Stochastic Geomechanics: From Experimentation to Forward Modeling

Topic Information

Dear Colleagues,

This Topic introduces a series of papers that address the impact of uncertainty during the sequence of scientific discovery, which is found across multiple disciplines working with different types, scales, and applications of geomaterials, including (i) experimentation, (ii) data analysis, and (iii) the formulation of corresponding forward models, either based on physical and/or life sciences, statistics, artificial intelligence, or a combination of them, when geomaterial properties and responses are defined in space and time.

This Topic has a special focus on cases wherein a series of a geomaterial experiments were collected in a laboratory setting or in the field and these were repeated under similar conditions to capture the space, time, or spatio-temporal variability of the geomaterial properties and response when subjected to varying control variables such as boundary conditions, initial and loading conditions, sensing technology, and even the operator’s experience. By capturing the effect of the expeimental variability and the associated material properties and response, it is hypothesized that a better understanding of geomaterial performance can be achieved, including its likely failure mechanisms. Consequently, it is anticipated that a more realistic definition of a geomaterial behavior will lead to improved risk assessment and management for physical and/or life processes that depend on it.

The original effort to define the scope of this multi-journal MDPI Topic started with the integration of a series of papers produced by the lead and associate guest editors, including the development of a comprehensive experimental database and the mechanical and stochastic modeling of sand specimens, built and tested under similar experimental conditions, which captured 3D displacement fields from their undeformed to their critical states. This allowed for the geomechanical kinematic analysis of localization effects, as well the computation of spatio-temporal statistics of both the displacement fields and of the kinematic effects. This set the basis for the use of other forward modeling methods, including the use of emerging artificial intelligence methods, in multiple geoscientific and geoengineering applications. We also welcome submissions in this field from Applied Sciences, Geosciences, Materials, Minerals, and Modelling.

Dr. Zenon Medina-Cetina
Dr. Yichuan Zhu
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Applied Sciences applsci	2.7	4.5	2011	16.9 Days	CHF 2400
Geosciences geosciences	2.7	5.2	2011	23.6 Days	CHF 1800
Materials materials	3.4	5.2	2008	13.9 Days	CHF 2600
Minerals minerals	2.5	3.9	2011	18.7 Days	CHF 2400
Modelling modelling	-	-	2020	15.8 Days	CHF 1000

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Published Papers (13 papers)

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18 pages, 9957 KiB  

Open AccessArticle

Calibration of Micro-Parameters of a Mortar Cylinder Specimen under Simple Compression Using a 2D Discrete Element Model

by Miguel Ortiz-Cahun, Luis Fernandez-Baqueiro and Zenon Medina-Cetina

Appl. Sci. 2023, 13(19), 10952; https://doi.org/10.3390/app131910952 - 04 Oct 2023

Viewed by 791

Abstract

Masonry systems have been used extensively in historical, commercial, and residential buildings. A large number of experimental and computational studies have been conducted to investigate the behavior of masonry components and systems, including mortar, units (e.g., blocks), and walls. The Discrete Element Method [...] Read more.

Masonry systems have been used extensively in historical, commercial, and residential buildings. A large number of experimental and computational studies have been conducted to investigate the behavior of masonry components and systems, including mortar, units (e.g., blocks), and walls. The Discrete Element Method (DEM) has been used to analyze masonry systems with a macro modeling methodology (i.e., structural systems like walls). Masonry systems and their components have not been analyzed using a micro-modeling methodology with the DEM. The objective of this paper is the deterministic calibration of micro-parameters of the mortar cylinder model based on a computationally efficient DEM model. To achieve this objective, a parametric analysis is introduced through a series of models of a mortar specimen tested under simple compression to explore the impact of the model micro-parameters when trying to reproduce a set of experimental observations conducted at the Universidad Autonoma de Yucatan Mexico (UADY). A calibration process based on optimization is implemented to determine the best estimates of the model’s micro-parameters. This paper is divided into three analyses. First, the particle size distribution of the mortar’s aggregate is used as a reference (i.e., scale 1), and then up-scaled 1.5 and two times using four particle sizes; second, using the two-times scaled particle size, the influence of varying particle sizes within a reference particle size distribution was explored (from one particle size to 4 particle sizes following the aggregate particle size distribution); and third, a parametric analysis is performed varying seven micro-parameters, one at the time, varying from 0.25 to 1.5, at 0.25 scale increments, on a model including four particle sizes. The results show micro-parameters and stress-strain curves of mortar for the different analyses, and a representation of the cross sections of the models, indicating the distributions of contact forces. All proposed models showed good agreement with the experimental observations (i.e., stress-strain curve). Also, it was observed from the proposed analyses that some micro-parameters vary as the particle size and the scaled particle size distributions change when using the same experimental stress-strain curve. Also, it was found that the proposed DEM must contain at least two particle sizes to significantly improve the particle interlocking to ensure that the mechanistic behavior reproduces the same experimental observations. Finally, from the results presented in this work, it is concluded that it is possible to produce a computationally efficient model that can later serve as a reference for future research accounting for other control variables such as particle shape, particle size distributions, the exploration of damage propagation effects, and most importantly their corresponding uncertainty quantification and propagation effects in masonry systems. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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35 pages, 33136 KiB  

