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物质点法在地质灾害动态模拟中的应用与发展研究动态

王梦晨, 李滨, 万佳威, 高杨, 王文沛

王梦晨,李滨,万佳威,等. 物质点法在地质灾害动态模拟中的应用与发展研究动态[J]. 中国地质灾害与防治学报,2024,35(0): 1-11. DOI: 10.16031/j.cnki.issn.1003-8035.202405006
引用本文: 王梦晨,李滨,万佳威,等. 物质点法在地质灾害动态模拟中的应用与发展研究动态[J]. 中国地质灾害与防治学报,2024,35(0): 1-11. DOI: 10.16031/j.cnki.issn.1003-8035.202405006
WANG Mengchen,LI Bin,WAN Jiawei,et al. Research progress on the application and development of the material point method in dynamic simulation of geological hazards[J]. The Chinese Journal of Geological Hazard and Control,2024,35(0): 1-11. DOI: 10.16031/j.cnki.issn.1003-8035.202405006
Citation: WANG Mengchen,LI Bin,WAN Jiawei,et al. Research progress on the application and development of the material point method in dynamic simulation of geological hazards[J]. The Chinese Journal of Geological Hazard and Control,2024,35(0): 1-11. DOI: 10.16031/j.cnki.issn.1003-8035.202405006

物质点法在地质灾害动态模拟中的应用与发展研究动态

基金项目: 国家自然科学基金联合基金重点支持项目(U2244226);中国地质调查局项目(DD20230538);中国电建集团项目(CD2C20230228;CD2C20231102)
详细信息
    作者简介:

    王梦晨(1998—),男,陕西咸阳人,博士研究生,主要从事地质灾害防灾减灾及地震工程方面的研究。E-mail:2020226082@chd.edu.cn

    通讯作者:

    李 滨(1980—),男,博士,研究员,主要从事工程地质与地质灾害研究工作。E-mail:libin1102@163.com

  • 中图分类号: 中图分类号: 文献标识码:A 文章编号:

Research progress on the application and development of the material point method in dynamic simulation of geological hazards

  • 摘要:

    在解决崩塌、滑坡、泥石流等大变形地质灾害问题时,常采用数值模拟的方法。如何准确高效地模拟这类问题一直以来都是个难题。物质点法(Material Point Method,MPM)作为一种新兴的数值方法,克服了传统有限元和有限差分等数值方法在模拟大变形时产生的网格畸变问题,并已成功应用于地质灾害中的大变形分析。为了解物质点法在地质灾害大变形模拟中的研究进展,本文在现有研究的基础上简要介绍了物质点法的基本原理,主要总结了物质点法在模拟滑坡、泥石流、地裂缝等地质灾害大变形问题中的应用以及最新的研究进展。同时,指出了物质点法在现有研究中存在的精度、计算效率、多物理场耦合等问题,并展望了物质点法在工程地质中进一步发展的趋势。

    Abstract:

    Numerical simulation is commonly used to address large deformation geological disasters such as collapses, landslides, and debris flows. Accurately and efficiently simulating these issues has always been a challenge. The Material Point Method (MPM), as emerging numerical method, overcomes the grid distortion problems of traditional numerical methods such as the finite element method (FEM) and finite difference method (FDM) when simulating large deformations, and has been successfully applied in the large deformation analysis of geological disasters. In order to understand the research progress of MPM in the large deformation simulation of geological disasters, this paper briefly introduces the basic principles of MPM based on current research. It also summarizes the application of MPM in simulating large deformations of geological disasters such as landslide, debris flow, and ground fracture, highlighting the latest research progress. Furthermore, it identifies issues in existing MPM research, such as accuracy, computational efficiency, and coupling of multi-physics fields, and discusses future trends in MPM development withinengineering geology.

