岩土工程学报

土木/岩土期刊版面费/审稿费大统计(已更新)希望以下信息对广大研究生论文投稿有帮助，同时欢迎网友补充。

不收审稿费+版面费的国内期刊：1.《建筑科学与工程学报》（中文核心）无版面费2.《城市环境与城市生态》（中文核心）无版面费3.《强度与环境》统计源期刊无版面费4.《洁净与空调技术》（有稿费）无版面费5.《砖瓦》建材核心有稿费无版面费6.《水利发展研究》无版面费7.《中国水利》给200左右的稿费无版面费8.《钢结构》无版面费9.《交通企业管理》有少量稿费无版面费10.《中国建筑防水》有稿费无版面费11.《城市交通》无版面费12.《新型建筑材料》无版面费13.《公路》（中文核心）无版面费14.《施工技术》无版面费（如果是高校作者，要交800元版面费）15.《建筑材料学报》EI收录，收100元审稿费，无版面费16.《建筑技术》（中文核心）无版面费17.《力学学报》（英文版无版面费）SCI收录(中文刊收版面费)18.《科学通报》（英文版无版面费）SCI收录(中文刊收版面费)*另大部分国外期刊都无审稿费+版面费-------------------------------------------------------------------------------------不收审稿费的国内期刊：1.《中国公路学报》（EI 期刊）2.《中国铁道科学》（EI 期刊）3.《中南大学学报》（EI 期刊）4.《土木工程学报》（EI 期刊）5.《水利水电科技进展》（核心）6.《工程勘察》（核心）7.《河海大学学报(自然科学版)》（核心）-------------------------------------------------------------------------------------征收审稿费+版面费的国内期刊：1.《岩土工程学报》月刊审稿费:100(录用后收) 版面费:200/页2.《建筑结构学报》3.《土木工程学报》月刊审稿费:0 版面费：300/页4.《岩石力学与工程学报》月刊审稿费:1005.《建筑结构》6.《工业建筑》7.《哈尔滨工业大学学报》审稿费：100（录用后收取）版面费：150/页(审稿周期3个月,EI 收录率高,主要收本校文章,选择地发表校外及海外作者省部级以上基金课题的优秀论文) 稿酬：1008.《中国给水排水》9.《岩土力学》月刊审稿费：100，版面费：220/版（审稿一般3个月）10.《给水排水》11.《施工技术》12.《建筑技术》13.《世界建筑》14.《建筑科学》15.《世界地震工程》16.《建筑学报》17.《混凝土》18.《工程勘察》月刊版面费：800/篇审稿周期：岩土工程约3个月，测绘工程约4个月，水文地质约4个月，工程物探约4个月。

欢迎订阅并积极投稿——《岩石力学与岩土工程学报》(英文)尊敬的读者、作者及科研人员：您是否对岩石力学与岩土工程领域的研究充满热情？是否渴望了解最新的研究成果和动态？如果是的话，那么《岩石力学与岩土工程学报》(英文)将是您不容错过的学术期刊。

