maximum biclique search, which finds the biclique with the maximum number of edges in a bipartite graph, is a fundamental problem with a wide spectrum of applications in different domains, such as ...E-Commerce, social analysis, web services, and bioinformatics. Unfortunately, due to the difficulty of the problem in graph theory, no practical solution has been proposed to solve the issue in large-scale real-world datasets. Existing techniques for maximum clique search on a general graph cannot be applied because the search objective of maximum biclique search is two-dimensional, i.e., we have to consider the size of both parts of the biclique simultaneously. In this paper, we divide the problem into several subproblems each of which is specified using two parameters. These subproblems are derived in a progressive manner, and in each subproblem, we can restrict the search in a very small part of the original bipartite graph. We prove that a logarithmic number of subproblems is enough to guarantee the algorithm correctness. To minimize the computational cost, we show how to reduce significantly the bipartite graph size for each subproblem while preserving the maximum biclique satisfying certain constraints by exploring the properties of one-hop and two-hop neighbors for each vertex. Furthermore, we study the diversified top-
k
biclique search problem which aims to find
k
maximal bicliques that cover the most edges in total. The basic idea is to repeatedly find the maximum biclique in the bipartite graph and remove it from the bipartite graph
k
times. We design an efficient algorithm that considers to share the computation cost among the
k
results, based on the idea of deriving the same subproblems of different results. We further propose two optimizations to accelerate the computation by pruning the search space with size constraint and refining the candidates in a lazy manner. We use several real datasets from various application domains, one of which contains over 300 million vertices and 1.3 billion edges, to demonstrate the high efficiency and scalability of our proposed solution. It is reported that 50% improvement on recall can be achieved after applying our method in Alibaba Group to identify the fraudulent transactions in their e-commerce networks. This further demonstrates the usefulness of our techniques in practice.
Graph partitioning is crucial to parallel computations on large graphs. The choice of partitioning strategies has strong impact on the performance of graph algorithms. For an algorithm of our ...interest, what partitioning strategy fits it the best and improves its parallel execution? Is it possible to provide a uniform partition to a batch of algorithms that run on the same graph simultaneously, and speed up each and every of them? This paper aims to answer these questions. We propose an application-driven hybrid partitioning strategy that, given a graph algorithm
A
, learns a cost model for
A
as polynomial regression. We develop partitioners that, given the learned cost model, refine an edge-cut or vertex-cut partition to a hybrid partition and reduce the parallel cost of
A
. Moreover, we extend the cost-driven strategy to support multiple algorithms at the same time and reduce the parallel cost of each of them. Using real-life and synthetic graphs, we experimentally verify that our partitioning strategy improves the performance of a variety of graph algorithms, up to
22.5
×
.
•The calculation formula for the isotropic releasable strain energy of rock mass unit that considering damage is obtained.•The damage variable is defined and embedded in the numerical simulation to ...modify the rock mass parameters.•The damage and failure law of rock mass in study area was preliminarily analyzed based on source parameters.
In mining process, the mechanical parameters of rock mass are deteriorating continuously. Fixed mechanical parameters were usually selected when using numerical simulation to analyze the damage process of rock mass, which led to the simulation results difficult to meet the actual situation. Microseismic monitoring system is an effective means to monitor the evolution of rock mass damage. It is of great significance to effectively combine the monitoring data with numerical simulation to correct rock mass parameters. In order to study the relationship between source parameters and rock mass damage, microseismic events of No. 15–16 exploratory line were analyzed from the project of Shirengou iron mine. Location verification was carried out on the established microseismic monitoring system and the microseismic events with larger errors were eliminated. The damage and failure characteristics of rock mass in this area were preliminarily analyzed based on the analysis of the temporal and spatial change of microseismic events and source parameters. In addition, based on the study of isotropic releasable strain energy, the damage model of rock mass was established by using the relationship between source parameters and releasable strain energy. The microseismic monitoring results were used as input of numerical simulation through FISH language existing in FLAC3D. Source parameters were used to modify rock mechanical parameters, so as to analyze the damage process of rock mass. Through the analysis of microseismic activity, the damage degree of rock mass and the change of plastic zone, the unstable areas were located, furthermore corresponding preventive measures were put forward.
Numerical simulation is a commonly used method for investigating rock failure. However, the numerical model is usually insufficient to predict real rock damage and failure because of rock ...microstructural heterogeneity. In fact, rock damage can be quantified using acoustic emission (AE) data. The aim of this study is to simulate and predict the failure of Brazilian and uniaxial compression specimens using AE data recorded during experiments. An AE data-driven model, in which cracks are assumed to be tensile in nature, is developed. AE data recorded from the test start up to a fraction of the peak stress (e.g., 20%, 40%, and 60%) are input into the data-driven model to predict the evolution of failure pattern beyond that stress level up to failure. First, we quantified stress-induced rock damage with AE data based on the tensile model. The results indicate that most of damage source radii are less than one millimeter, and the corresponding damage degree is close to one. Then, the inversed damage is input as the initial conditions for the numerical simulation to predict the future damage and failure of rock. With the increase of damage elements driven by AE data, the inversed damage zone develops from diffuse to localized, and the dominant factor for rock failure transits from microstructural heterogeneity into stress-induced rock damage. The damage and failure pattern of rock is well predicted when sufficient AE data are taken into account as known conditions.
The deformation and failure process of rock masses is accompanied by the initiation, propagation and connection of fractures. The behaviors of fractures under engineering disturbance can be ...effectively determined by microseismic (MS) monitoring, and such information is essential for the stability analysis of rock masses. Based on moment tensor theory, the geometric properties of focal planes and the failure mechanisms of the seismic source can be determined, and this study proposes criteria for extracting the reasonable fracture from focal planes associated with different failure mechanisms and provides a detailed example. The fracture identified by the proposed criteria is called MS-derived fracture, and a formula describing the aperture is derived from the moment tensor theory and the motion characteristics of the MS-derived fractures associated with different failure mechanisms. This work chose the Shirengou Iron Mine as a case and selected an area exhibiting seepage and rock mass failure as the study area. Based on a three-dimensional noncontact discontinuity scan, a natural discrete fracture network (DFN) was generated. With the help of the proposed fracture generation method, a new DFN based on MS data was generated and is referred to as the MS-derived DFN. With the aid of Oda’s theory, the changes in the permeability value, principal direction and anisotropy degree in the study area were analyzed based on the MS-derived DFN, and the seepage channels in the study area were also determined. Therefore, the research methods in this paper could be used to better understand the changes in the permeability of rock masses based on MS data.
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