  • 由于气候的复杂多变,崩塌、滑坡及泥石流等大变形地质灾害频发[1],数值模拟是解决这类问题的主要方法之一。目前,模拟岩土体变形方法主要分为:有限差分法(FLAC3D)、有限元法(Abaqus、Ansys)、离散元法(PFC、UDEC、3DEC)以及SPH、MPM为代表的无网格法。有限差分法易于理解和实现,适用于规则的几何形状和边界条件,数值稳定性好;然而对于复杂的几何形状和非线性问题,需要进行网格生成和边界条件处理,计算效率较低。有限元法适用于复杂的几何形状和非线性问题,可以灵活处理各种边界条件,数值稳定性好。但是需要进行网格生成和单元划分,计算过程复杂,耗费计算资源较多。离散元法适用于模拟颗粒物体的运动和相互作用,可以考虑颗粒之间的接触和碰撞,适用于模拟颗粒性材料的行为;离散元法属于非连续介质力学的范畴,而对于连续介质和液态物质的模拟效果较差,计算效率较低。其中SPH方法主要常用于流体动力学模拟,对于模拟固体颗粒的动力分析,数值稳定性较低。准确地分析滑坡、崩塌、泥石流等大变形地质灾害的运动过程不仅具有实际工程意义,还具有重要的理论研究价值。因此,为了解决这类大变形问题,国内外学者提出了一种新的数值计算方法——物质点法。

    物质点法是一种基于连续介质力学范畴的数值计算方法。它通过将连续体离散成一组质点来携带材料的所有物质信息(如质量、速度、应力、应变等),在背景网格上进行本构计算。该方法采用拉格朗日离散来避免非线性对流项产生的数值求解困难,背景网格采用欧拉描述,从而避免了网格畸变问题。由于物质点法的独有特点,物质点法在模拟岩土工程中的大变形过程时能够较好地捕捉材料的变形行为和相互作用,适用于复杂的多相材料和边界条件情况。因此,物质点法在岩土工程领域得到了广泛的应用。随着物质点法的不断发展,目前已被广泛应用于超高速碰撞、冲击侵蚀、爆炸、裂纹扩展、材料破坏、颗粒材料流动和岩土冲击失效等与材料特大变形问题相关的领域[23]

    近年来,物质点法被用来分析诸如边坡稳定性、泥石流和同震滑坡等问题,引发了大量工程地质专家的关注。为展示物质点法在地质灾害大变形模拟中的最新研究进展,在查阅大量文献的基础上,本文首先简要阐述了物质点法的基本原理;其次,重点总结了近年来物质点法在模拟地质灾害大变形问题中各研究领域方面的最新研究进展,指出了现有研究的不足与今后研究亟待解决的关键科学问题;最后,给出了物质点法在模拟地质灾害大变形问题的发展趋势,并指出了进一步的研究方向。

    更新拉格朗日格式的连续体动量微分方程为:

    $$ \rho \ddot{u}=\rho b+\nabla \sigma $$ (1)

    式中: ρ——物体的密度;

    $ \ddot{u} $——位移关于时间的二阶导数;

    b——单位质量的体积力;

    $ \nabla $——对空间坐标的导数;

    σ——Cauchy应力。

    动量方程(1)在连续体的现时构型Ω内处处满足,边界条件为

    $$ \left\{\begin{split} &({n}_{j}{{\sigma }_{ij}\left)\right|}_{{\varGamma }_{t}}=\bar{{t}_{i}}\\ &{v}_{i}{|}_{{\varGamma }_{u}}=\bar{{\nu }_{i}}\end{split}\right. $$ (2)

    式中:$ {n}_{j} $——边界$ {\varGamma }_{t} $的外法线单位向量;

    $ {\sigma }_{ij} $——Cauchy应力;

    $ {\varGamma }_{t} $$ {\varGamma }_{u} $——给定的面力边界和位移边界;

    $ \bar{{t}_{i}} $——作用在边界$ {\varGamma }_{u} $上的面力;

