Vahab Sarfarazi, Hadi Haeri, Jinwei Fu, Amir Namdarmanesh, Gholamreza Saeedi, Naser Golsanami
This paper investigates the influence of indenter shape and rock texture on the crack growth properties and rock hardness. For this purpose, two different rock specimens such as basalt and marble with various textures were prepared and tested by Vickers indentation hardness device with rhombus indenter shape under two different temperatures of 35°C and 100°C. Concurrent with the experimental test, Vickers indentation simulations have been done on three calibrated rock models with nine different indenter shapes. The tensile strength of marble was 8 MPa, while basalt had a tensile strength of 10.8 MPa. Regarding compressive strength, marble exhibited 71 MPa, whereas basalt had a compressive strength of 153 MPa. Marble and basalt had elastic moduli of 45 and 95 GPa, respectively. The physical loading was applied vertically at a rate of 0.004 mm/min. The rock's texture and temperature significantly impact Vickers indentation hardness. Penetration by the Vickers indenter creates an elastic‐plastic stress field, leading to radial cracks due to exceeding the critical stress level. Ring cracks are caused by bulging of the test material and nested cracks directly under the indentation due to high shear and bending stresses in the region. The indentation shape affected the extent of the damage zone below it, leading to increased crack growth with smaller indentation diameters. The radial fracture number increased when the cross‐section changed from circular to quadrilateral shape. The crack growth and damage zone area increased with higher rock temperature due to increased rock brittleness.
{"title":"Experimental and Numerical Indentation Tests to Study the Crack Growth Properties Caused by Various Indenters Under High Temperature","authors":"Vahab Sarfarazi, Hadi Haeri, Jinwei Fu, Amir Namdarmanesh, Gholamreza Saeedi, Naser Golsanami","doi":"10.1002/nag.3885","DOIUrl":"https://doi.org/10.1002/nag.3885","url":null,"abstract":"This paper investigates the influence of indenter shape and rock texture on the crack growth properties and rock hardness. For this purpose, two different rock specimens such as basalt and marble with various textures were prepared and tested by Vickers indentation hardness device with rhombus indenter shape under two different temperatures of 35°C and 100°C. Concurrent with the experimental test, Vickers indentation simulations have been done on three calibrated rock models with nine different indenter shapes. The tensile strength of marble was 8 MPa, while basalt had a tensile strength of 10.8 MPa. Regarding compressive strength, marble exhibited 71 MPa, whereas basalt had a compressive strength of 153 MPa. Marble and basalt had elastic moduli of 45 and 95 GPa, respectively. The physical loading was applied vertically at a rate of 0.004 mm/min. The rock's texture and temperature significantly impact Vickers indentation hardness. Penetration by the Vickers indenter creates an elastic‐plastic stress field, leading to radial cracks due to exceeding the critical stress level. Ring cracks are caused by bulging of the test material and nested cracks directly under the indentation due to high shear and bending stresses in the region. The indentation shape affected the extent of the damage zone below it, leading to increased crack growth with smaller indentation diameters. The radial fracture number increased when the cross‐section changed from circular to quadrilateral shape. The crack growth and damage zone area increased with higher rock temperature due to increased rock brittleness.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142589024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiangyun Zhou, Qingkai Zhang, De'an Sun, You Gao, Minjie Wen, Yunzhi Tan
Energy piles are commonly deployed in vertically layered geological conditions due to the geological structure and pile foundation backfill. The imperfect contact between adjacent soil layers results in resistance to heat transfer at the interface, known as the interfacial thermal resistance effect. In this paper, the energy pile was simplified as a finite‐length solid cylindrical heat source, and an analytical model was established for layered heat transfer of energy piles considering the interfacial thermal resistance effect. The Laplace‐domain solutions to the temperatures in the layered ground were derived by using the finite Hankel and Laplace transforms. The Crump method was subsequently employed to numerically invert Laplace‐domain solutions to the time‐domain solutions. The proposed model was validated by comparing with an analytical solution of a homogeneous model and COMSOL numerical solution. These solutions were used to analyze the temperature response around energy piles considering interfacial thermal resistance. Finally, a parametric study was performed to explore the effects of interfacial thermal resistance and other thermal properties of the soil layer on the layered heat transfer of energy piles.