Open AccessEditor’s ChoiceArticle

Numerical Modeling of an Asteroid Impact on Earth: Matching Field Observations at the Chicxulub Crater Using the Distinct Element Method (DEM)

by Tam N.-M. Duong, Billy Hernawan, Zenon Medina-Cetina and Jaime Urrutia Fucugauchi

Geosciences 2023, 13(5), 139; https://doi.org/10.3390/geosciences13050139 - 09 May 2023

Cited by 1 | Viewed by 3339

Abstract

In recent years, an international consortium of research organizations conducted investigations at the Chicxulub Crater in Yucatan, Mexico, to better understand the crater’s formation mechanisms and the effects produced by the impact of the asteroid that is hypothesized to have caused one of [...] Read more.

In recent years, an international consortium of research organizations conducted investigations at the Chicxulub Crater in Yucatan, Mexico, to better understand the crater’s formation mechanisms and the effects produced by the impact of the asteroid that is hypothesized to have caused one of the major life extinctions on Earth. This study aims to reproduce the asteroid’s impact mechanics by matching computer simulations obtained with the use of the distinct element method (DEM) against the latest topographic data observed across the crater footprint. A 2D model was formulated using ITASCA’s PFC2D software to reproduce the asteroid’s impact on Earth. The model ground conditions prior to impact were replicated based on available geological and geophysical field information. Also, the proposed DEM model configuration was designed to reproduce a far-field effect to ascertain the energy dissipation of the asteroid’s impact at the model’s boundaries. Impact conditions of the asteroid were defined based on previous asteroid impact investigations. A parametric analysis including the asteroid’s impact angle and the asteroid’s impact velocity was conducted to assess their influence on the crater formation process. Results of the simulations included the final crater topography and stratigraphy, stress profiles, contact force chains, and velocity fields. Numerical simulations showed that both the asteroid velocity and impact inclination play a major role in the crater formation process, and that the use of DEM provides interesting insights into impact crater formation. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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17 pages, 5234 KiB  

Open AccessArticle

Effect of Random Lateral Ballast Resistance on Force-Deformation Characteristics of CWR with a Small-Radius Curve

by Huan Wang, Chengwei Xing and Xiaohui Deng

Materials 2023, 16(7), 2876; https://doi.org/10.3390/ma16072876 - 04 Apr 2023

Cited by 1 | Viewed by 1001

Abstract

To address the randomness of lateral ballast resistance in the field and its effect on the force-deformation behavior of Continuous Welded Rail (CWR) with small-radius curves, field tests were first conducted to investigate longitudinal and lateral ballast resistance on a 250 m-radius curve. [...] Read more.

To address the randomness of lateral ballast resistance in the field and its effect on the force-deformation behavior of Continuous Welded Rail (CWR) with small-radius curves, field tests were first conducted to investigate longitudinal and lateral ballast resistance on a 250 m-radius curve. It was found that the lateral ballast resistance follows a normal distribution based on the Shapiro–Wilk test. A finite element model of a small-radius curve CWR track was then established based on actual field conditions, and the force-deformation characteristics were analyzed under thermal loading. The results showed that it is of great significance to incorporate the randomness of the lateral ballast resistance as the deformation mode is closer to the actual field situation. In particular, attention should be given to areas where the lateral ballast resistance is weak. The research presented here has significant implications for railway maintenance practice. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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17 pages, 7669 KiB  

Open AccessArticle

Modeling of Sand Triaxial Specimens under Compression: Introducing an Elasto-Plastic Finite Element Model to Capture the Impact of Specimens’ Heterogeneity

by Ahran Song, Alma Rosa Pineda-Contreras and Zenon Medina-Cetina

Minerals 2023, 13(4), 498; https://doi.org/10.3390/min13040498 - 31 Mar 2023

Cited by 2 | Viewed by 1292

Abstract

This paper follows up on a series of reference papers that inspired MDPI’s Topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, where global and local deformation effects on sand specimens are fully described from high-resolution boundary displacement fields, as supported by a comprehensive [...] Read more.