《岩石力学与岩土工程学报》(英文)是一本专注于岩石力学与岩土工程领域的国际学术期刊，致力于为全球的科研人员提供一个展示研究成果、交流学术思想的平台。

我们诚挚邀请您订阅我们的期刊，并积极投稿，共同推动岩石力学与岩土工程领域的发展。

作为一本高水平的学术期刊，《岩石力学与岩土工程学报》(英文)涵盖了岩石力学、岩土工程、地质灾害防治、地下工程、土木工程等多个领域的研究内容。

我们的期刊注重创新性和实用性，旨在为科研人员提供有价值的研究成果和实际应用案例。

我们诚挚邀请您订阅我们的期刊，并积极投稿。

订阅我们的期刊，您将第一时间获取最新的研究成果和动态，与全球的科研人员保持同步。

投稿我们的期刊，您将有机会展示您的研究成果，获得同行的认可和赞赏。

我们相信，您的加入将为《岩石力学与岩土工程学报》(英文)注入新的活力，推动期刊的发展。

我们期待您的投稿，期待与您共同探讨岩石力学与岩土工程领域的热点问题，共同推动该领域的研究和应用。

感谢您对《岩石力学与岩土工程学报》(英文)的关注和支持。

让我们携手共进，共同推动岩石力学与岩土工程领域的发展。

期待您的加入！诚挚地，《岩石力学与岩土工程学报》(英文)编辑部《岩石力学与岩土工程学报》(英文)始终致力于为科研人员提供一个开放、包容、高效的学术交流平台。

我们深知，每一位科研人员都渴望将自己的研究成果分享给更多的同行，同时也期待着从他人的研究中汲取灵感和知识。

为此，我们不断提升期刊的服务质量，简化投稿流程，缩短审稿周期，确保每一位作者的辛勤工作都能得到及时的反馈和公正的评价。

我们鼓励创新思维，支持跨学科研究，特别是那些能够解决实际工程问题、提升工程安全性和效率的研究。

国内岩土类、地质类核心期刊导引国内岩土工程期刊1．工程地质学报2．岩土力学3．岩石力学与工程学报4．岩石学报5．土木工程学报6．岩土工程界7．岩土工程师8．工程勘察9．地震工程与工程振动10．岩土工程技术11．施工技术12．地基处理13．冰川冻土14．地下空间与工程学报15．现代隧道技术16．工程力学17．力学学报18．建筑结构国内土木工程EI及核心期刊《岩土工程学报》（EI，CSCD核心，全国中文核心）《土木工程学报》（EI，CSCD核心，全国中文核心）《建筑结构学报》（EI，CSCD核心，全国中文核心）《岩土力学》（EI，CSCD核心，全国中文核心）《重庆大学学报》（EI，CSCD核心，全国中文核心）《煤炭学报》（EI，CSCD核心，全国中文核心）《中国矿业大学学报》（EI，CSCD核心，全国中文核心）《中南大学学报》（EI，CSCD核心，全国中文核心）《东南大学学报》（EI，CSCD核心，全国中文核心）《同济大学学报》（EI，CSCD核心，全国中文核心）《矿业研究与开发》（全国中文核心）《采矿与安全工程学报》（EI，全国中文核心）《岩石力学与工程学报》（EI，全国中文核心）《工业建筑》（CSCD核心，全国中文核心）《混凝土》（全国中文核心）《水文地质工程地质》（CSCD核心，全国中文核心）《水利学报》（EI，全国中文核心）《人民长江》（CSCD核心，全国中文核心）《长江科学院院报》（全国中文核心）《矿业安全与环保》（全国中文核心）《中外公路》《现代隧道技术》《工程爆破》（全国中文核心）《有色金属》（全国中文核心）《现代矿业》（中国核心期刊，国家级普通期刊）《建筑工业》（CSCD核心，全国中文核心）。

1. Canadian Geotechnical Journal 加拿大岩土工程学报1963年开始出版，世界上发行量最大的三家岩土工程学术期刊之一，以刊登有关基础、隧道、水坝、边坡问题精彩文章及相关学科的新技术、新发展而闻名月刊SCI期刊ISSN : 1208-6010主编：Dr. Ian Moore, Queen's Universityhttp://pubs.nrc-cnrc.gc.ca/rp-ps ... de=cgj&lang=eng/ehost/d ... #db=aph&jid=35HPublished since 1963, this monthly journal features articles, notes, and discussions related to new developments in geotechnical and geoenvironmental engineering, and applied sciences. The topics of papers written by researchers, theoreticians, and engineers/scientists active in industry include soil and rock mechanics, material properties and fundamental behaviour, site characterization, foundations, excavations, tunnels, dams and embankments, slopes, landslides, geological and rock engineering, ground improvement, hydrogeology and contaminant hydrogeology, geochemistry, waste management, geosynthetics, offshore engineering, ice, frozen ground and northern engineering, risk and reliability applications, and physical and numerical modelling. Papers on actual case records from practice are encouraged and frequently featured.2. Geotechnical Engineering, Proceedings of ICE 岩土工程/journals/英国土木工程师协会（ICE）主办，集中了岩土工程实践中的所有方面内容，包括工程实例、工程设计讨论、计算机辅助设计等SCI期刊双月刊影响因子(2006): 0.286 ISSN 1353-2618 (Print) ISSN 1751-8563 (Online)Geotechnical Engineering covers all aspects of geotechnical engineering including tunnelling, foundations, retaining walls, embankments, diaphragm walls, piling, subsidence, soil mechanics and geoenvironmental engineering. Presented in the form of reports, design discussions, methodologies and case records it forms an invaluable reference work, highlighting projects which are interesting and innovative.Geotechnical Engineering publishes six issues per year.3. Géotechnique, Proceedings of ICE 土工国际著名的有关土力学、岩石力学、工程地质、环境岩土工程的岩土技术期刊，每期只刊登几篇文章，都是鸿篇巨著。

岩土工程学报编辑部岩土工程学报是一本专门致力于岩土工程领域研究的期刊杂志，旨在传播岩土工程方面的最新研究成果和学术观点。

作为岩土工程领域的重要学术期刊，岩土工程学报编辑部担负着严谨的审稿和编辑工作，确保发表的论文具备高质量和科学的价值。

一、编辑部介绍岩土工程学报的编辑部设立于国内知名的高校或科研机构，由一支由资深岩土工程专家组成的编辑团队负责日常的运营和管理工作。

编辑部的工作内容主要包括论文审核、投稿管理、稿件修改、发稿领域等多个方面。

二、论文审核岩土工程学报编辑部对每一篇投稿的论文进行严谨的审核工作，以确保论文的内容具有科学性和可信度。

在论文审核过程中，编辑部主要从以下几个方面进行评估：1. 学术质量评估：编辑部对论文的学术质量进行评估，包括是否符合岩土工程学报的研究方向和重点，是否有独到的观点和创新性的研究成果。