{"title":"Analytical Model for Heat Transfer Around Energy Piles in Layered Soil With Interfacial Thermal Resistance by Integral Transform Method","authors":"Xiangyun Zhou, Qingkai Zhang, De'an Sun, You Gao, Minjie Wen, Yunzhi Tan","doi":"10.1002/nag.3883","DOIUrl":"https://doi.org/10.1002/nag.3883","url":null,"abstract":"Energy piles are commonly deployed in vertically layered geological conditions due to the geological structure and pile foundation backfill. The imperfect contact between adjacent soil layers results in resistance to heat transfer at the interface, known as the interfacial thermal resistance effect. In this paper, the energy pile was simplified as a finite‐length solid cylindrical heat source, and an analytical model was established for layered heat transfer of energy piles considering the interfacial thermal resistance effect. The Laplace‐domain solutions to the temperatures in the layered ground were derived by using the finite Hankel and Laplace transforms. The Crump method was subsequently employed to numerically invert Laplace‐domain solutions to the time‐domain solutions. The proposed model was validated by comparing with an analytical solution of a homogeneous model and COMSOL numerical solution. These solutions were used to analyze the temperature response around energy piles considering interfacial thermal resistance. Finally, a parametric study was performed to explore the effects of interfacial thermal resistance and other thermal properties of the soil layer on the layered heat transfer of energy piles.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142589025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jie Jiang, Yonglin Ai, Lijun Chen, Wencheng Chai, Mingxi Chen, Xiaoduo Ou
The large diameter piles are widely used in structures such as offshore wind turbines due to their superior lateral load‐bearing capacity. To explore the lateral response of a large‐diameter pile under combined horizontal dynamic and axial static loads in nonhomogeneous soil, a simplified analytical model of the pile–soil interaction is developed. This model represents the pile as a Timoshenko beam resting on the Pasternak foundation, incorporating the double‐shear effect by considering both pile and soil shear. The governing matrix equations for the pile elements are derived from the principle of virtual work. Further, the pile's lateral deformations and internal forces are obtained using the modified finite beam element method (FBEM) and then validated through existing analytical solutions. Finally, the contribution of various properties of pile, soil, and applied load to the pile's lateral vibration response are performed. It is found that both pile and soil shear effects significantly impact the lateral dynamic response of a large‐diameter pile. Additionally, in nonhomogeneous soil, decreasing surface soil strength and dimensionless frequency lead to increased lateral displacements and bending moments of the pile, which are significantly affected by the P‐Δ effect under increasing axial load.
{"title":"Lateral Response Analysis of a Large‐Diameter Pile Under Combined Horizontal Dynamic and Axial Static Loads in Nonhomogeneous Soil","authors":"Jie Jiang, Yonglin Ai, Lijun Chen, Wencheng Chai, Mingxi Chen, Xiaoduo Ou","doi":"10.1002/nag.3884","DOIUrl":"https://doi.org/10.1002/nag.3884","url":null,"abstract":"The large diameter piles are widely used in structures such as offshore wind turbines due to their superior lateral load‐bearing capacity. To explore the lateral response of a large‐diameter pile under combined horizontal dynamic and axial static loads in nonhomogeneous soil, a simplified analytical model of the pile–soil interaction is developed. This model represents the pile as a Timoshenko beam resting on the Pasternak foundation, incorporating the double‐shear effect by considering both pile and soil shear. The governing matrix equations for the pile elements are derived from the principle of virtual work. Further, the pile's lateral deformations and internal forces are obtained using the modified finite beam element method (FBEM) and then validated through existing analytical solutions. Finally, the contribution of various properties of pile, soil, and applied load to the pile's lateral vibration response are performed. It is found that both pile and soil shear effects significantly impact the lateral dynamic response of a large‐diameter pile. Additionally, in nonhomogeneous soil, decreasing surface soil strength and dimensionless frequency lead to increased lateral displacements and bending moments of the pile, which are significantly affected by the <jats:italic>P</jats:italic>‐Δ effect under increasing axial load.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142580360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhongxian Liu, Shuo Zhu, Alexander H. D. Cheng, Zhenen Huang
The inversion of subsurface geological structures is a crucial approach for gaining insights into the internal composition of the earth. In this paper, we propose a novel inversion method combining the nonsingular indirect boundary element method (IBEM) with the multistrategy particle swarm optimization (MSPSO) algorithm, tailored for accurately inverting 3D subsurface cavities. Leveraging the semi‐analytical nature of IBEM offers advantages such as dimensionality reduction, automatic fulfillment of radiation conditions at infinity, and high computational accuracy. Furthermore, to augment global optimization and local search capabilities, an MSPSO algorithm is introduced. Employing multiple optimization strategies enhances particle diversity, accelerates algorithm convergence, and mitigates the risk of local optima. Through the consideration of subsurface cavities with varying parameters, this method quickly identifies the approximate location of the cavity within a wide search range. The final results demonstrate that the proposed method can simultaneously and accurately invert the 3D spatial position, size, and orientation of the cavity.