This paper follows up on a series of reference papers that inspired MDPI’s Topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, where global and local deformation effects on sand specimens are fully described from high-resolution boundary displacement fields, as supported by a comprehensive experimental database (which includes varying degrees of specimen’s heterogeneity) that is available to the scientific community for further study. This paper presents an elasto-plastic comparative analysis of different finite element models reproducing different sand specimen heterogeneity configurations as follows: loose, dense, and half-dense half-loose specimens. The experimental conditions for these specimens’ heterogeneity configurations were simulated with an axisymmetric finite element model. To characterize the stress-strain response obtained from the experiments, an elasto-plastic constitutive model with strain-hardening and softening laws was adopted to reproduce the sand specimens’ mechanistic response. An expert-based calibration of the numerical models accounted for both global and local effects by making use of global observations captured by the triaxial point sensors (i.e., axial force and displacement) and by local observations captured by 3D digital image correlation analysis (i.e., 3D boundary displacement fields). Results show that predictions of the proposed numerical models are in good agreement with the experimental observations, both global and local responses. The combined use of global and local observations to calibrate sand triaxial specimens sets the basis for a more comprehensive parameterization process. For the first model set, three experiments were assumed with homogeneous materials. While both dense and loose models showed good agreement with the experiments, the displacement field prediction of the half-dense half-loose layered model identified limitations in reproducing heterogeneous configurations. Afterward, the second set compared and analyzed the half-dense half-loose layered models by implementing a heterogeneous model, showing significantly better model predictions (i.e., after the implementation of the heterogeneous model, which accounts for a transition zone between the upper and lower segments). Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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17 pages, 5220 KiB  

Open AccessArticle

Escape Mechanism with Shallow Ramp and Décollements in Southwest Taiwan

by Fang-Yi Lee, Eh Tan and Emmy T.-Y. Chang

Geosciences 2023, 13(2), 41; https://doi.org/10.3390/geosciences13020041 - 30 Jan 2023

Viewed by 1309

Abstract

The escape structure in southwest Taiwan has long been discussed. The counterclockwise rotation in GPS ground motion is argued to be evidence of tectonic escape. However, tectonic escape events worldwide are always bounded by lithosphere-cutting strike-slip faults at the boundary of the lithospheric-scale [...] Read more.

The escape structure in southwest Taiwan has long been discussed. The counterclockwise rotation in GPS ground motion is argued to be evidence of tectonic escape. However, tectonic escape events worldwide are always bounded by lithosphere-cutting strike-slip faults at the boundary of the lithospheric-scale rotating block, and these have not observed in Taiwan. In this study, we propose that the escape structure in southwest Taiwan is a thin-skinned deformation due to the open boundary in the continental slope, the ramp, and the shallow décollements. We tested this shallow escape hypothesis using a 3D numerical simulation with elastoplastic rheology. We found that a conjugate pair of forethrust and backthrust developed above the ramp. The strike and location of the forethrust mainly follow the ramp. However, the strike of the forethrust rotates perpendicular to the open boundary when in proximity. From north to south, the strike of the forethrust transfers from NNE to NE, and the deformation transfers from thrust to dextral thrust. This leads to a counterclockwise rotation in ground motion, which matches the GPS observation. This research provides a different explanation of the mechanism for the escape structure in southwest Taiwan. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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16 pages, 3422 KiB  

Open AccessArticle

Study on the Influence of Groundwater Variation on the Bearing Capacity of Sandy Shallow Foundation

by Wenfeng Chen, Weishu Xia, Shanshan Zhang and Erlei Wang

Appl. Sci. 2023, 13(1), 473; https://doi.org/10.3390/app13010473 - 29 Dec 2022

Cited by 2 | Viewed by 1617

Abstract

Groundwater variation has a significant effect on the bearing capacity of sandy shallow foundations. Groundwater and capillary water in the shallow foundation would result in the various water distributions in the soil mass. Therefore, there are three types of water conditions in the [...] Read more.

