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Bowen Zheng
Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, People’s Republic of China

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Original paper
Published: 08 January 2021 in Bulletin of Engineering Geology and the Environment
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The fractal geometry method has been employed to quantitatively characterize the roughness of a rock discontinuity, which is one of the key factors affecting its shear strength and the seepage characteristics of a rock mass. However, the current fractal methods involving the three-dimensional discontinuity morphology suffer from one or more problems, such as a complicated calculation procedure, an inaccurate calculation result and an inability to characterize the undulation and anisotropy of a discontinuity. To cope with these problems, the discontinuities in artificial granite samples with irregular and undulating surfaces were taken as examples, and a quantitative study on the discontinuity morphology was conducted based on the method of three-dimensional laser scanning in combination with ArcGIS data processing, geographical research, theoretical calculations and regression analysis. After performing systematic research, we proposed an extensive 3D fractal dimension including three discontinuity morphological parameters, i.e. the fractal dimension of discontinuity morphology, the ratio between the maximal undulating amplitude and the discontinuity length, and the average value of all the apparent dip angles of the discontinuity surfaces dipping opposite the shear direction. The extensive 3D fractal dimension can comprehensively characterize the roughness, undulation and anisotropy of the discontinuity morphology. A set of theoretical calculation methods were then developed to determine the three discontinuity morphological parameters of the extensive 3D fractal dimension based on ArcGIS. We finally established a mathematical expression of the extensive 3D fractal dimension. Compared with the current fractal methods, the extensive 3D fractal dimension can effectively compensate for the inability to characterize the undulation and anisotropy of the discontinuity morphology. Its calculation methods have the advantages of simplification, low-time consumption and high precision.

ACS Style

Bowen Zheng; Shengwen Qi; Guangming Luo; Fangcui Liu; Xiaolin Huang; Songfeng Guo. Characterization of discontinuity surface morphology based on 3D fractal dimension by integrating laser scanning with ArcGIS. Bulletin of Engineering Geology and the Environment 2021, 80, 2261 -2281.

AMA Style

Bowen Zheng, Shengwen Qi, Guangming Luo, Fangcui Liu, Xiaolin Huang, Songfeng Guo. Characterization of discontinuity surface morphology based on 3D fractal dimension by integrating laser scanning with ArcGIS. Bulletin of Engineering Geology and the Environment. 2021; 80 (3):2261-2281.

Chicago/Turabian Style

Bowen Zheng; Shengwen Qi; Guangming Luo; Fangcui Liu; Xiaolin Huang; Songfeng Guo. 2021. "Characterization of discontinuity surface morphology based on 3D fractal dimension by integrating laser scanning with ArcGIS." Bulletin of Engineering Geology and the Environment 80, no. 3: 2261-2281.

Journal article
Published: 06 December 2020 in Engineering Geology
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Laboratory tests revealed that by enhancing the weathering degree, a transition of pre-peak mechanical responses of crystalline rocks under unconfined compression from approximate linearity to nonlinearity was evident, as was the weakening of macro-mechanical properties. However, thus far, very few numerical studies have been conducted to quantitatively characterize the strong-to-weak transition of the mechanical behaviors of crystalline rocks modulated by the weathering degree. We propose an advanced grain-based model (AGBM) using Universal Distinct Element Code (UDEC) to characterize mechanical characteristics of crystalline rocks with different weathering degrees. The weathering-induced deterioration of microstructures was treated as loosening of grain contacts and weakening of their properties. It was proved that the grain contact model that considered hardening nonlinear deformation in compression and linearly elastic deformation in tension or shear was feasible and applicable to characterize the mechanical behaviors of crystalline rocks with different weathering degrees. The compression hardening deformation of grain contacts significantly affected the macro nonlinear stress-strain relation and stress thresholds of crack closure, crack imitation, stable crack growth, and unstable crack growth. We acquired new insights on the weathering-induced weakening of macro-mechanical characteristics of crystalline rock, which resulted from weakening of deformation properties of the grain contact more than grain contact strength.

ACS Style

Xiaolin Huang; Shengwen Qi; Bowen Zheng; Ning Liang; Lihui Li; Lei Xue; Songfeng Guo; Xiang Sun; Daping Tai. An advanced grain-based model to characterize mechanical behaviors of crystalline rocks with different weathering degrees. Engineering Geology 2020, 280, 105951 .