{"title":"Nonsingular Indirect Boundary Element Method and Multistrategy Particle Swarm Optimization Algorithm Applied to 3D Subsurface Cavity Inversion","authors":"Zhongxian Liu, Shuo Zhu, Alexander H. D. Cheng, Zhenen Huang","doi":"10.1002/nag.3879","DOIUrl":"https://doi.org/10.1002/nag.3879","url":null,"abstract":"The inversion of subsurface geological structures is a crucial approach for gaining insights into the internal composition of the earth. In this paper, we propose a novel inversion method combining the nonsingular indirect boundary element method (IBEM) with the multistrategy particle swarm optimization (MSPSO) algorithm, tailored for accurately inverting 3D subsurface cavities. Leveraging the semi‐analytical nature of IBEM offers advantages such as dimensionality reduction, automatic fulfillment of radiation conditions at infinity, and high computational accuracy. Furthermore, to augment global optimization and local search capabilities, an MSPSO algorithm is introduced. Employing multiple optimization strategies enhances particle diversity, accelerates algorithm convergence, and mitigates the risk of local optima. Through the consideration of subsurface cavities with varying parameters, this method quickly identifies the approximate location of the cavity within a wide search range. The final results demonstrate that the proposed method can simultaneously and accurately invert the 3D spatial position, size, and orientation of the cavity.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142589030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hamza Mhamdi Alaoui, Chaofa Zhao, Wenbo Niu, Pierre‐Yves Hicher
Most soils and rocks contain varying fractions of clay minerals within their solid matrix. These geomaterials can exhibit a significant swelling potential toward chemo‐thermo‐hydromechanical loadings. Several multiscale modeling techniques have been developed to ascertain their swelling behavior across various scales, with molecular dynamics (MD), micromechanics‐based approaches, and double‐porosity models being the most common. MD simulation is a computational technique that applies Newton's second law of motion to depict the movement of particles within a granular system. Micromechanics‐based approaches upscale the poro‐elasticity law from the clay layer level to the sample scale through homogenization. Dual‐porosity models are generally based on elasto‐plasticity, incorporating different hydro‐mechanical laws at two distinct scales. These models have been extensively used, particularly for clayey soils and bentonites, though their application to clayey rocks has not been reported in the literature. Although their significant contribution to the understanding of clay swelling behavior, these techniques have been insufficiently reviewed, compared, and discussed mutually in the literature. This paper aims to provide a cross‐look on these multiscale approaches by presenting the theoretical background of existing formulations, highlighting breakthrough results, discussing major differences and current challenges, and proposing future perspectives.