2. 方法和实验设计评估：编辑部关注论文中使用的方法和实验设计是否科学合理，以及其可靠性和可重复性。

3. 结论和讨论评估：编辑部对论文中的结论和讨论进行评估，检查是否与研究内容相符，是否有合理的解释和推导。

三、投稿管理编辑部负责岩土工程学报的投稿管理工作，包括与作者的沟通和稿件的管理。

具体工作内容如下：1. 网络投稿平台管理：编辑部维护岩土工程学报的网络投稿平台，处理作者提交的稿件并与作者保持及时的沟通。

2. 投稿状态跟踪：编辑部跟踪和记录每一篇投稿论文的状态，确保所有投稿的论文都得到及时处理和回复。

3. 通知作者：编辑部向每位作者发送有关论文审核和修改的通知，提供详细的修改意见和建议。

四、稿件修改一般来说，岩土工程学报编辑部会对接收的论文提出修改意见，以提高论文的学术质量和可读性。

具体修改工作如下：1. 提供修改意见：编辑部会详细阅读论文并提供修改意见，包括对论文结构、内容和语言进行建议，以确保论文的质量达到刊发标准。

2. 沟通与作者：编辑部与作者保持及时的沟通，详细解答作者对修改意见的疑问，促进论文修改的顺利进行。

岩土工程学报排版格式1.引言1.1 概述概述部分是岩土工程学报排版格式.article的引言部分，用于引入读者对整篇文章的主题和背景进行介绍。

需要根据具体情境编写。

因此，请提供更多关于具体主题的信息，我将根据所提供的信息来编写概述部分的内容。

文章结构可以根据研究的内容和方法来安排。

一般来说，岩土工程学报的论文结构可以包括以下部分：1. 引言：在引言部分，可以对研究的背景和意义进行介绍，并阐述研究的目的和意义。

同时，还可以简要概述后续章节的内容和结构。

2. 文献综述：在文献综述部分，可以对相关的前期研究进行回顾和总结，指出已有研究的不足之处，并说明本研究的创新点和研究价值。

3. 研究方法：在研究方法部分，可以详细描述所采用的实验方法、计算方法和数据处理方法，以及所使用的设备和试验样品。

同时，还可以说明实验设计的合理性和可行性。

4. 实验结果与分析：在实验结果与分析部分，可以展示实验所得的数据和实验结果，并对实验结果进行统计分析和数据解读，得出初步结论。

5. 结果讨论：在结果讨论部分，可以对实验结果进行深入讨论，与文献综述的结果进行对比和分析，总结出本研究的主要发现，并解释其原因和机制。

6. 结论：在结论部分，可以简要总结研究的整体目的、方法和结果，强调研究的创新点和重要性。

同时，还可以提出后续研究的方向和建议。

7. 致谢：在致谢部分，可以感谢给予指导和支持的导师、实验室成员以及其他相关人士和机构。

8. 参考文献：在参考文献部分，要格式规范地列出所有在文中引用过的文献，包括期刊论文、会议论文、专著、标准等。

根据以上结构，我们可以在具体撰写文章1.2文章结构部分时，简要概述以上各个部分的内容，并解释其相互关系和作用。

同时，可以根据实际情况适当调整部分标题的层次结构和命名，以更好地符合研究内容和逻辑发展。

目的部分是文章引言的一部分，需要对研究的目的进行阐述。

在岩土工程学报排版格式的文章中，目的部分旨在明确研究的目标和意义，为读者提供对后续内容的预期和理解。

岩土领域内几个SCI期刊1. Canadian Geotechnical Journal 加拿大岩土工程学报1963年开始出版，世界上发行量最大的三家岩土工程学术期刊之一，以刊登有关基础、隧道、水坝、边坡问题精彩文章及相关学科的新技术、新发展而闻名月刊 SCI期刊主编：Dr. Ian Moore, Queen's University/rp-ps ... de=cgj&lang=eng/ehost/d ... #db=aph&jid=35Hmonthly ISSN : 1208-6010 影响因子 Impact factor: 0.542 NATL RESEARCH COUNCIL CANADA, RESEARCH JOURNALS,MONTREAL RD, OTTAWA, CANADA, K1A 0R6Published since 1963, this monthly journal features articles, notes, and discussions related to new developments in geotechnical and geoenvironmental engineering, and applied sciences. The topics of papers written by researchers, theoreticians, and engineers/scientists active in industry include soil and rock mechanics, material properties and fundamental behaviour, site characterization, foundations, excavations, tunnels, dams and embankments, slopes, landslides, geological and rock engineering, ground improvement, hydrogeology and contaminant hydrogeology, geochemistry, waste management, geosynthetics, offshore engineering, ice, frozen ground and northern engineering, risk and reliability applications, and physical and numerical modelling. Papers on actual case records from practice are encouraged and frequently featured.2. Geotechnical Engineering, Proceedings of ICE 岩土工程/journals/英国土木工程师协会（ICE）主办，集中了岩土工程实践中的所有方面内容，包括工程实例、工程设计讨论、计算机辅助设计等SCI期刊双月刊影响因子(2006): 0.286Geotechnical Engineering covers all aspects of geotechnical engineering including tunnelling, foundations, retaining walls, embankments, diaphragm walls, piling, subsidence, soil mechanics and geoenvironmental engineering.Presented in the form of reports, design discussions, methodologies and case records it forms an invaluable reference work, highlighting projects which are interesting and innovative.Geotechnical Engineering publishes six issues per year.ISSN 1353-2618 (Print)ISSN 1751-8563 (Online)Impact Factor (2006): 0.2863. Géotechnique, Proceedings of ICE土工国际著名的有关土力学、岩石力学、工程地质、环境岩土工程的岩土技术期刊，每期只刊登几篇文章，都是鸿篇巨著。

第xx卷第x期岩土工程学报Vol.xx No.x xxxx年 x月 Chinese Journal of Geotechnical Engineering xxxx, xxxx 基于混沌优化的高阶段充填体可靠性分析刘志祥，李夕兵，张义平(中南大学，湖南长沙 410083)摘要：对高阶段充填体进行了力学分析，推导了分层充填力学计算公式，用可靠性理论研究了高阶段充填体稳定性。