Groundwater variation has a significant effect on the bearing capacity of sandy shallow foundations. Groundwater and capillary water in the shallow foundation would result in the various water distributions in the soil mass. Therefore, there are three types of water conditions in the shallow foundation. They are the total saturated, capillary-water-effect zone and dry soil. In this study, a physical mode experimental was developed to investigate the effect of groundwater variation on the deformation behavior under different loading conditions. The effect of water level and fluctuation times were examined by a novel setup with a water-pressure control system. A total of 10 group model tests were carried out. The results indicated that the relationship between water level height and foundation bearing capacity is negatively correlated. In addition, the numerical analysis was carried out to investigate the effect of water-level change on the bearing capacity of the foundation. The bearing capacity of the foundation decreases as the water-level cycles increase. The increase in the fluctuation range of the water level will decrease the bearing capacity of the foundation. The outcome of this study would be helpful to predict the bearing capacity of shallow foundations due to the change of the water level. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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14 pages, 25487 KiB  

Open AccessArticle

Statistical Characterization of Boundary Kinematics Observed on a Series of Triaxial Sand Specimens

by Yichuan Zhu and Zenon Medina-Cetina

Appl. Sci. 2022, 12(22), 11413; https://doi.org/10.3390/app122211413 - 10 Nov 2022

Cited by 1 | Viewed by 1052

Abstract

This paper follows up on a reference paper that inspired MDPI’s topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, in which the authors populated a spatio–temporal database of boundary displacement fields from a series of triaxial sand specimens using three-dimensional (3D) digital image [...] Read more.

This paper follows up on a reference paper that inspired MDPI’s topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, in which the authors populated a spatio–temporal database of boundary displacement fields from a series of triaxial sand specimens using three-dimensional (3D) digital image correlation analysis. The database was curated and is currently available to the scientific community for further study. This paper uses a subset of this database, in which the experimental conditions were similar, to statistically investigate the dominant kinematic phenomena observed on the boundary of triaxial sand specimens under compression. The first-order 3D kinematic operators under the cylindrical coordinates, comprised of the divergence, curl, and gradient, were applied to the boundary displacement fields to illustrate the localization deformation patterns including the translational, rotational, shearing, and volumetric behaviors throughout the triaxial compression processes. Subsequently, the first-order statistics of the kinematic results are estimated, with the aim of revealing the evolution of associated localization effects as well as their corresponding uncertainties in space and time. The results of this research provide an innovative statistical interpretation of the localization effects on soil specimens under three-dimensional stress conditions. The proposed approach advances the interpretation of granular material’s responses under triaxial compression experimental conditions, while opening an opportunity to reproduce the material’s kinematic responses under the triaxial experimental conditions through constitutive modeling or machine learning techniques. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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28 pages, 5641 KiB  

Open AccessArticle

Assessment of Spatio-Temporal Kinematic Phenomena Observed along the Boundary of Triaxial Sand Specimens

by Yichuan Zhu and Zenon Medina-Cetina

Appl. Sci. 2022, 12(16), 8091; https://doi.org/10.3390/app12168091 - 12 Aug 2022

Cited by 2 | Viewed by 1416

Abstract

This paper follows up on a reference paper that inspired MDPI’s topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, in which global and local deformation effects on sand specimens were fully described from high-resolution boundary displacement fields. This paper is supported by that [...] Read more.

This paper follows up on a reference paper that inspired MDPI’s topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, in which global and local deformation effects on sand specimens were fully described from high-resolution boundary displacement fields. This paper is supported by that study’s experimental database, which is open to the scientific community for further study. This paper focuses on the analysis of this experimental study to investigate strain localization effects on a subset of tests included in this database. Strain localization is defined here as associated with the non-homogeneous deformation process occurring in elastoplastic materials, including sands. Many experimental and numerical studies have been conducted during the last two decades to explore the characteristics of localization effects on sand, and to determine how these contribute to the failure mechanisms of specific sands. Under a triaxial compression condition, localization effects have been studied mainly with regard to particle kinematics and translational strain of the specimen’s displacement fields. However, to the best of the authors’ knowledge, there has been no 3D experimental kinematic analysis performed on sands to study the localization phenomena that can directly relate the impact of a specimen’s initial and boundary conditions to a failure mechanism during a triaxial test. In this paper, we introduce a full set of 3D kinematic operators under cylindrical coordinates to assess the boundary localization effects of deforming sand specimens under triaxial loading conditions. Furthermore, a set of experiments were carried out under varying experimental conditions to study the impact of variability in these localization effects. Results show that patterns of kinematic effects are quantifiable and can be used to assess likely failure-influencing factors, such as confining pressure, initial density, sample geometry, and sample heterogeneity, in the development of specific failure mechanisms. Spatio-temporal interdependencies between localization effects, such as the interactions between shear, expansion, and compaction bands observed during the specimen’s shearing process, were also studied. We therefore hypothesize that the proposed framework will serve as the basis for quantifying the uncertainty associated with the development of localization effects over the boundary of sand-deforming specimens. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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28 pages, 24355 KiB  