{"title":"Modeling the Swelling Behavior of Clayey Geomaterials Across Scales: Advances and Challenges","authors":"Hamza Mhamdi Alaoui, Chaofa Zhao, Wenbo Niu, Pierre‐Yves Hicher","doi":"10.1002/nag.3881","DOIUrl":"https://doi.org/10.1002/nag.3881","url":null,"abstract":"Most soils and rocks contain varying fractions of clay minerals within their solid matrix. These geomaterials can exhibit a significant swelling potential toward chemo‐thermo‐hydromechanical loadings. Several multiscale modeling techniques have been developed to ascertain their swelling behavior across various scales, with molecular dynamics (MD), micromechanics‐based approaches, and double‐porosity models being the most common. MD simulation is a computational technique that applies Newton's second law of motion to depict the movement of particles within a granular system. Micromechanics‐based approaches upscale the poro‐elasticity law from the clay layer level to the sample scale through homogenization. Dual‐porosity models are generally based on elasto‐plasticity, incorporating different hydro‐mechanical laws at two distinct scales. These models have been extensively used, particularly for clayey soils and bentonites, though their application to clayey rocks has not been reported in the literature. Although their significant contribution to the understanding of clay swelling behavior, these techniques have been insufficiently reviewed, compared, and discussed mutually in the literature. This paper aims to provide a cross‐look on these multiscale approaches by presenting the theoretical background of existing formulations, highlighting breakthrough results, discussing major differences and current challenges, and proposing future perspectives.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The nonlocal general particle dynamics (NGPD) has been successfully developed to model crack propagation and large deformation problems. In this paper, the semi‐Lagrangian nonlocal general particle dynamics (SL‐NGPD) is proposed to solve brittle failure in rock slopes. In SL‐NGPD, the interaction between particles due to deformation is calculated in the initial configuration, while the friction contact interaction from discontinuities is calculated in the current configuration. The Van der Waals force model is utilized for friction contact. The bond‐level energy‐based failure criterion is developed to predict tensile/compressive‐shear mix‐mode cracks. The artificial viscosity and damage correction are used to enhance the numerical stability and accuracy when modeling brittle failure. The SL‐NGPD paradigm is numerically implemented through adaptive dynamic relaxation and predictor–corrector schemes for stable numerical solutions. The stability and accuracy of SL‐NGPD are verified by simulating compression tests. Thereafter, the crack coalescence patterns of double‐flaw specimens are investigated to understand the triggering failure mechanism of jointed rock slopes. Finally, the progressive failure process of the rock slope with step‐path joints is simulated to demonstrate its validity and robustness in modeling brittle failure in rockslides. The numerical results illustrate that the proposed SL‐NGPD is promising and performant for analyzing brittle failure problems in geotechnical engineering.
{"title":"Modeling Brittle Failure in Rock Slopes Using Semi‐Lagrangian Nonlocal General Particle Dynamics","authors":"Peng Yin, Xiao‐Ping Zhou, Jinhu Pan","doi":"10.1002/nag.3882","DOIUrl":"https://doi.org/10.1002/nag.3882","url":null,"abstract":"The nonlocal general particle dynamics (NGPD) has been successfully developed to model crack propagation and large deformation problems. In this paper, the semi‐Lagrangian nonlocal general particle dynamics (SL‐NGPD) is proposed to solve brittle failure in rock slopes. In SL‐NGPD, the interaction between particles due to deformation is calculated in the initial configuration, while the friction contact interaction from discontinuities is calculated in the current configuration. The Van der Waals force model is utilized for friction contact. The bond‐level energy‐based failure criterion is developed to predict tensile/compressive‐shear mix‐mode cracks. The artificial viscosity and damage correction are used to enhance the numerical stability and accuracy when modeling brittle failure. The SL‐NGPD paradigm is numerically implemented through adaptive dynamic relaxation and predictor–corrector schemes for stable numerical solutions. The stability and accuracy of SL‐NGPD are verified by simulating compression tests. Thereafter, the crack coalescence patterns of double‐flaw specimens are investigated to understand the triggering failure mechanism of jointed rock slopes. Finally, the progressive failure process of the rock slope with step‐path joints is simulated to demonstrate its validity and robustness in modeling brittle failure in rockslides. The numerical results illustrate that the proposed SL‐NGPD is promising and performant for analyzing brittle failure problems in geotechnical engineering.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Raúl Castro, Diego Oyarzo, René Gómez, Kimie Suzuki, Miguel Cifuentes
The extraction and propagation of caving are complex phenomena involving the breaking of the rock mass, the formation of a column of broken material, and the extraction from the column base. Geomechanical modeling in cave mining commonly uses approaches to model the rock mass as a continuous material, while discontinuous modeling is frequently used for the column of broken material. However, it remains complex to include all mechanisms in a single model. Therefore, to achieve a better representation of ore breakage and extraction in caving mining, this work couples FLAC3D, a continuous finite volume tool, with FlowSim, a discrete tool based on cellular automata, to determine the air gap volume. The methodology first defines the height of caving propagation and the cave back with a tool that models solid rock mass in a continuous manner, which are used to constrain the cellular automata tool that simulates the flow of broken material. The results show that unidirectional FLAC3D‐FlowSim coupling reproduces the generation of cave backs and air gaps in the propagation of caving, rendering the methodology valuable for preliminary estimation of air volumes over fragmented material and the generation of supportive data to control the caving process.