考虑高阶段充填体可靠性分析的状态函数求导困难，提出了基于混沌优化的可靠性计算方法，为工程中复杂函数计算可靠性指标提供了一种新的方法。

高阶段充填体力学研究表明：缩短采场长度和增大采场宽度有利于充填体稳定性和降低充填成本。

为了评价高阶段充填体稳定性，分别在实验室配制充填料浆和采场取样试验了尾砂胶结充填体强度，分析了采场原位充填体强度与实验室试验强度的差异。

研究认为：采用实验室力学参数进行充填设计，最小设计安全系数为1.6～1.8，最小可靠性指标为1.8～2.0比较合理。

用本文方法对安庆铜矿3号高阶段采场充填体进行了可靠性分析，并评价了充填设计的可行性。

关键词：尾砂胶结充填体；分层充填；可靠性；混沌优化中图分类号：TD853.34 文献标识码：A 文章编号：1000–4548(2006)03–0348–05作者简介：刘志祥(1967–)，男，湖南宁乡人，中南大学博士后，从事采矿与岩石力学研究。

Reliability analysis of high level backfill based on chaotic optimizationLIU Zhi-xiang, LI Xi-bing, ZHANG Yi-ping(Central South University, Changsha 410083, China)Abstract:Through the mechanical analysis of high backfill, the calculation formulae of the stratified backfill practice were deduced and reliability analysis of their stabilities were studied. In reliability analysis of high backfill, because the differential of status function was difficult to be obtained, a calculating method of reliability based on chaotic optimization was proposed, which was a new method of reliability analysis for complex status function in engineering practice. The mechanical researches showed that reducing length or increasing width of stope were propitious to improve stability of backfill and to lower filling cost. In order to evaluate the stability of backfill, a series of strength experiments of cemented tailings backfill both in the laboratory and under filling stope conditions were done, and their differences of strength were analyzed, as well as a conclusion was drawn that if the mechanical parameters in lab were used as the basis of filling design, the minimum safety factor should be1.6 to 1.8, and the minimum index of reliability should be 1.8 to2.0. Using the present method, the reliable indexes of backfillin stope No. 3 in Anqing copper mine, Anhui province, were calculated, and the feasibility of filling design were evaluated.Key words:consolidated tailings backfill; stratified filling; reliability; chaotic optimization0 引言高阶段采矿是一高效采矿技术[1]，大都采用尾砂嗣后充填（矿房胶结充填、矿柱非胶结充填）。

