一种考虑液相惯性的一维准静力固结模型
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摘要
经典Terzaghi一维固结理论不考虑孔隙流体惯性影响,且该理论在不同时期模型推导和表述结果差别较大,导致当前仍存在诸多困惑甚至认识混乱的现象.在笔者前期研究大变形动力固结理论框架内,忽略固相惯性而重点考虑液相惯性影响,经过合理简化建立反映孔隙流体惯性的一维小变形固结波动模型.该固结波模型具有频散和耗散特性.采用分离变量法,可得到单面排水和瞬时加载条件下无量纲形式固结波解析解答.算例分析结果表明:固结波发展规律受无量纲数D_c变化影响而呈现不同性态;D_c数值较大时固结波响应会出现阶跃和正负波动现象;当D_c值较小时,可能出现Mandel-Cryer效应等特殊现象.通过对早期和后期Terzaghi固结模型的分析和对比,初步探明Terzaghi固结理论模型内部的矛盾性,在普通土体坐标和固相体积坐标两种不同解读条件下,早期Terzaghi(1923,1925)模型可以分别诠释为具有小变形和大变形属性的不同固结模型.在经典一维固结理论模型的不同诠释背景下,固结波模型也可以据此作出相应拓展和表述.固结波理论揭示缩尺固结试验中土体物理力学参数与固结波响应两种因素之间存在一种不确定性矛盾,据此建议微观土力学研究重视尺度效应.固结波模型的意义还在于,可为Terzaghi经典固结模型理论精度分析提供新的依据.
Terzaghi's one-dimensional classic consolidation theory ignores inertia of pore water in saturated soils, and has outstanding differences in its derivation and formulation during various publication periods. This leads to a strange phenomenon that considerable misunderstandings and confusion of it still prevail in the current literature. Within the previous framework of large strain dynamic consolidation theory, a one-dimensional infinitesimal strain consolidation wave model is obtained to consider the effect of inertia of pore water with necessary simplification and hypotheses. The present consolidation wave model is characterized by velocity dispersion and dissipative attenuation. The method of separation of variables is used to obtain an analytical solution for a consolidation wave model under the condition of one-way drainage and instantaneous loading. A numerical case study shows that behaviors of consolidation wave are actually controlled by the value of a dimensionless number D_c. For cases of higher values of D_c, jump and fluctuation of dimensionless excess pore water pressure between positive and negative values are prone to occur, in contrast with the cases of lower values of D_c that result into special phenomena including the Mandel-Cryer effect observed in laboratory tests. The inherent ambiguities about Terzaghi's classic theory models proposed in the early stage and the later stage respectively are investigated to draw a conclusion that the early Terzaghi's(1923,1925) consolidation model can be interpreted as a large strain model with respect to the general soil coordinates contrasted with an infinitesimal strain model with respect to the solid-phase volume coordinates. Accordingly, the present consolidation wave model can be extended to various formulations based on the corresponding coordinate properties. Consolidation wave theory is of significance to probe into an innovative uncertainty principle which shows that for scale model testing, the observed consolidation wave response of undisturbed soil samples cannot equal the response of the same soil in practical conditions. Therefore, it is advisable to pay attention to the size effect of soil samples in consolidation study from the perspective of microscopic soil mechanics.The theoretical precision of evaluated excess pore water pressure by classic Terzaghi's consolidation model varies with the value of dimensionless quantity D_c, which is a vital parameter in the proposed consolidation wave theory.
Terzaghi's one-dimensional classic consolidation theory ignores inertia of pore water in saturated soils, and has outstanding differences in its derivation and formulation during various publication periods. This leads to a strange phenomenon that considerable misunderstandings and confusion of it still prevail in the current literature. Within the previous framework of large strain dynamic consolidation theory, a one-dimensional infinitesimal strain consolidation wave model is obtained to consider the effect of inertia of pore water with necessary simplification and hypotheses. The present consolidation wave model is characterized by velocity dispersion and dissipative attenuation. The method of separation of variables is used to obtain an analytical solution for a consolidation wave model under the condition of one-way drainage and instantaneous loading. A numerical case study shows that behaviors of consolidation wave are actually controlled by the value of a dimensionless number D_c. For cases of higher values of D_c, jump and fluctuation of dimensionless excess pore water pressure between positive and negative values are prone to occur, in contrast with the cases of lower values of D_c that result into special phenomena including the Mandel-Cryer effect observed in laboratory tests. The inherent ambiguities about Terzaghi's classic theory models proposed in the early stage and the later stage respectively are investigated to draw a conclusion that the early Terzaghi's(1923,1925) consolidation model can be interpreted as a large strain model with respect to the general soil coordinates contrasted with an infinitesimal strain model with respect to the solid-phase volume coordinates. Accordingly, the present consolidation wave model can be extended to various formulations based on the corresponding coordinate properties. Consolidation wave theory is of significance to probe into an innovative uncertainty principle which shows that for scale model testing, the observed consolidation wave response of undisturbed soil samples cannot equal the response of the same soil in practical conditions. Therefore, it is advisable to pay attention to the size effect of soil samples in consolidation study from the perspective of microscopic soil mechanics.The theoretical precision of evaluated excess pore water pressure by classic Terzaghi's consolidation model varies with the value of dimensionless quantity D_c, which is a vital parameter in the proposed consolidation wave theory.