{"title":"Coupling Geomechanical and Gravity Flow Models to Obtain More Representative Flow Simulations and Air‐Gap Risk Identification in Caving Mining","authors":"Raúl Castro, Diego Oyarzo, René Gómez, Kimie Suzuki, Miguel Cifuentes","doi":"10.1002/nag.3880","DOIUrl":"https://doi.org/10.1002/nag.3880","url":null,"abstract":"The extraction and propagation of caving are complex phenomena involving the breaking of the rock mass, the formation of a column of broken material, and the extraction from the column base. Geomechanical modeling in cave mining commonly uses approaches to model the rock mass as a continuous material, while discontinuous modeling is frequently used for the column of broken material. However, it remains complex to include all mechanisms in a single model. Therefore, to achieve a better representation of ore breakage and extraction in caving mining, this work couples FLAC<jats:sup>3D</jats:sup>, a continuous finite volume tool, with FlowSim, a discrete tool based on cellular automata, to determine the air gap volume. The methodology first defines the height of caving propagation and the cave back with a tool that models solid rock mass in a continuous manner, which are used to constrain the cellular automata tool that simulates the flow of broken material. The results show that unidirectional FLAC<jats:sup>3D</jats:sup>‐FlowSim coupling reproduces the generation of cave backs and air gaps in the propagation of caving, rendering the methodology valuable for preliminary estimation of air volumes over fragmented material and the generation of supportive data to control the caving process.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142490788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cristina De Nardi, Sina Sayadi, Iulia Mihai, Anthony Jefferson
Throughout history, architectural heritage has been constructed using masonry, clay or stone elements, and lime‐based mortars. Over time, old buildings are subjected to different degrees of movement and degradation, leading to the formation of microcracks. Water dissolves and transports lime in mortar, but when the water evaporates, the lime is deposited and heals cracks in a process known as autogenous healing. Lime‐based mortars can regain some mechanical properties due to their healing capacity, given certain conditions. In the present work, a constitutive formulation has been developed to simulate cracking and healing in lime‐based mortars. The proposed model captures the residual displacements within cracks, associated with interacting crack surface asperities, as well as the healing effect on mechanical properties. A new approach is described which expresses these mechanisms mathematically within a micromechanical formulation. The proposed model was validated by comparing the outputs with experimental data. The results show that the new continuum micromechanical damage‐healing model could capture the damage‐healing cycle with good accuracy.
{"title":"Simulation of Autogenous Self‐Healing in Lime‐Based Mortars","authors":"Cristina De Nardi, Sina Sayadi, Iulia Mihai, Anthony Jefferson","doi":"10.1002/nag.3870","DOIUrl":"https://doi.org/10.1002/nag.3870","url":null,"abstract":"Throughout history, architectural heritage has been constructed using masonry, clay or stone elements, and lime‐based mortars. Over time, old buildings are subjected to different degrees of movement and degradation, leading to the formation of microcracks. Water dissolves and transports lime in mortar, but when the water evaporates, the lime is deposited and heals cracks in a process known as autogenous healing. Lime‐based mortars can regain some mechanical properties due to their healing capacity, given certain conditions. In the present work, a constitutive formulation has been developed to simulate cracking and healing in lime‐based mortars. The proposed model captures the residual displacements within cracks, associated with interacting crack surface asperities, as well as the healing effect on mechanical properties. A new approach is described which expresses these mechanisms mathematically within a micromechanical formulation. The proposed model was validated by comparing the outputs with experimental data. The results show that the new continuum micromechanical damage‐healing model could capture the damage‐healing cycle with good accuracy.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142490357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Robert P. Chapuis, Coline Taveau, François Duhaime, Simon Weber, Vahid Marefat, Lu Zhang, Daniela Blessent, Najib Bouaanani, Dominique Pelletier
Unsaturated zones are important for geotechnical design, geochemical reactions, and microbial reactions. The numerical analysis of unsaturated seepage is complex because it involves highly nonlinear partial differential equations. The permeability can vary by orders of magnitude over short vertical distances. This article defines and uses H‐convergence tests to quantify numerical errors made by uniform meshes with element size (ES) for 1D steady‐state conditions. The quantitative H‐convergence should not be confused with a qualitative mesh sensitivity study. The difference between numerical and mathematical convergences is stated. A detailed affordable method for an H‐convergence test is presented. The true but unknown solution is defined as the asymptote of the numerical solutions for all solution components when ES decreases to zero. The numerical errors versus ES are then assessed with respect to the true solution, and using a log–log plot, which indicates whether a code is correct or incorrect. If a code is correct, its results follow the rules of mathematical convergence in a mathematical convergence domain (MCD) which is smaller than the numerical convergence domain (NCD). If a code is incorrect, it has an NCD but no MCD. Incorrect algorithms of incorrect codes need to be modified and repaired. Existing codes are shown to converge numerically within large NCDs but generate large errors, up to 500%, in the NCDs, a dangerous situation for designers.
