Pub Date : 2020-09-26DOI: 10.1201/9781003077497-68
I. Vardoulakis
In this paper the basic mathematical structure of a thermo-poro-mechanical model for faults under rapid shear is discussed. The analysis is 1D in space and concerns the infinitely extended fault. The gauge material is considered as a two-phase material consisting of a thermo-elastic fluid and of a thermoporo-elasto-viscoplastic skeleton. The governing equations are derived from first principles, expressing mass, energy and momentum balance inside the fault. They are a set of coupled diffusion-generation equations that contain three unknown functions, the pore-pressure, the temperature and the velocity field inside the fault. The original mathemetically ill-posed problem is regularized using a viscous-type and a 2 gradient regularization. Numerical results are presented and discussed. ) t , z ( p , the temperature ) t , z ( θ and the velocity ) t , z ( v are assumed to be functions only of the time t and of the position z in normal to the band direction (Figure 1). Figure 1. The deforming shear-band with heat and fluid fluxes As is shown in Vardoulakis (2000) mass and energy balance equations together with Darcy's and Fourier's laws lead to a set of coupled diffusiongeneration equations for the pore-water pressure ) t , z ( p and the temperature field ) t , z ( θ inside the shear band. For easy reference we summarize here these equations and define the pertinent material parameters.
本文讨论了快速剪切作用下断层热孔力学模型的基本数学结构。该分析在空间上是一维的，涉及到无限扩展的断层。压力表材料被认为是由热弹性流体和热弹性-弹-粘塑性骨架组成的两相材料。控制方程由第一性原理导出，表达了断层内部的质量、能量和动量平衡。它们是一组耦合的扩散生成方程，包含断层内部的孔隙压力、温度和速度场三个未知函数。利用粘滞型正则化和2梯度正则化对原数学病态问题进行正则化。给出了数值结果并进行了讨论。假设t, z (p，温度)t, z (θ)和速度)t, z (v)仅是时间t和位置z垂直于带方向的函数(图1)。根据Vardoulakis(2000)的质量和能量平衡方程，结合Darcy定律和Fourier定律，可以得到剪切带内孔隙水压力t, z (p)和温度场t, z (θ)的耦合扩散生成方程。为了方便参考，我们在这里总结了这些方程并定义了相关的材料参数。
{"title":"Thermo-poro-mechanical analysis of rapid fault deformation","authors":"I. Vardoulakis","doi":"10.1201/9781003077497-68","DOIUrl":"https://doi.org/10.1201/9781003077497-68","url":null,"abstract":"In this paper the basic mathematical structure of a thermo-poro-mechanical model for faults under rapid shear is discussed. The analysis is 1D in space and concerns the infinitely extended fault. The gauge material is considered as a two-phase material consisting of a thermo-elastic fluid and of a thermoporo-elasto-viscoplastic skeleton. The governing equations are derived from first principles, expressing mass, energy and momentum balance inside the fault. They are a set of coupled diffusion-generation equations that contain three unknown functions, the pore-pressure, the temperature and the velocity field inside the fault. The original mathemetically ill-posed problem is regularized using a viscous-type and a 2 gradient regularization. Numerical results are presented and discussed. ) t , z ( p , the temperature ) t , z ( θ and the velocity ) t , z ( v are assumed to be functions only of the time t and of the position z in normal to the band direction (Figure 1). Figure 1. The deforming shear-band with heat and fluid fluxes As is shown in Vardoulakis (2000) mass and energy balance equations together with Darcy's and Fourier's laws lead to a set of coupled diffusiongeneration equations for the pore-water pressure ) t , z ( p and the temperature field ) t , z ( θ inside the shear band. For easy reference we summarize here these equations and define the pertinent material parameters.","PeriodicalId":166080,"journal":{"name":"Powders and Grains 2001","volume":"2 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121003282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-26DOI: 10.1201/9781003077497-82
P. Schiffer, I. Albert, J. Sample, A.-L. Barabäsi
{"title":"The drag force in granular media","authors":"P. Schiffer, I. Albert, J. Sample, A.-L. Barabäsi","doi":"10.1201/9781003077497-82","DOIUrl":"https://doi.org/10.1201/9781003077497-82","url":null,"abstract":"","PeriodicalId":166080,"journal":{"name":"Powders and Grains 2001","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126564928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-26DOI: 10.1201/9781003077497-60
T. Sitharam, S. Dinesh, N. Shimizu
{"title":"Phase Transformation behavior in Granular Materials using DEM","authors":"T. Sitharam, S. Dinesh, N. Shimizu","doi":"10.1201/9781003077497-60","DOIUrl":"https://doi.org/10.1201/9781003077497-60","url":null,"abstract":"","PeriodicalId":166080,"journal":{"name":"Powders and Grains 2001","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126571031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-26DOI: 10.1201/9781003077497-149
N. Roussel, C. Lanos, Y. Mélinge
{"title":"Drainage condition of saturated granular media under shearing","authors":"N. Roussel, C. Lanos, Y. Mélinge","doi":"10.1201/9781003077497-149","DOIUrl":"https://doi.org/10.1201/9781003077497-149","url":null,"abstract":"","PeriodicalId":166080,"journal":{"name":"Powders and Grains 2001","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127817670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-26DOI: 10.1201/9781003077497-99
M. Luong
{"title":"X-ray computed tomography of sugar crystals flow in silo","authors":"M. Luong","doi":"10.1201/9781003077497-99","DOIUrl":"https://doi.org/10.1201/9781003077497-99","url":null,"abstract":"","PeriodicalId":166080,"journal":{"name":"Powders and Grains 2001","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132607145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-26DOI: 10.1201/9781003077497-62
K. Iwashita, M. Oda
{"title":"Numerical simulation of granular materials subjected to cyclic loading under constant volume by modified Distinct Element Method","authors":"K. Iwashita, M. Oda","doi":"10.1201/9781003077497-62","DOIUrl":"https://doi.org/10.1201/9781003077497-62","url":null,"abstract":"","PeriodicalId":166080,"journal":{"name":"Powders and Grains 2001","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127581924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-26DOI: 10.1201/9781003077497-132
M. Shapiro, V. Dudko, V. Royzen, A. Alexeev, A. Goldshtein
{"title":"Vibrofluidization of vibrated granular layers: Experiments and simulations","authors":"M. Shapiro, V. Dudko, V. Royzen, A. Alexeev, A. Goldshtein","doi":"10.1201/9781003077497-132","DOIUrl":"https://doi.org/10.1201/9781003077497-132","url":null,"abstract":"","PeriodicalId":166080,"journal":{"name":"Powders and Grains 2001","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122648371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-26DOI: 10.1201/9781003077497-17
Y. Yamazaki, T. Mizuguchi
{"title":"Labyrinthine pattern by front aggregation in drying water-granule systems","authors":"Y. Yamazaki, T. Mizuguchi","doi":"10.1201/9781003077497-17","DOIUrl":"https://doi.org/10.1201/9781003077497-17","url":null,"abstract":"","PeriodicalId":166080,"journal":{"name":"Powders and Grains 2001","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123220970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-26DOI: 10.1201/9781003077497-112
N. Mitarai, H. Nakanishi
{"title":"Instability of Granular Flow on Rough Inclined Plane","authors":"N. Mitarai, H. Nakanishi","doi":"10.1201/9781003077497-112","DOIUrl":"https://doi.org/10.1201/9781003077497-112","url":null,"abstract":"","PeriodicalId":166080,"journal":{"name":"Powders and Grains 2001","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129931564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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