Expanding collapse in partially submerged granular soil slopesRadoslaw L.MichalowskiAbstract:The traditional approach to stability analysis of granular slopes leads to the safety factor that is associated with a planar failure surface approaching the slope face,whether the slope is‘‘dry’’or submerged.However,for partially sub-merged slopes,a more critical,nonplanar failure surface can be formed.A family of geometrically similar surfaces can be found that is characterized by the same safety factor.If the safety factor drops down to unity and the slope becomes unsta-ble,then a mechanism of any size can form.Alternatively,the failure may start at some small region and then the volume of the mechanism of failure can expand,giving rise to a progressive failure of a different kind that is typically associated with slopes.This progression has the character of a‘‘disturbance’’or a shock-like kinematic discontinuity propagating into the soil at rest.A quantitative analysis is presented and it is demonstrated that the soil dilates while the mechanism ex-pands,leaving the slope weakened and susceptible to a deep failure.This is a plausible mode of failure of partially sub-merged slopes,the type that is most likely responsible for large subaqueous landslides,and is similar to the well-documented instability propagation in‘‘quick clay.’’Key words:slopes,limit state analysis,progressive failure,submerged slopes.Re´sume´:L’approche traditionnelle pour l’analyse de stabilite´des pentes faites de mate´riaux granulaires permet d’obtenir un facteur de se´curite´associe´a`une surface de rupture plane,pre`s de la surface de la pente,que ce soit pour une pente«se`che»ou submerge´e.Cependant,dans le cas des pentes partiellement submerge´es,une surface de rupture non plane,et plus critique,peut eˆtre forme´e.Une famille de surface ayant une ge´ome´trie similaire,et caracte´rise´e par le meˆme facteur de se´curite´,peut eˆtre forme´e.Si le facteur de se´curite´descend a`une valeur de1et que la pente devient instable,alorsn’importe quelle taille de me´canisme peut se former.D’un autre coˆte´,la rupture peut de´buter dans une petite re´gion,en-suite le volume du me´canisme de rupture peut prendre de l’expansion,ce qui ame`ne a`un type diffe´rent de rupture progres-sive qui est normalement associe´e aux pentes.Cette progression ressemble a`une perturbation ou une discontinuite´cine´tique de type onde de choc qui se propage a`travers le sol au repos.Une analyse quantitative est pre´sente´e,et de´mon-tre que le sol se dilate a`mesure que le me´canisme prend de l’expansion,laissant ainsi la pente affaiblie et susceptible a` une rupture en profondeur.Ce mode de rupture est plausible pour des pentes partiellement submerge´es et est probablement responsable des importants glissements de terrains sous-marins,en plus d’eˆtre similaire a`la propagation des instabilite´s dans l’«argile rapide»qui elle est bien documente´e.Mots-cle´s:pentes,analyse de l’e´tat limite,rupture progressive,pentes submerge´es.[Traduit par la Re´daction]IntroductionMost stability considerations of slopes built of frictional soils associate a collapse with a planar failure surface ap-proaching the slope face,and the safety factor for granular slopes is expressed as F¼tan f=tan b,where f is the internal friction angle of the soil and b is the slope inclination angle. This safety factor is independent of whether the slope is submerged or not(Fig.1a).This generally accepted percep-tion was put to the test by Baker et al.(2005),who found that for partially submerged granular slopes a mechanism may form with a nonplanar failure surface that produces a safety factor lower than the one produced using the tradi-tional approach.Baker et al.concluded that the most critical pool level is about the mid point of the slope height.In a more recent note(Michalowski2009)it was pointed out that a family of geometrically similar failure surfaces can be identified(of the type shown in Fig.1b),each surface in-dependent of the slope height and characterized with the same safety factor.Each of these surfaces intersects the slope face above and below the water table,as shown in Fig.2.An argument will be made that the mechanism of the type shown in Fig.1b can form in a small region close to the water table,and then expand into the soil at rest.Such a progressive(expanding)failure of the partially submerged slope has a boundary that has the nature of a‘‘disturbance’’moving into the intact soil.This is contrary to the traditional perception(and analyses)where a simultaneous triggering of the failure in the entire landslide is considered or where the progression of failure is limited to a well-defined volume with gradually increasing distortions.Received20December2007.Accepted19May2009.Published on the NRC Research Press Web site at cgj.nrc.ca on20November 2009.R.L.Michalowski.Department of Civil And Environmental Engineering,University of Michigan,2340G.G.Brown Bldg.,Ann Arbor, MI48109,USA(e-mail:rlmich@).1371BackgroundIt is a standard approach to consider the failure of a slope as a simultaneous collapse of the entire region defined by the boundaries of the failure mechanism.While this ap-proach has been successfully used for practical estimates of the safety factor of earth slopes,there is evidence that land-slide mechanisms of subaqueous slopes do not start simulta-neously in their entire mass (Hampton et al.1996).One possible mechanism entails a local failure triggered in a small region and propagation of the failure front throughout a large mass of the sediment.Submarine landslides covering large regions with volumes of thousands of cubic kilometres have been reported in the literature (e.g.,Hampton et al.1996).These landslides have not occurred simultaneously in their entire volume.It will be argued that a similar mecha-nism is plausible in partially submerged slopes in granular soils.Two different mechanisms of progressive failure of suba-queous slopes have been documented (Van den Berg et al.2002):(i )where the soil liquefies and (ii )the breaching process.The first one is encountered in loose to medium-dense sands susceptible to compaction and,as a result,is susceptible to the increase in the pore-water pressure.The second type of failure occurs in dense sands where thin slabs of sand ‘‘flake off’’of the face of the slope.This process is governed by the shear of sand,which in the dense sand is associated with dilation and suction in the granular material.The failure of a thin slab of the sand occurs once suctioninFig.1.Collapse mechanisms for partially submerged slopes in granular soils.