    $ \bar{{\nu }_{i}} $——位移边界$ {\varGamma }_{u} $的速度。

    动量方程(1)需在求解域Ω内处处满足,求解困难。因此引入虚位移$ \delta {u}_{i} $作为权函数,其动量方程的等效积分弱形式为:

    $$ \underset{\Omega }{\int }\rho {\ddot{u}}_{i}\delta {u}_{i}dV+\underset{\Omega }{\int }\rho {\sigma }_{ij}^{s}\delta {u}_{i,j}dV-\underset{\Omega }{\int }\rho {b}_{i}\delta {u}_{i}dV-\underset{\Omega }{\int }\rho {\bar{t}}_{i}^{s}\delta {u}_{i}dA=0 $$ (3)

    上式也称虚功方程,

    式中:$ {\sigma }_{ij}^{s}=\sigma /\rho $——比应力;

    $ {\bar{t}}_{i}^{s}=\bar{{t}_{i}}/\rho $——比边界面力。

    虚位移满足:

    $$ \delta {u}_{i}\in \left\{\delta {u}_{i}|\delta {u}_{i}\in {C}^{0},{\delta {u}_{i}|}_{{\varGamma }_{u}}=0\right\} $$ (4)

    式中:C0——连续函数集。

    物质点法将连续体离散为一系列质点(图1),连续体的密度可近似为:

    图  1  物质点离散示意图
    Figure  1.  Schematic diagram of material point discretization
    $$ \rho \left({x}_{i}\right)=\sum _{p=1}^{{n}_{p}}{m}_{p}\delta ({x}_{i}-{x}_{ip}) $$ (5)

    式中:$ {n}_{p} $——质点总数;

    $ {m}_{p} $——质点ρ的质量;

    δ——Dirac Delta函数;

    $ {x}_{ip} $——质点P的坐标。

    将式(5)带入虚功方程(3)中,可将虚功方程转化为求和的形式:

    $$ \begin{split} &\sum _{p=1}^{{n}_{p}}{m}_{p}{\ddot{u}}_{ip}\delta {u}_{ip}+\sum _{p=1}^{{n}_{p}}{m}_{p}{\sigma }_{ijp}^{s}\delta {u}_{ip,j}-\\ &\sum _{p=1}^{{n}_{p}}{m}_{p}{b}_{ip}\delta {u}_{ip}-\sum _{p=1}^{{n}_{p}}{m}_{p}{\bar{t}}_{ip}^{s}{h}^{-1}\delta {u}_{ip}=0 \end{split}$$ (6)

    式中,带下标P的量代表物质点P所携带的量。h是为了将式(3)左端最后一项转化为体积分而引入的假想边界层厚度。从式(6)可以看出,物质点法将式(3)中的各项积分转化为被积函数在各质点处的值与该质点所代表的体积之积的和,即采用了质点积分。

    求解动量方程时,背景网格和质点不产生相对移动,可通过建立在背景网格结点上的有限元形函数$ {N}_{I}\left({x}_{i}\right) $来实现质点和背景网格结点之间信息的映射。因此,质点P的位移$ {u}_{ip} $、位移导数$ {u}_{ip,j} $、虚位移$ {\delta u}_{ip} $可分别表示为:

    $$ {u}_{ip}={N}_{Ip}{u}_{iI} $$ (7)
    $$ {u}_{ip,j}={N}_{Ip,j}{u}_{iI} $$ (8)
    $$ {\delta u}_{ip}={N}_{Ip}\delta {u}_{iI} $$ (9)

    将(6)-(8)式带入虚功方程(6)中,可得到背景网格结点的运动方程:

    $$ {\dot{p}}_{iI}={f}_{iI}^{int}+{f}_{iI}^{ext},{x}_{i}\notin {\varGamma }_{u} $$ (10)
    $$ {f}_{iI}^{int}=-\sum _{p=1}^{{n}_{p}}{N}_{Ip,j}{\sigma }_{ijp}\frac{{m}_{p}}{{\rho }_{p}} $$ (11)
    $$ {f}_{iI}^{ext}=\sum _{p=1}^{{n}_{p}}{m}_{p}{N}_{Ip}{b}_{ip}+\sum _{p=1}^{{n}_{p}}{N}_{Ip}{\bar{t}}_{ip}{h}^{-1}\frac{{m}_{p}}{{\rho }_{p}} $$ (12)