AMA Style

Xiaolin Huang, Shengwen Qi, Bowen Zheng, Ning Liang, Lihui Li, Lei Xue, Songfeng Guo, Xiang Sun, Daping Tai. An advanced grain-based model to characterize mechanical behaviors of crystalline rocks with different weathering degrees. Engineering Geology. 2020; 280 ():105951.

Chicago/Turabian Style

Xiaolin Huang; Shengwen Qi; Bowen Zheng; Ning Liang; Lihui Li; Lei Xue; Songfeng Guo; Xiang Sun; Daping Tai. 2020. "An advanced grain-based model to characterize mechanical behaviors of crystalline rocks with different weathering degrees." Engineering Geology 280, no. : 105951.

Journal article
Published: 12 November 2020 in Materials
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Characterization of the tensile mechanical behaviors of rocks under dynamic loads is of great significance for the practical engineering. However, thus far, its micromechanics have rarely been studied. This paper micromechanically investigated the compression-induced tensile mechanical behaviors of the crystalline rock using the grain-based model (GBM) by universal distinct element code (UDEC). Results showed that the crystalline rock has the rate- and heterogeneity-dependency of tensile behaviors. Essentially, dynamic Brazilian tensile strength increased in a linear manner as the loading rate increased. With the size distribution and morphology of grain-scale heterogeneity weakened, it increased, and this trend was obviously enhanced as the loading rate increased. Additionally, the rate-dependent characteristic became strong with the grain heterogeneity weakened. The grain heterogeneity prominently affected the stress distribution inside the synthetic crystalline rock, especially in the mixed compression and tension zone. Due to heterogeneity, there were tensile stress concentrations (TSCs) in the sample which could favor microcracking and strength weakening of the sample. As the grain heterogeneity weakened or the loading rate increased, the magnitude of the TSC had a decreasing trend and there was a transition from the sharp TSC to the smooth tensile stress distribution zone. The progressive failure of the crystalline rock was notably influenced by the loading rate, which mainly represented the formation of the crushing zone adjacent to two loading points. Our results are meaningful for the practical engineering such as underground protection works from stress waves.

ACS Style

Bowen Zheng; Shengwen Qi; Xiaolin Huang; Ning Liang; Songfeng Guo. Compression-Induced Tensile Mechanical Behaviors of the Crystalline Rock under Dynamic Loads. Materials 2020, 13, 5107 .

AMA Style

Bowen Zheng, Shengwen Qi, Xiaolin Huang, Ning Liang, Songfeng Guo. Compression-Induced Tensile Mechanical Behaviors of the Crystalline Rock under Dynamic Loads. Materials. 2020; 13 (22):5107.

Chicago/Turabian Style

Bowen Zheng; Shengwen Qi; Xiaolin Huang; Ning Liang; Songfeng Guo. 2020. "Compression-Induced Tensile Mechanical Behaviors of the Crystalline Rock under Dynamic Loads." Materials 13, no. 22: 5107.

Journal article
Published: 22 October 2020 in Materials
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The shear strength characteristics of rock masses containing non-persistent discontinuities are strongly affected by discontinuities and rock bridges. The linear Jennings criterion cannot reflect the nonlinear mechanical behavior during progressive failure of rock masses with non-persistent discontinuities. In this study, a new nonlinear shear strength criterion was developed. First of all, a series of shear test data about artificial rock mass samples were collected on the basis of the published literatures, and five types of samples were differentiated according to the positions of discontinuities. After that, a new nonlinear shear strength criterion was proposed by introducing two correction coefficients A and B into the basic form of the Jennings criterion, which could correct the weight of the cohesion and the internal friction coefficient of rock bridges respectively. Then, the new criterion was determined by fitting the basic form of the Jennings criterion with the laboratory data. It was found that the parameters A and B had a nonlinear exponential and negative exponential relation with the connectivity rate respectively. It indicated that both the cohesion and the internal friction coefficient estimated by the new criterion were superior to those estimated by the Jennings criterion. Compared with the linear Jennings criterion, the new nonlinear shear strength criterion had a better applicability.

ACS Style

Bowen Zheng; Shengwen Qi; Songfeng Guo; Xiaolin Huang; Ning Liang; Yu Zou; Guangming Luo. A New Shear Strength Criterion for Rock Masses with Non-Persistent Discontinuities Considering the Nonlinear Progressive Failure Process. Materials 2020, 13, 4694 .