(a )‘‘shallow’’translational failure;(b )rotational failure.H ,height of the slope;h ,height of the mechanism;L ,water level below slope crest;l ,water level below the mechanism’s uppermost point;r ,log-spiral radius;r 0,initial radius;v ,velocity;v 0,initial velocity associated with initial radius;q ,coordinate angle;q 0,initial coordinate angle for log-spiral surface;q h ,terminal angle for log-spiral surface;u ,angular velocity about the rotation centerO.Fig.2.Equivalent failure surfaces for partially submerged slope.d ,angle defining location of instantaneous centers of rotation.1372Can.Geotech.J.Vol.46,2009the slope is released.This process is also encountered in dredging operations(Van den Berg et al.2002)—at this time,still awaiting its mathematical description.Here,a progressive failure is considered where the local collapse is initiated close to the pool level,and the collapse region expands rapidly into the stationary soil.Application of the kinematic approach of limit analysis to granular slopes is described briefly in the next section,followed by a discussion of a progressive failure mechanism.The mass balance equation is then used to relate the speed of the prop-agating boundary of the mechanism to the material veloc-ities in the dilating soil.Finally,a quantitative analysis of an expanding failure mechanism is developed.Limit analysis of granular slopesThe kinematic approach of limit analysis in soil mechan-ics is well established(e.g.,Chen1975).Application of the kinematic approach to problems where pore-water pressure is involved was first considered in Michalowski(1995),and the specific issues related to submerged slopes can be found in the recent papers of Viratjandr and Michalowski(2006) and Michalowski(2009).Following the last reference in the previous sentence,the balance of the work rate in a rota-tional mechanism with a log-spiral failure surface in granu-lar slopes leads to the following equation:½1 g wg¼Àf1Àf2Àf3Àf4f5where g w/g is the ratio of the unit weight of the pore fluid to the unit weight of the soil(saturated).Coefficients f i are de-pendent on the geometry of the slope,geometry of the me-chanism,and the internal friction angle(they originate from the rate of work of the gravity forces and water pressure). Coefficients f1through f4can be found in Chen(1975). Coefficient f5includes the influence of the pore-and sur-face-water pressure.This coefficient does not have a conve-nient analytical form and has to be evaluated numerically (see Viratjandr and Michalowski2006).Because this consideration is based on the kinematic ap-proach of limit analysis,ratio g w/g in eq.[1]is the upper bound estimate of the value at which the slope loses its stability(the pore-water pressure is considered an external load and this external load increases with the increase in g w).This is not a very practical interpretation of this equa-tion,as ratio g w/g is typically known for a given slope. However,this equation can be used to find the lower-bound estimate to the internal friction angle necessary to avoid fail-ure of the slope when ratio g w/g is given.Because functions f i in eq.[1]depend on the geometry of the failure mecha-nism and the internal friction angle(f),the procedure must be iterative(the geometric parameters are varied in the search for maximum f).The solution to maximum f re-vealed an interesting characteristic:the most critical mecha-nism is a log-spiral failure surface that intersects the slope as shown in Fig.1b.The geometry of the mechanism at which the maximum f (best lower bound)was found is independent of the slope height.Because this solution is size-independent,a mecha-nism of any size will produce the same solution to maxi-mum f.The geometry of the mechanism is related to the water table in the pool(l/h,Fig.1b),but not to its specific level characterized by L/H.Consequently,the geometrically similar failure mechanisms for a granular slope illustrated in Fig.2are all characterized by the same solution to maxi-mum f and,consequently,the same safety factor.This safety factor can be calculated as tan f=tan f m,where f m is the iterative solution to maximum f from eq.[1].The result of calculations for slopes with different inclinations is pre-sented in Fig.3(for g w/g=0.6).It is clear that the log-spiral mechanism for a partially submerged slope produces a lower safety factor than the traditional formula tan f=tan b.Because eq.[1]yields a size-independent solution f m,the safety fac-tor tan f=tan f m is independent of the specific pool level,i.e., the critical pool level is not well defined and small collapse mechanisms can form with very high or very low water ta-bles in the pool.This issue was a focus of the previous note (Michalowski2009).Here it will be argued that the mecha-nism of collapse can expand,starting from a small failure in the neighborhood of the water table and moving into the soil at rest,engaging a progressively larger volume of the soil. Expanding failure mechanismsProgressive and quasi-steady mechanismsWhereas most practical analyses of slope stability assume a simultaneous trigger of the kinematic process in the entire failure region,the true nature of a collapse is usually pro-gressive.At least two types of progressive failure in soils can be distinguished:(i)a process where the features of the mechanism progressively develop in the material to reach the stage where a kinematic mechanism is formed and (ii)nucleation of a kinematic field(mechanism)in a small region and subsequent expansion of this region into the sta-tionary soil.The first type often includes progressive development of shear bands in the soil,such as those under a footing(e.g., Michalowski and Shi2003),or gradual development of the ‘‘failure surface’’in slopes(Palmer and Rice1973).The sec-ond type entails an expanding region of failure with the boundaries moving into the stationary material.An example of such a process is wedge indentation(Drescher and Mi-chalowski1984)or a three-dimensional problem of a pyra-mid indentation into the material at rest(Michalowski 1985).The limit analysis of wedge indentation in a dilating soil is illustrated in Fig.4.The mechanism of deformation is fully developed at every instant of the process,but it ex-pands as the wedge is being driven into the soil.Boundary BCD is a kinematic discontinuity that propagates into the stationary soil,with the speed dependent on the speed of wedge indentation.The inclination of the lip AB is then part of the solution and to conserve mass it must be so. This mechanism of wedge indentation involves a propa-gating‘‘disturbance’’or a‘‘failure front,’’leading to expan-sion of the mechanism.A well-documented failure of‘‘quick clay’’(Gregersen and Loken1979)also had the character of a moving disturbance through the soil.Another phenomenon of a similar nature is propagation of the rarefaction wave in storage containers for granular material,which causes a drop in the material bulk density once the wave passes through the material(Michalowski1987).This type of disturbance will be referred to here as a‘‘shock-like’’discontinuity.ItMichalowski1373will be suggested that the failure of