    式中:$ {\dot{p}}_{iI} $——第I个网格结点在i方向上的动量;

    $ {f}_{iI}^{int} $$ {f}_{iI}^{ext} $——结点的内力和结点外力;

    $ {\sigma }_{ijp} $——质点P的应力,可利用本构方程由应变增 量和旋量增量得到[4]

    根据上述理论,物质点法的求解示意图如图2所示,具体步骤可概括为:

    图  2  物质点法求解示意图(① 物质点信息映射 ②动量方程求解 ③更新物质点信息)
    Figure  2.  Schematic diagram of material point method solution (①Mapping of material point information, ②Solving the momentum equation, ③Updating material point information)

    (1)、将物质点携带信息映射到背景网格上;

    (2)、在背景网格结点处求解动量方程,计算背景网格结点的结点力、应变增量、旋量增量、密度等参数;

    (3)、将背景网格结点动量方程计算结果映射回物质点,更新物质点的位置和速度。

    在使用物质点法时,主要涉及变形和破坏两类问题[5]。第一类问题是固体力学问题,使用了Sulsky[6]提出的MPM公式来进行描述。而第二类问题则是土水耦合问题,在Zienkiewicz[7]和Verruijt[8]提出的公式中进行建立。在本节中,主要介绍MPM在模拟岩土材料变形和破坏方面的应用,包括滑坡、泥石流等。

    滑坡问题一直都是工程地质领域的重要研究课题。近年来,一些学者利用物质点法对边坡工程做了大量研究。

    Beuth[910]最早将MPM应用于滑坡问题中,模拟了滑坡触发-运动-静止的全过程。黄鹏[1112]利用D-P本构模型,运用MPM对滑坡问题进行了模拟分析,并讨论了粘性和非粘性土质边坡的变形破坏特征。Llano-Serna[13]运用MPM对意大利Vajont滑坡进行了模拟,模拟结果显示Vajont滑坡运动时间为32 s,与实际观测的实际运动时间45 s接近,证实了物质点法具有还原实际滑坡的能力与精度。Li[14]利用MPM对王家岩滑坡的动态过程进行了模拟,并研究了其对建筑物的影响。宰德志[15]利用MPM研究了岩土体强度与滑坡滑动距离之间的关系。姚云[16]利用MPM方法研究了不同剪胀角对土质边坡稳定性的影响,结果显示剪胀角的大小与边坡的稳定程度成正相关关系。杨婷婷[17]利用MPM方法模拟了粘性土和无粘性土坡破坏的大变形问题,并分析了材料摩擦角、粘聚力和高宽比等因素对土体滑动距离的影响规律。Qu[18]利用随机物质点法研究了粘聚力和摩擦角之间的相互关联对边坡失稳概率的问题。Yerro[19]研究了材料脆性对边坡稳定性以及破坏后运动特性的影响。Liu[20]基于MPM研究了土体参数的空间分布与边坡破坏模式之间的关系。刘磊磊[2122]使用随机多重响应面物质点法和随机物质点法(RMPM),分别研究了土体参数旋转各向异性空间变异性对边坡大变形特征的影响规律,以及不排水条件下土体空间变异性的非平稳性对边坡大变形特性的影响。Li[23]利用MPM研究了土石混合边坡中粘聚力、摩擦角对其稳定性的影响。

    (1)流固耦合

    降雨入渗是引发滑坡的重要因素之一[2427]。为研究降雨对边坡稳定性的影响,首先须专注于水土耦合问题。一般来说,土-水耦合MPM公式可以分为两类:(a)单层MPM,用于描述饱和和非饱和土壤的单个物质点层,主要用于模拟水与土壤的相互作用和土壤体的滑动阶段,具有较高的计算效率,但忽略了土-水之间的相对速度;(b)多层MPM,用于描述饱和和非饱和土壤的多个物质点层,主要研究固相和流体相的作用,使用两组拉格朗日物质点来描述土壤骨架和水分子层,可用于模拟土壤和水之间的相互作用[28]