AMA Style

Bowen Zheng, Shengwen Qi, Songfeng Guo, Xiaolin Huang, Ning Liang, Yu Zou, Guangming Luo. A New Shear Strength Criterion for Rock Masses with Non-Persistent Discontinuities Considering the Nonlinear Progressive Failure Process. Materials. 2020; 13 (21):4694.

Chicago/Turabian Style

Bowen Zheng; Shengwen Qi; Songfeng Guo; Xiaolin Huang; Ning Liang; Yu Zou; Guangming Luo. 2020. "A New Shear Strength Criterion for Rock Masses with Non-Persistent Discontinuities Considering the Nonlinear Progressive Failure Process." Materials 13, no. 21: 4694.

Original paper
Published: 29 September 2020 in Natural Hazards
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Empirical methods are commonly employed to predict the PGA distribution of an earthquake and are widely used. However, current empirical methods assume the seismic source to be a point source, a line source, or a plane source, where the energy is concentrated and released uniformly. An empirical attenuation model of the near-field peak ground acceleration (PGA) was proposed that considers a nonuniform spatial distribution of seismic fault energy and its 3D scale. Then, this model was used to reconstruct the PGA distribution of the 2008 Wenchuan, China, Mw7.9 earthquake based on the data of a seismic fault model and ground acceleration records of the mainshock and aftershocks collected by seismic stations. The predicted PGA values show similar attenuation characteristics to the interpolated map of the PGA recorded by seismic stations. A comparison with the results of a finite-fault model developed by the USGS indicates that the proposed model can provide more details and give a more precise result in the near field. The analysis of landslides triggered by the Wenchuan earthquake demonstrates that the PGA distribution estimated by this model can be used to validate the findings of other researchers.

ACS Style

Xianglong Yao; Shengwen Qi; Chunling Liu; Songfeng Guo; Xiaoling Huang; Chong Xu; Bowen Zheng; Zhifa Zhan; Yu Zou. An empirical attenuation model of the peak ground acceleration (PGA) in the near field of a strong earthquake. Natural Hazards 2020, 105, 691 -715.

AMA Style

Xianglong Yao, Shengwen Qi, Chunling Liu, Songfeng Guo, Xiaoling Huang, Chong Xu, Bowen Zheng, Zhifa Zhan, Yu Zou. An empirical attenuation model of the peak ground acceleration (PGA) in the near field of a strong earthquake. Natural Hazards. 2020; 105 (1):691-715.

Chicago/Turabian Style

Xianglong Yao; Shengwen Qi; Chunling Liu; Songfeng Guo; Xiaoling Huang; Chong Xu; Bowen Zheng; Zhifa Zhan; Yu Zou. 2020. "An empirical attenuation model of the peak ground acceleration (PGA) in the near field of a strong earthquake." Natural Hazards 105, no. 1: 691-715.

Journal article
Published: 06 September 2020 in Materials
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This paper microscopically investigated progressive failure characteristics of brittle rock under high-strain-rate compression using the bonded particle model (BPM). We considered the intact sample and the flawed sample loaded by split Hopkinson pressure bar respectively. Results showed that the progressive failure characteristics of the brittle rock highly depended on the strain rate. The intact sample first experienced in microcracking, then crack coalescing, and finally splitting into fragments. The total number of the micro cracks, the proportion of the shear cracks, the number of fragments and the strain at the peak stress all increased with the increasing strain rate. Also, a transition existed for the failure of the brittle rock from brittleness to ductility as the strain rate increased. For the flawed sample, the microcracking initiation position and the types of the formed macro cracks were influenced by the flaw angle in the initial stage. However, propagation of these early-formed macro cracks were prohibited in the later stages. New micro cracks were produced and then coalesced into diagonal macro cracks which could all form ‘X’-shape failure configuration regardless of the incline angle of the flaw. We explored micromechanics on progressive failure characteristics of the brittle rock under dynamic loads.

ACS Style

Xiaolin Huang; Shengwen Qi; Bowen Zheng; Songfeng Guo; Ning Liang; Zhifa Zhan. Progressive Failure Characteristics of Brittle Rock under High-Strain-Rate Compression Using the Bonded Particle Model. Materials 2020, 13, 3943 .