partially submerged slopes can be described by a nucleation of the collapse in a small region,and subsequent expansion into the stationary soil,similar to the process of wedge indentation in Fig.4.The velocity of the material on the two sides of a shock-like discontinuity and the discontinuity’s speed of propaga-tion are related through the principle of mass conservation.This relation will be considered in the next subsection.Shock-like kinematic discontinuityThe wedge indentation (Fig.4)is a process characterized by a progressive mechanism (expansion of the failure re-gion).Such mechanisms often are described as self-similar (or quasi-steady),with geometric similarity at every stage (Hill et al.1947).In such problems,the boundary of the mechanism is considered as an ‘‘instability front’’or a ‘‘dis-turbance’’moving into the material at rest.Care is needed to assure that the mathematical description of such a process is consistent with conservation of mass.Stationary and shock-like velocity discontinuities in gran-ular media were considered earlier by Drescher and Micha-lowski (1984)and,for completeness,this is summarized below.A continuity condition for a flux of matter across a stationary discontinuity can be written as ½2r 1v n 1¼r 2v n2where r is the density of the medium and v n is the velocitycomponent normal to the discontinuity;subscripts 1and 2denote the density and velocity on one side or the other of the discontinuity (see Fig.5a ).Hence,any discontinuity in the normal component of the material velocity needs to be associated with a discontinuity in the mass density.In short,this condition can be written as zero mass flux increment ½3½r v n ¼0where square brackets denote the discontinuity (‘‘jump’’).The velocities in eq.[2]are measured with respect to the discontinuity.Therefore,if the discontinuity is not station-ary,then eq.[2]has to be rewritten as ½4r 1ðv n 1Àv n p Þ¼r 2ðv n 2Àv np Þwhere v n p is the normal speed of propagation of the shock-like discontinuity.We now set v 1=0on side 1(Fig.5c )to relate the shock propagation speed v n p to the velocity of the material v n2when the shock moves into a stationary field ½5v n p¼Àv n 212For a dilative process we have r 1/r 2>1,and a minus sign indicates that the shock propagates in the direction op-posite to the velocity of the material on side 2.For incom-pressible materials (volume-preserving materials),r 2=r 1and v n 2¼v n 1;thus,eq.[4]leads to the trivial statement v np ¼v n p and eq.[5]is not applicable.Pseudo-steady mechanism of slope collapseThe wedge indentation problem in Fig.4is special in that the pattern of deformation remains geometrically similar at every stage of the process (quasi-steady).It is now sug-gested that the failure of partially submerged slopes may very well be described with a quasi-steady mechanism.Be-cause any size of collapse of a partially submerged granular slope is equally realistic (as argued earlier,Fig.2),the mechanism may nucleate in some small region close to the pool level and then expand into the stationary soil,as illus-trated in Fig.6a .Such a mechanism is plausible when the safety factor for the slope is equal to unity,and the safety factor is equal to unity for all geometrically similar surfaces illustrated in Fig. 2.This mechanism could not occur in slopes with some cohesive component of strength as the ex-pansion of the mechanism in such slopes is related to the change in the safety factor,with larger mechanisms having a smaller safety factor.Hence,the initial mechanism in such slopes is likely to include the entire height of the slope,as opposed to the partially submerged granular slopes.One should point out a substantial difference between the expanding mechanism due to wedge indentation and the ex-pansion of the slope failure.In the former,the velocities of the material and the propagation velocities of the shock-like discontinuities are uniquely determined by the speed of wedge penetration,v 0.This is illustrated in the hodograph in the center of Fig.4.Consequently,the change in the soil density during the mechanism expansion is also uniquely de-termined.In the slope case,Fig.6a ,the instantaneous speed of the soil particles along the moving log-spiral boundary AB is determinedbyFig.3.Safety factor for granular slopes as a function of slope in-clination and internal friction angle (adapted from Michalowski2009).Fig.4.Wedge indentation into dilatant soil (adapted from Drescher and Michalowski 1984).1374Can.Geotech.J.Vol.46,2009½6v ¼v ðq h Àq 0Þtan fwhere v 0is the particle speed at q =q 0(point A in Fig.1b ).However,the speed of propagation of log-spiral AB into the stationary soil is not the material speed.To describe the slope expanding failure mechanism quan-titatively,one needs to find the relation between the veloc-ities of the material and the speed of the moving kinematic discontinuity into the soil at rest.Propagation of points A and B up and down the slope (Fig.6a )will now be related to material velocity,v 0,through the relation in eq.[5].This will require that the change in density during the mechanism expansion be estimated based on material properties (dense soils will dilate more than looser soils).At the instant considered,the velocity of the material par-ticle at point A (Fig.6)is v 0=u r 0,where u is the angular ve-locity about the instant rotation center O i and r 0is the radius from O i to point A.Velocity v n 2in eq.[5]now becomes the component of v 0normal to the discontinuity at point A,and the geometrical relations in Fig.6b lead to the propagation ve-locity of (nonmaterial)point A,v A ,up the slope surface ½7v A ¼Àv 0ðr 1=r 2ÞA À1sin fcos ðb þq 0Àf Þwhere (r 1/r 2)A is the ratio of the density of the stationary soil at point A to the density just inside the failure mechan-ism at point A.Now,considering the velocity of the mate-rial at point B as resulting from eq.[6]and repeating the steps as for point A,the nonmaterial velocity of point B down the slope becomes½8 v B ¼v 0ðr 1=r 2ÞB À1sin fcos ðb þq h Àf Þe ðq h Àq 0Þtan fBoth v A and v B are negative,indicating that the propaga-tion of the discontinuity is opposite to the normal compo-nents of the particle velocities.This mechanism is characterized by the well-defined ratio l/h that follows from the limit state analysis as discussed in an earlier section.To preserve the geometrical similarity of the expanding mecha-nism,ratio v A /v B must be equal to l /(h –l ).Therefore,the density will not change uniformly in the entire mechanism (see Appendix A).It may seem surprising at first that even though the dilatancy angle is constant along the entire fail-ure surface,the change in density is not uniform.Such is the direct consequence of the principle of mass conservation and the self-similarity of the mechanism.Velocity v 0in eqs.