Open AccessArticle

Analysis of Slip Failure Characteristics and Support Deformation Law of Structural Planes and Rock Foundation Pits with Developed Karst Caves

by Jin Xu and Yansen Wang

Appl. Sci. 2022, 12(8), 4076; https://doi.org/10.3390/app12084076 - 18 Apr 2022

Cited by 1 | Viewed by 1689

Abstract

This paper establishes a numerical analysis model for the slope of a high-inclined angle stratified foundation pit using support methods including row piles, pile-anchor supports, and combined pile-bracing-anchor supports. The reliability of the analysis conclusion was verified by comparing the stress and deformation [...] Read more.

This paper establishes a numerical analysis model for the slope of a high-inclined angle stratified foundation pit using support methods including row piles, pile-anchor supports, and combined pile-bracing-anchor supports. The reliability of the analysis conclusion was verified by comparing the stress and deformation laws of the support structures on the bedding rock side and the toppling rock side in different schemes, in conjunction with the measured data from Sanhuan South Road Station of Xuzhou Metro Line 3. In addition, on the basis of summarizing the deformation characteristics of the support structures on the bedding rock side and the toppling rock side, the design concept of sectionalized support based on the spatial effect was proposed, and the advantages of the sectionalized support design were elaborated in combination with the numerical analysis results. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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23 pages, 11222 KiB  

Open AccessArticle

Spatio-Temporal Statistical Characterization of Boundary Kinematic Phenomena of Triaxial Sand Specimens

by Yichuan Zhu, Zenon Medina-Cetina and Alma Rosa Pineda-Contreras

Materials 2022, 15(6), 2189; https://doi.org/10.3390/ma15062189 - 16 Mar 2022

Cited by 4 | Viewed by 1947

Abstract

This paper follows up on a reference paper that inspired MDPI’s Topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, where global and local deformation effects on sand specimens are fully described from high resolution boundary displacement fields, and supported by its experimental database, [...] Read more.

This paper follows up on a reference paper that inspired MDPI’s Topic “Stochastic Geomechanics: From Experimentation to Forward Modeling”, where global and local deformation effects on sand specimens are fully described from high resolution boundary displacement fields, and supported by its experimental database, which is open to the scientific community for further study. This paper introduces the use of spatio-temporal statistics from a subset of such an experimental database to characterize the specimens’ spatio-temporal displacement fields, populated by repeating a set of triaxial compression tests on drained, dry, vacuum-consolidated sand specimens, tested under similar experimentally controlled conditions. A three-dimensional digital image correlation (3D-DIC) technique was used to measure the specimens’ boundary displacement fields throughout the course of shearing under axial compression. Spatio-temporal first- and second-order statistics were computed for different data dimensionality conditions (0D, 0D-T, 1D-T, 3D-T) to identify and characterize the dominant failure mechanisms across different testing specimens. This allowed us to quantify localization phenomena’s spatio-temporal uncertainty. Results show that the uncertainty captured along the deformation process across different dimensionality conditions can be directly associated with different failure mechanisms, including localization patterns, such as the onset and evolution of shear, compression, and expansion bands. These spatio-temporal observations show the dependencies between locally distinctive displacement regions over a specimen’s surface, and across different times during a specimen’s shearing process. Results of this work provide boundary spatio-temporal statistics of experimental evidence in sands, which sets the basis for the development of research on the numerical simulation of sand’s constitutive behavior. Moreover, it allows to add a new understanding on the effect of uncertainty on the mechanistic interpretation of sands’ kinematic phenomena. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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19 pages, 4760 KiB  

Open AccessArticle

Modeling the Simultaneous Effects of Particle Size and Porosity in Simulating Geo-Materials

by Jichao Sun and Yuefei Huang

Materials 2022, 15(4), 1576; https://doi.org/10.3390/ma15041576 - 20 Feb 2022

Cited by 25 | Viewed by 2149

Abstract

The particle discrete element method (PDEM) is widely used to simulate rock and soil materials to obtain stress and strain. However, there are three shortcomings: (1) Single sphere or ellipsoids directly replace the soil particles; (2) it treats the diameters of spheres or [...] Read more.