AMA Style

Xiaolin Huang, Shengwen Qi, Bowen Zheng, Songfeng Guo, Ning Liang, Zhifa Zhan. Progressive Failure Characteristics of Brittle Rock under High-Strain-Rate Compression Using the Bonded Particle Model. Materials. 2020; 13 (18):3943.

Chicago/Turabian Style

Xiaolin Huang; Shengwen Qi; Bowen Zheng; Songfeng Guo; Ning Liang; Zhifa Zhan. 2020. "Progressive Failure Characteristics of Brittle Rock under High-Strain-Rate Compression Using the Bonded Particle Model." Materials 13, no. 18: 3943.

Journal article
Published: 13 July 2020 in Applied Sciences
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A rock mass often contains joints filled with a viscoelastic medium of which seismic response is significant to geophysical exploration and seismic engineering design. Using the propagator matrix method, an analytical model was established to characterize the seismic response of viscoelastic filled joints. Stress wave propagation through a single joint highly depended on the water content and thickness of the filling as well as the frequency and incident angle of the incident wave. The increase in the water content enhanced the viscosity (depicted by quality factor) of the filled joint, which could promote equivalent joint stiffness and energy dissipation with double effects on stress wave propagation. There existed multiple reflections when the stress wave propagated through a set of filled joints. The dimensionless joint spacing was the main controlling factor in the seismic response of the multiple filled joints. As it increased, the transmission coefficient first increased, then it decreased instead, and at last it basically kept invariant. The effect of multiple reflections was weakened by increasing the water content, which further influenced the variation of the transmission coefficient. The water content of the joint filling should be paid more attention in practical applications.

ACS Style

Xiaolin Huang; Shengwen Qi; Bowen Zheng; Youshan Liu; Lei Xue; Ning Liang. Stress Wave Propagation through Rock Joints Filled with Viscoelastic Medium Considering Different Water Contents. Applied Sciences 2020, 10, 4797 .

AMA Style

Xiaolin Huang, Shengwen Qi, Bowen Zheng, Youshan Liu, Lei Xue, Ning Liang. Stress Wave Propagation through Rock Joints Filled with Viscoelastic Medium Considering Different Water Contents. Applied Sciences. 2020; 10 (14):4797.

Chicago/Turabian Style

Xiaolin Huang; Shengwen Qi; Bowen Zheng; Youshan Liu; Lei Xue; Ning Liang. 2020. "Stress Wave Propagation through Rock Joints Filled with Viscoelastic Medium Considering Different Water Contents." Applied Sciences 10, no. 14: 4797.

Journal article
Published: 08 July 2020 in Sustainability
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A gigantic project named Gully Land Consolidation (GLC) was launched in the hill-gully region of the Chinese Loess Plateau in 2011 to cope with land degradation and create new farmlands for cultivation. However, as a particular kind of remolded loess, the newly created and backfilled farmland may bring new engineering and environmental problems because the soil structure was disturbed and destroyed. In this study, current situations and characteristics of GLC are introduced. Test results show that physical-mechanical properties and microstructural characteristics of backfilled loess of one-year and five-year farmland are significantly affected by the Gully Land Consolidation project. Compared to natural loess, the moisture content, density, and internal friction angle of backfilled loess increase. On the contrary, the porosity, plasticity index, particle size index, and cohesion index decrease. Through SEM tests, it is observed that the particles of backfilled loess are rounded, with large pores filled with crushed fine particles, which results in skeleton strength weakness among particles and pores. The pore size distribution (PSD) of the four types of loess (Q3 loess, Q2 loess, one-year farmland, and five-year farmland) was measured using mercury intrusion porosimetry (MIP) tests, showing that the pore size of Q3 loess is mainly mesopores 4000–20,000 nm in size, accounting for 67.5%. The Q2, five-year, and one-year farmland loess have mainly small pores 100–4000 nm in size, accounting for 52.5%, 51.7%, and 71.7%, respectively. The microscopic analysis shows that backfill action degrades the macropores and mesopores into small pores and micropores, leading to weak connection strength among soil particles, which further affects the physical-mechanical properties of loess. The disturbance of backfilled loess leads to an obvious decrease in cohesion and a slight increase in internal friction compared to natural loess. The farming effect becomes prominent with increased backfill time, while the loess soil moisture content increases gradually. Both the cohesion and internal friction of the backfilled loess soil decrease to different degrees. This study is helpful to investigate sustainable land use in the Chinese Loess Plateau and similar areas.