[7]and [8]is dependent on the angular speed u and is equal to u r 0,but r 0is increasing as the mechanism expands.As the mechanism is geometrically similar,the ratio of radius r 0to the distance PA (Fig.6a )is equal to the ratio of their rates,hence ½9d r 0d t ¼Àv A sin ðd þb Þsin ðd Àq 0Þwhere t is time,angle d is uniquely determined from thegeometrical relations in Fig.6a (see Appendix A),and the minus sign is to assure a positive rate d r 0/d t with negative speed v A following from eq.[7].Now,using the expression in eq.[7]and considering that v 0=u r 0,we have½10d r 0d t ¼u r 0ðr 1=r 2ÞA À1sin f cos ðb þq 0Àf Þsin ðd þb Þsin ðd Àq 0Þ¼u r 0ðr 1=r 2ÞA À1MandFig.5.(a )Velocities at stationary kinematic discontinuity,(b )ho-dograph,(c )velocities at shock-like discontinuity moving into sta-tionary region,and (d )normal components.v p ,speed ofpropagation.Fig.6.(a )Propagation of the shock-like kinematic discontinuity (‘‘failure front’’)into the slope and (b )schematic for derivation of velocity of point A.O i ,instantaneous rotation center;r h ,terminal radius of the log-spiral surface;v A ,propagation velocity of point A (nonmaterial).Michalowski1375½11Z r0r01d r0r0¼Mðr1=r2ÞAÀ1Z tuðtÞd twhere M can be inferred from eq.[10]and r01is the value of r0at t=0.Subscript0in r0does not pertain to initial time,but to the radius at angle q0,and such a notation was adopted so that it is consistent with the original development of the log-spiral mechanism(Chen1975).After integrating eq.[11],we ob-tain½12 r0¼r01expMðr1=r2ÞAÀ1D qwhere D q is the angular displacement since the beginning of the process(t=0)½13 D q¼Z tuðtÞd tThe minimum magnitude of r01may be dependent on the capillary rise,causing‘‘apparent cohesion’’and preventing a small initial size of the failure region.The size of the in-itial mechanism may also be dependent on other factors, such as the distribution of local imperfections.The angular velocity as a function of time in eq.[11]can-not be easily assessed(unless a dynamic problem is solved), and the utility of eq.[12]is qualitative:the mechanism size expands exponentially with the increase in angular displace-ment,but the speed of the mechanism propagation is not di-rectly involved in eq.[12].This equation,however,confirms that the assumption of neglecting the change in the slope ge-ometry during the propagation of failure is reasonable.It is practical to assume that the velocity of the soil at the front of the mechanism expansion(for instance,v0of the particle at point A,Fig.6a)is constant and to calculate the rate of expansion of the mechanism(speed of the failure front propagation)as a function of that material speed.Such an assumption is intuitive but reasonable,and it implies that the angular rotation speed is a hyperbolic function of r0(u= v0/r0),where r0itself is increasing with time;integrating eq.[10]with constant v0=u r0yields½14 r0¼r01þMðr1=r2ÞAÀ1v0twhere t is time from the start of the process(v0t is not a material displacement as the particle at point A is subjected to v0only instantaneously,when the failure front passes through the particle at A).Example and discussionConsider a partially submerged slope with an angle of in-clination b=308and the ratio of the water unit weight to the saturated soil unit weight g w/g=0.5.Now,use eq.[1]to cal-culate the internal friction angle,f,necessary to maintain limit equilibrium.Coefficients f i are functions of f,slope in-clination,and the geometry of the mechanism(q0,l/h).Equa-tion[1]was derived directly from the kinematic theorem of limit analysis and it can be used to find the best lower bound to f necessary to maintain limit equilibrium.Such calcula-tions are iterative,and they are described in more detail in Michalowski(2009).Parameters q0and l/h were varied in the process of maximizing f.The best estimate of f=318 was found,at q0=74.88and l/h=0.484(q h=105.58,but for a mechanism intersecting the slope face,q h is not an in-dependent parameter;see Fig.1b for q0,q h,l,and h).Now, let the failure start in a small region defined by vertical di-mension h t=0= 2.0m(and l=0.968m).Radius r0is uniquely related to h through geometrical relations in Fig.6a,and the initial r0=r01=5.48m.The problem is considered quasi-static,and the velocity of the mechanism expansion can only be assessed with re-spect to the given velocity boundary condition.The given boundary velocity is v0—the instantaneous velocity of a material particle at point A.Whereas the geometric location of point A changes with the progress of the mechanism,v0 is the velocity of the particle currently at point A.This ve-locity is likely to be of the order10–1m/s,and it is assumed that v0=0.1m/s and that it is not dependent on time.The sand with f=318is fairly loose and will dilate very little, say3%at point A,i.e.,(r1/r2)A&1.03.The dilation rate varies along failure surface AB to reach about4%at point B(eq.[A2]in Appendix A).What is surprising is the speed at which the mechanism expands.While the particle at the advancing front at point A moves at the assumed0.1m/s, the front propagates at a speed more than60times faster (6.15and6.56m/s at points A and B,respectively,calcu-lated from eqs.[7]and[8],respectively).The height of the failure zone reaches65m in10s.If the soil were to dilate more,the expansion of the mech-anism would be slower.For instance,if the dilation was to be10%((r1/r2)A&1.11),the speed of point A on the shock propagating up the slope would be only1.68m/s, and the height of the mechanism would grow to about20m after10s.In both examples,the speed of mechanism expan-sion is strongly dependent(proportional)on the assumed v0=0.1m/s and on the change in the density caused by the propagating shock.The angular displacement(rotation)of the soil mass can be calculated from eq.[12],as r0follows from eq.[14]at every instant of the process.The total rotation D q after10s in the first example(3%dilation)is only1.158,and it is 2.748in the second case.This angular displacement does not have a straightforward interpretation,as the rotation oc-curs about a moving center(center of instantaneous rota-tion).Roughly half of that rotation took place in the first 2s,as the rate of rotation drops off exponentially with an increase in the size of the mechanism(maintaining constant v0at moving point A).Only the material within the volume of the originally nucleated mechanism(2m in height)was subjected to the total rotation calculated,whereas the rest of the material‘‘participated’’in the process for some fraction of the10s period.These examples demonstrate that an expansion of the mechanism in a partially submerged slope is not only plausi-ble,but it is a realistic mode of failure in granular soils.This mode is consistent with mechanisms of subaqueous failures (Hampton et al.1996).The true process of failure expansion, however,is modified by the rate effects caused by water movement in the soil.Dilatancy of sand causes a temporary1376Can.Geotech.J.Vol.46,2009。