The particle discrete element method (PDEM) is widely used to simulate rock and soil materials to obtain stress and strain. However, there are three shortcomings: (1) Single sphere or ellipsoids directly replace the soil particles; (2) it treats the diameters of spheres or ellipsoids as the soil particle size; (3) the overlapping particle volume is not deducted in calculating the porosity. Hence, it is difficult for the simulation of the geological body to agree with reality. This research found a rotation calculation model and a pixel counting method to make joint soil particles more accurately simulate geological materials to solve the three shortcomings. The model successfully obtained the gradation curve and porosity of the simulated geological body with joint particles. This research will further enrich and broaden the application prospects of PDEM and provide a reference for scientific research and engineering fields in geological engineering, geotechnical engineering, and petroleum engineering. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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23 pages, 15951 KiB  

Open AccessArticle

Global and Local Deformation Effects of Dry Vacuum-Consolidated Triaxial Compression Tests on Sand Specimens: Making a Database Available for the Calibration and Development of Forward Models

by Zenon Medina-Cetina, Ahran Song, Yichuan Zhu, Alma Rosa Pineda-Contreras and Amy Rechenmacher

Materials 2022, 15(4), 1528; https://doi.org/10.3390/ma15041528 - 18 Feb 2022

Cited by 4 | Viewed by 1879

Abstract

A comprehensive experimental database containing results of a series of dry vacuum-consolidated triaxial compression tests was populated. The tests were performed on sand specimens and conducted under similar experimental conditions, in which specimens’ boundary deformation was captured using a three-dimensional digital image correlation [...] Read more.

A comprehensive experimental database containing results of a series of dry vacuum-consolidated triaxial compression tests was populated. The tests were performed on sand specimens and conducted under similar experimental conditions, in which specimens’ boundary deformation was captured using a three-dimensional digital image correlation analysis (3D-DIC). The use of a standard triaxial device along with the 3D-DIC technology allowed the specimens’ global and local boundary displacement fields to be computed from start to end of the compression phase. By repeating each test under the same experimental conditions and building the specimens using the same type of sand, the boundary deformation patterns could be identified, and the statistics associated with both global and local displacement fields could be assessed. Making this experimental database available to others should serve to calibrate as well as develop new forward models to account for effects associated with the specimens’ local displacements and material heterogeneity and include statistics to represent a specimen’s random response. Moreover, this work will serve as a basis for the statistical characterization of spatio-temporal boundary localization effects used to develop stochastic models and machine-learning models, and simulate virtual triaxial tests. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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16 pages, 4026 KiB  

Open AccessArticle

A New Index of Energy Dissipation Considering Time Factor under the Impact Loads

by Xuesong Wang, Lianjun Guo, Zhenyang Xu, Junxiang Wang, Ding Deng, Jinglong Xu and Zhihang Hu

Materials 2022, 15(4), 1443; https://doi.org/10.3390/ma15041443 - 15 Feb 2022

Cited by 4 | Viewed by 1455

Abstract

Rock failure phenomena are accompanied by abundant energy variation, and the energy dissipation can explain the dynamic mechanical characteristics of the rock. In this study, a series of granite specimens (a total of 60) with different aspect ratios were dynamically loaded by a [...] Read more.

Rock failure phenomena are accompanied by abundant energy variation, and the energy dissipation can explain the dynamic mechanical characteristics of the rock. In this study, a series of granite specimens (a total of 60) with different aspect ratios were dynamically loaded by a split Hopkinson pressure bar (SHPB) to explain the energy dissipation and the rock-crushing degree under dynamic load. A new index, namely energy time density (w_td), is proposed to evaluate the energy dissipation considering the time factor. The relationships between strain rate, energy time density, and specific energy absorption are analyzed. A metric (K_u) is defined to describe the degree of rock fragmentation quantitatively. The correlations of fractal dimension and K_u with different impact pressures are compared. It was concluded that there is a noticeable peak point in the energy time density curve. The energy time density of the stress equilibrium point is three times that of the peak point. The energy time density declines after the peak point, then the energy consumption density tends to be stable. The linear relationship between strain rate and peak point energy time density is stronger. The new index can describe energy dissipation well under dynamic loading. In addition, the experimental results indicate that the degree of crush K_u can describe the degree of crush, and the effect of fractal dimension to quantify the fracture characteristics of the rocks is less good in this test. The crushing degree of rocks increases with the increase of strain rate. Furthermore, the prediction effect of energy time density is better than that of strain rate about K_u. Full article

(This article belongs to the Topic Stochastic Geomechanics: From Experimentation to Forward Modeling)

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