ACS Style

Lina Ma; Shengwen Qi; Bowen Zheng; Songfeng Guo; Qiangbing Huang; Xinbao Yu. Farming Influence on Physical-Mechanical Properties and Microstructural Characteristics of Backfilled Loess Farmland in Yan’an, China. Sustainability 2020, 12, 5516 .

AMA Style

Lina Ma, Shengwen Qi, Bowen Zheng, Songfeng Guo, Qiangbing Huang, Xinbao Yu. Farming Influence on Physical-Mechanical Properties and Microstructural Characteristics of Backfilled Loess Farmland in Yan’an, China. Sustainability. 2020; 12 (14):5516.

Chicago/Turabian Style

Lina Ma; Shengwen Qi; Bowen Zheng; Songfeng Guo; Qiangbing Huang; Xinbao Yu. 2020. "Farming Influence on Physical-Mechanical Properties and Microstructural Characteristics of Backfilled Loess Farmland in Yan’an, China." Sustainability 12, no. 14: 5516.

Journal article
Published: 14 June 2020 in Applied Sciences
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The shear strength of the rock discontinuities under different shear rates is of great importance to evaluate the stability of rock mass engineering, which is remarkably influenced by the size effects induced by both the length and the undulated amplitude of discontinuities. An advanced shear strength criterion taking into account the size and the shear rate simultaneously was proposed. There is an advantage of the dimension unity in terms of the new shear strength criterion in comparison to previous related empirical equations. Additionally, it can be degraded into the International Society for Rock Mechanics (ISRM)-suggested Barton shear strength empirical equation on the peak shear strength of the rock discontinuities. Then, based on a new dynamic direct shear testing device on rock joints, the granite discontinuities with various lengths (200 mm to 1000 mm) and undulated amplitudes (3 mm to 23 mm) were designed to conduct direct shear tests under different low shear rates (0 mm/s to 1 mm/s) to verify the involved empirical equations. It was found that the results predicted by the new shear strength criterion agreed well with the experimental results. It was proved that the new shear strength criterion had a better applicability to characterize the shear strength of the rock discontinuities.

ACS Style

Bowen Zheng; Shengwen Qi; Xiaolin Huang; Songfeng Guo; Chonglang Wang; Zhifa Zhan; Guangming Luo. An Advanced Shear Strength Criterion for Rock Discontinuities Considering Size and Low Shear Rate. Applied Sciences 2020, 10, 1 .

AMA Style

Bowen Zheng, Shengwen Qi, Xiaolin Huang, Songfeng Guo, Chonglang Wang, Zhifa Zhan, Guangming Luo. An Advanced Shear Strength Criterion for Rock Discontinuities Considering Size and Low Shear Rate. Applied Sciences. 2020; 10 (12):1.

Chicago/Turabian Style

Bowen Zheng; Shengwen Qi; Xiaolin Huang; Songfeng Guo; Chonglang Wang; Zhifa Zhan; Guangming Luo. 2020. "An Advanced Shear Strength Criterion for Rock Discontinuities Considering Size and Low Shear Rate." Applied Sciences 10, no. 12: 1.

Journal article
Published: 01 December 2017 in Engineering Geology
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ACS Style

Songfeng Guo; Shengwen Qi; Zhifa Zhan; Bowen Zheng. Plastic-strain-dependent strength model to simulate the cracking process of brittle rocks with an existing non-persistent joint. Engineering Geology 2017, 231, 114 -125.

AMA Style

Songfeng Guo, Shengwen Qi, Zhifa Zhan, Bowen Zheng. Plastic-strain-dependent strength model to simulate the cracking process of brittle rocks with an existing non-persistent joint. Engineering Geology. 2017; 231 ():114-125.

Chicago/Turabian Style

Songfeng Guo; Shengwen Qi; Zhifa Zhan; Bowen Zheng. 2017. "Plastic-strain-dependent strength model to simulate the cracking process of brittle rocks with an existing non-persistent joint." Engineering Geology 231, no. : 114-125.