    针对MPM的水土耦合问题,已经开展了大量基于水土耦合的MPM研究。Wang[29]根据Jassim[30]的完全饱和土的V-W公式,提出了适用于描述非饱和土的单层MPM公式。Girardi[31]提出了一种单物质点两项在非饱和土瞬态水力边界条件下应用的MPM公式,并通过二维坝堤渗流问题进行了验证。Higo[32]将MPM与FDM耦合,研究了完全饱和以及部分饱和弹塑性土的响应问题。Zheng[33]基于MPM提出了一种分析饱和弹塑性土工材料大变形的数值方法,通过模拟基础承载力、边坡破坏及基础-边坡相互作用等问题,证实了该方法用于解决流体-力学耦合和涉及大变形等岩土工程问题的适用性。Abe[34]基于Biot混合理论,提出了求解大变形饱和土耦合流体力学问题的MPM,通过对模拟一维固结试验的模拟,得到的数值解与理论解析解一致(图3)。

    图  3  固结程度和时间因子关系图(修改自Abe,2014)
    Figure  3.  Relationship diagram between degree of consolidation and time factor (Modified from Abe, 2014)

    Sołowski[35]基于MPM提出了非饱和流动问题的理论,并通过非饱和颗粒材料筒仓卸料以及非饱和颗粒雪崩两个算例验证了该理论用于非饱和问题的可靠性。

    (2)降雨入渗诱发滑坡

    Zhan[36]考虑了孔隙度变化对保水曲线和渗透的影响,并提出了一种能够解决非饱和土中自由水渗入问题的MPM,并模拟了非饱和土质边坡在降雨作用下的破坏过程。Feng[37]基于非饱和土理论建立了两层流固耦合的物质点法,并研究了非饱和土坡在降雨作用下的破坏机理。Ceccato[38]基于MPM提出了非饱和土渗流-变形耦合过程的计算框架,并应用于降雨导致的边坡破坏问题。Tran[39]利用GIMP研究了斜坡的渗流及渐进破坏问题。王升[36]推导了考虑孔隙水压力效应的等效摩擦角公式,并使用MPM模拟了深圳“12.20”滑坡的失稳、运动和冲击过程,模拟得到的滑面与实际滑面对比信息如表1所示,结果验证了MPM在滑坡失稳过程数值模拟中的适用性。

    表  1  模拟滑面与实际滑面对比信息表(王升,2022)
    Table  1.  Comparison table of simulated slip surface and observed slip surface(Wang Sheng,2022)
    滑面对比 剪出口水平距
    /m(后缘)
    剪出口高差
    /m(后缘)
    滑面最大
    深度/m
    滑带角度
    /(°)
    模拟滑面 544.5 111.9 53.9 5.3
    实际滑面 457.0 92.1 49.7 2.2
    下载: 导出CSV 
    | 显示表格

    Wang[40]提出了一种流固耦合物质点法,并模拟了降雨引起的边坡破坏过程,同时探讨了降雨强度对边坡破坏过程的影响。He[41]使用MPM再现了滑坡活化的全过程,并讨论了前期降雨和地下水对滑坡运动和沉积物形态的影响。Lee[42]使用MPM研究了降雨诱发滑坡从滑坡前阶段到破坏后阶段的运动过程,并分析了降雨强度对孔隙水压力发展、滑坡触发时间、地表位移和速度的影响。