非饱和区对岩土工程设计、地球化学反应和微生物反应都很重要。非饱和渗流的数值分析非常复杂，因为它涉及高度非线性的偏微分方程。在很短的垂直距离内，渗透率可能会有数量级的变化。本文定义并使用 H- 收敛测试来量化一维稳态条件下元素尺寸（ES）均匀网格的数值误差。定量 H 趋同不应与定性网格敏感性研究相混淆。说明了数值收敛与数学收敛之间的区别。介绍了 H 收敛测试的详细实惠方法。真实但未知的解被定义为 ES 降为零时所有解成分的数值解的渐近线。然后，相对于真实解，使用对数-对数图评估数值误差与 ES 的关系，从而显示代码的正确与否。如果代码正确，则其结果遵循数学收敛域（MCD）中的数学收敛规则，该收敛域小于数值收敛域（NCD）。如果代码不正确，则有 NCD 而无 MCD。不正确代码的不正确算法需要修改和修复。现有的代码在较大的 NCD 范围内可以数值收敛，但在 NCD 范围内会产生较大的误差，误差率最高可达 500%，这对设计人员来说是一个危险的情况。
{"title":"Using H‐Convergence to Calculate the Numerical Errors for 1D Unsaturated Seepage Under Steady‐State Conditions","authors":"Robert P. Chapuis, Coline Taveau, François Duhaime, Simon Weber, Vahid Marefat, Lu Zhang, Daniela Blessent, Najib Bouaanani, Dominique Pelletier","doi":"10.1002/nag.3876","DOIUrl":"https://doi.org/10.1002/nag.3876","url":null,"abstract":"Unsaturated zones are important for geotechnical design, geochemical reactions, and microbial reactions. The numerical analysis of unsaturated seepage is complex because it involves highly nonlinear partial differential equations. The permeability can vary by orders of magnitude over short vertical distances. This article defines and uses H‐convergence tests to quantify numerical errors made by uniform meshes with element size (<jats:italic>ES</jats:italic>) for 1D steady‐state conditions. The quantitative H‐convergence should not be confused with a qualitative mesh sensitivity study. The difference between numerical and mathematical convergences is stated. A detailed affordable method for an H‐convergence test is presented. The true but unknown solution is defined as the asymptote of the numerical solutions for all solution components when <jats:italic>ES</jats:italic> decreases to zero. The numerical errors versus <jats:italic>ES</jats:italic> are then assessed with respect to the true solution, and using a log–log plot, which indicates whether a code is correct or incorrect. If a code is correct, its results follow the rules of mathematical convergence in a mathematical convergence domain (MCD) which is smaller than the numerical convergence domain (NCD). If a code is incorrect, it has an NCD but no MCD. Incorrect algorithms of incorrect codes need to be modified and repaired. Existing codes are shown to converge numerically within large NCDs but generate large errors, up to 500%, in the NCDs, a dangerous situation for designers.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142489005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Patrick Staubach, Lukas Knittel, Torsten Wichtmann
Experimental evidence indicates that multidimensional cyclic loading of soils causes larger accumulation of deformations than equivalent one‐dimensional loading. The response of sand to high‐cyclic loading with 10,000 cycles and up to four‐dimensional stress paths (i.e., four independent oscillating components) is examined in 120 triaxial and hollow cylinder tests in this work to extend these findings. With increasing number of oscillating stress components, the accumulation of permanent strains tends to increase. It is demonstrated that the definition of the multidimensional strain amplitude incorporated in the high‐cycle accumulation (HCA) model can account for this. The validation of the HCA model for complex cyclic loading is complemented by the simulation of model tests on monopile foundations of offshore wind turbines subjected to multidirectional cyclic loading, for which the consideration of spatially variable cyclic loading with nonconstant load amplitudes in the HCA model is discussed. For this purpose, an extension of the HCA model considering multiple strain amplitudes is presented.
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