引文
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2 Lambe TW,Whitman RV.Soil Mechanics,SI Version.New York John Wiley&Sons,1979:406-422
3 Terzaghi K.Erdbaumechanik auf Bodenphysikalischer Grundlage Leipzig und Wien:Franz Deuticke,1925:140-152
4 Poskitt TJ.Discussion:The origins of the theory of consolidation the Terzaghi-Fillunger dispute.Geotechnique,1997,47(4):893-895
5 de Boer R,Schiffman RL,Gibson RE.The origins of the theory of consolidation:The Terzaghi-Fillunger dispute.Geotechnique,199646(2):175-186
6 Gibson RE,England GL,Hussey MJL.The theory of onedimensional consolidation of saturated clays.I.Finite non-linear consolidation of thin homogeneous layers.Geotechnique,196717(3):261-273
7 Znidarcic D,Schiffman RL.On Terzaghi’s concept of consolidation Geotechnique,1982,32(4):387-389
8 Lee K,Szalwinski CM.Discussion on‘On Terzaghi’s concept of consolidation’.Geotechnique,1984,34(1):130-134
9 Terzaghi K.Theoretical Soil Mechanics.New York:John Wiley&Sons,Inc.,1943:265-296
10 Terzaghi K,Jelinek R.Theoretische Bodenmechanik Berlin/Heidelberg:Springer-Verlag,1954:268-300
11 Terzaghi K,Peck RB,Mesri G.Soil Mechanics in Engineering Practice,3rd ed.New York:Wiley,1996:223-236
12龚晓南,谢康和.土力学.北京:中国建筑工业出版社,2002:92-109(Gong Xiaonan,Xie Kanghe.Soil Mechanics.Beijing:China Architecture&Building Press,2002:92-109(in Chinese))
13钱家欢.土力学.南京:河海大学出版社,1988:72-101(Qian Jiahuan.Soil Mechanics.Nanjing:Hohai University,1988:72-101(in Chinese))
14李广信,张丙印,于玉贞.土力学,第2版.北京:清华大学出版社,2013:153-164(Li Guangxin,Zhang Bingyin,Yu Yuzhen.Soi Mechanics,2nd ed.Beijing:Tstinghua Unviersity Press,2013:153- 164(in Chinese))
15赵成刚,白冰.土力学原理,第2版.北京:北京交通大学出版社,清华大学出版社,2017:175-186(Zhao Chenggang,Bai Bing.Principles of Soil Mechanics,2nd ed.Beijing:Beijing Jiaotong University Press,Tsinghua University Press,2017:175-186(in Chinese))
16李广信.高等土力学,第2版.北京:清华大学出版社,2016:319- 361(Li Guangxin.Advanced Soil Mechanics,2nd ed.Beijing:Tsinghua University Press,2016:319-361(in Chinese))
17陈仲颐,周景星,王洪瑾.土力学.北京:清华大学出版社,1994:143-157(Chen Zhongyi,Zhou Jingxing,Wang Hongjin.Soil Mechanics.Beijing:Tsinghua Universtiy Press,1994:143-157(in Chinese))
18高大钊.土力学与基础工程.北京:中国建筑工业出版社,1999:92-102(Gao Dazhao.Soil Mechanics and Foundation Engineering.Beijing:China Architecture&Building Press,1999:92-102(in Chinese))
19 Kaliakin V.Soil Mechanics:Calculations,Principles and Methods.Oxford:Butterworth-Heinemann,2017:377-418
20洪毓康.土质学与土力学,第2版.北京:人民交通出版社,1995:106-119(Hong Yukang.Soil Science and Soil Mechanics,2nd ed.Beijing:China Communications Press,1999:106-119(in Chinese))
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