    Moormann[43]通过在模型底部增加一层粒子来替代刚性边界,最早将物质点法应用于地震边坡分析。Alsardi[4445]使用MPM进行了地震反应分析,并与振动台试验和有限元数值模拟结果进行对比,验证了MPM在地震反应分析方面的适用性。He[46]利用MPM模拟了08年汶川地震产生的大光包滑坡,通过在模型底部施加160s的地震加速度时程,最终得到了与现场实测结果相吻合的几何形状。Xu[47]用MPM技术建立了三维边坡模型,对地震荷载下的红石岩滑坡进行了模拟。Feng[4849]利用域约简法[5051]将谱元法(SEM)与MPM进行耦合,提出了一种模拟多尺度三维同震滑坡的框架,并使用MPM模拟了地震荷载作用下的同震边坡稳定性问题。Kohler[5254]基于物质点法提出了一种地震反应分析的框架,并利用该方法预测了同震滑坡产生的小位移。Tran[55]提出了一种结合土力学、流体力学和固体力学的土-流-结构相互作用模型,并利用MPM模拟了地震诱发海底滑坡的全过程。Fernández[56]建立了一个三维大光包地质模型,并利用MPM模拟了其中汶川地震诱发滑坡的破坏、运动、平稳的整个过程。

    吴方东[57]利用MPM方法研究了边坡坡顶堆载对斜坡稳定性的影响,研究结果显示滑坡前缘运动特征量与堆载载荷大小成正相关。Xie[58]利用MPM研究了边坡坡顶处基础设施对边坡稳定性的影响,并讨论了基础后退距离、坡角以及土体强度参数引起的承载力变化问题。Zhu[59]利用MPM研究了超载作用下深埋管道路堑边坡的变形破坏机理。Troncone[60]利用MPM分析了边坡坡脚处开挖而产生滑坡的运动变形全过程。Acosta[61]利用MPM研究了不同基础条件下的土体冲击过程中挡土结构的破坏问题,以及由施工引起的边坡破坏问题。

    关于泥石流的分析,可以使用单层和多层MPM来模拟土-水耦合问题。而颗粒流可以被视为一种特殊的泥石流,近年来也有许多学者对颗粒流进行了大量研究。Ng[62]利用MPM分析了屏障变化对颗粒流冲击力的影响;Ceccato[63]利用MPM研究了干燥颗粒的冲击问题,并分析了初始孔隙度、前倾角和速度对冲击过程的影响;Wyser[64]利用MPM研究了固体颗粒的三维崩塌问题;Lei[65]利用MPM研究了三维土-结构相互作用的问题,并通过模拟斜面上钢球滚动与解析解的对比证明了该方法的可靠性(图4);

    图  4  不同摩擦系数下钢球质点位置随时间变化(修改自Lei,2022)
    Figure  4.  Variation of steel ball particle position over time under different friction coefficients (modified from Lei, 2022)

    Lei[66]基于基面数字地形模型(DTM),在MPM框架内开发了一种新型多材料接触模型,以模拟复杂自然地形上的颗粒流问题;Cuomo[67]利用MPM研究了干燥和饱和颗粒流对刚性壁面的冲击问题。

    Li[68]提出了一种基于MPM的计算框架,用于研究滑坡泥石流与挡板的相互作用问题。研究指出,挡板的排列方式和几何形状对泥石流的运动过程有重要影响。Abe[69]提出了一种基于MPM的计算框架(DAMPM),用于模拟泥石流运动过程。通过与干湿砂水槽试验和模拟结果的对比,验证了该计算框架的有效性,并讨论了流变模型的差异对泥石流运动的影响。Zhao[70]提出了一种基于MPM的方法,可以模拟软质材料与刚性物体之间的复杂几何形状相互作用,并利用该方法模拟了泥石流的流动过程。Li[71]提出了一种将MPM应用于流固耦合问题的建模方法,并研究了溃坝对弹性障碍物的冲击、干砂对刚性结构的冲击,以及有无斜对称排水槽的泥石流问题。Perna[72]提出了一种固定在地基上的刚性屏障,利用MPM分析了泥石流与受冲击防护结构之间的相互作用机制问题。Cuomo[73]提出了一种可变性土工合成增强屏障(即通过土工格栅加固的粗粒土层构成的路堤),利用MPM研究了该屏障在泥石流冲击过程中的能耗影响。Kazmi[74]利用MPM研究了地震引发的泥石流问题,并讨论了内摩擦角、密度、膨胀角和粘聚力等因素对泥石流运动特征的影响。Wong[75]提出了一种耗散泥石流能量的阶梯池结构,并利用MPM分析了人工阶梯池的内摩擦角、粘聚力和高度对泥石流消能敏感性的影响。Vicari[76]利用MPM研究了河床物质的夹带对安装在泥石流通道上游的柔性屏障的影响。