Journal article
Published: 01 April 2017 in Materials
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In rocks or rock-like materials, the constituents, e.g. quartz, calcite and biotite, as well as the microdefects have considerably different mechanical properties that make such materials heterogeneous at different degrees. The failure of materials subjected to external loads is a cracking process accompanied with stress redistribution due to material heterogeneity. However, the latter cannot be observed from the experiments in laboratory directly. In this study, the cracking and stress features during uniaxial compression process are numerically studied based on a presented approach. A plastic strain dependent strength model is implemented into the continuous numerical tool—Fast Lagrangian Analysis of Continua in three Dimensions (FLAC3D), and the Gaussian statistical function is adopted to depict the heterogeneity of mechanical parameters including elastic modulus, friction angle, cohesion and tensile strength. The mean parameter μ and the coefficient of variance (hcv, the ratio of mean parameter to standard deviation) in the function are used to define the mean value and heterogeneity degree of the parameters, respectively. The results show that this numerical approach can perfectly capture the general features of brittle materials including fracturing process, AE events as well as stress-strain curves. Furthermore, the local stress disturbance is analyzed and the crack initiation stress threshold is identified based on the AE events process and stress-strain curves. It is shown that the stress concentration always appears in the undamaged elements near the boundary of damaged sites. The peak stress and crack initiation stress are both heterogeneity dependent, i.e., a linear relation exists between the two stress thresholds and hcv. The range of hcv is suggested as 0.12 to 0.21 for most rocks. The stress concentration degree is represented by a stress concentration factor and found also heterogeneity dominant. Finally, it is found that there exists a consistent tendency between the local stress difference and the AE events process.

ACS Style

Songfeng Guo; Shengwen Qi; Yu Zou; Bowen Zheng. Numerical Studies on the Failure Process of Heterogeneous Brittle Rocks or Rock-Like Materials under Uniaxial Compression. Materials 2017, 10, 378 .

AMA Style

Songfeng Guo, Shengwen Qi, Yu Zou, Bowen Zheng. Numerical Studies on the Failure Process of Heterogeneous Brittle Rocks or Rock-Like Materials under Uniaxial Compression. Materials. 2017; 10 (4):378.

Chicago/Turabian Style

Songfeng Guo; Shengwen Qi; Yu Zou; Bowen Zheng. 2017. "Numerical Studies on the Failure Process of Heterogeneous Brittle Rocks or Rock-Like Materials under Uniaxial Compression." Materials 10, no. 4: 378.

Journal article
Published: 01 July 2016 in Journal of Applied Geophysics
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This paper investigates the propagation of high amplitude stress waves through a filled joint using a modified steel split Hopkinson pressure bar (SHPB) system. Quartz sand fillings with various thickness are placed in a steel tube and then sandwiched between the incident and transmitted bars to simulate the filled rock joints. Using SHPB, the incident stress waves with similar frequency spectrum but varying amplitude are induced to load the artificial filled joints. The particle size distributions of the fillings after tests are analyzed. It is discovered that as the amplitude of the incident wave increases, the fillings experience three stages of deformation: initial compaction, crushing and crushing and compaction. In the initial compaction stage and the crushing and compaction stage, the fillings are mainly compacted, and thus the transmission coefficient increases with the amplitude of the incident wave. However in the crushing stage, the transmission coefficient decreases with the increase of the amplitude of the incident wave. This is a result of energy consumption due to particle crushing. The observed dependence of the transmission coefficient on the wave amplitude is consistent with the particle size distribution of recovered fillings.

ACS Style

Xiaolin Huang; Shengwen Qi; Kaiwen Xia; Hong Zheng; Bowen Zheng. Propagation of high amplitude stress waves through a filled artificial joint: An experimental study. Journal of Applied Geophysics 2016, 130, 1 -7.

AMA Style

Xiaolin Huang, Shengwen Qi, Kaiwen Xia, Hong Zheng, Bowen Zheng. Propagation of high amplitude stress waves through a filled artificial joint: An experimental study. Journal of Applied Geophysics. 2016; 130 ():1-7.

Chicago/Turabian Style

Xiaolin Huang; Shengwen Qi; Kaiwen Xia; Hong Zheng; Bowen Zheng. 2016. "Propagation of high amplitude stress waves through a filled artificial joint: An experimental study." Journal of Applied Geophysics 130, no. : 1-7.