    物质点法除了应用于滑坡、泥石流等常见的地质灾害中,近年来还被用于隧道施工引起的地质灾害、地裂缝、边坡支护、液化问题。

    Xie[7778]使用MPM分析了盾构隧道中水涌的演化过程以及对周围土体的影响,并研究了涌水位置、隧道埋深和土体参数对涌水过程的影响。张春新[79]使用MPM研究了隧道周围砂土地层在支护压力减小过程中的变形破坏机理问题,并分析了隧道埋深比和砂土内摩擦角对土拱效应强弱、极限支护压力和地层变形的影响。王曼灵[80]应用自适应正交改进插值移动最小二乘法(AOIIMLS)改进了对流粒子域插值物质点法(CPDI)方法,解决了传统MPM中质点穿越误差的问题,并模拟了青岛地铁4号线静沙区间地面塌陷的整个过程,模拟结果与隧道坍塌现场基本一致。王桂林[81]利用MPM研究了带有裂损的地铁隧道在爆炸作用下的二次损伤响应,结果表明初始裂损不仅导致衬砌结构刚度下降,还加速了隧道结构的损伤速度。Tu[82]使用MPM研究了饱和地层中隧道开挖工作面临界支护压力及破坏机理的问题。Cheng[83]利用MPM研究了二维平面应变条件下的巷道掘进引起的塌陷和地面沉降问题。

    Li[84]通过将MPM与断裂力学框架耦合,探讨了泵送诱发地裂缝的成因机制。李克智[85]利用MPM研究了人工裂缝与天然裂缝之间的交互作用,并预测了人工压裂的改造范围。

    Liang[86]则运用MPM研究了溢流作用对河堤稳定性的影响。Talbot[87]使用MPM模拟了著名的Fernando大坝破坏事件,研究结果与实测数据基本一致。徐云卿[88]将人工状态方程引入B样条物质点法,研究了溃坝流问题。Remmerswaal[89]则利用MPM研究了坝堤的残余阻力问题。Zhao[90]研究了不同宽高比的溃坝问题。冯晓青[91]推导了固液两项MPM算法的基本公式,研究了动力荷载下饱和地基的液化问题。

    Liang[92]将MPM与DEM耦合,研究了颗粒砂中锚杆的拉拔问题。高宇新[93]利用MPM模拟了砂土中锚板的上拔过程,并探讨了不同埋深条件下土体位移场的分布以及锚板的上拔破坏机制,研究了砂土密实度、锚板尺寸和埋深等因素对其极限承载力的影响。

    如上所述,尽管物质点法目前已经在模拟地质灾害大变形分析过程中取得了不少的研究成果,但以下缺点限制了它在地质灾害大变形的应用。

    1、模型准确性:物质点法通常采用质点来代表地质体。这种简化模型可能无法完全反映地质体的复杂结构和力学特性。模拟地质灾害大变形时往往需要考虑复杂的地质结构和地形,网格的分辨率和计算精度会对模拟结果产生影响,特别是在局部细节上容易出现误差。如何提高复杂模型的精度和可靠性,使其更好地反映实际地质灾害的发生和演化过程,是一个亟待解决的问题。

    2、计算成本较高:在处理复杂地质问题时,物质点法的计算成本较高,需要大量的计算资源和时间。这限制了其在大规模实际工程中的应用。因此,如何提高模拟的计算效率,降低计算成本,尤其是在处理大规模地质灾害问题时,是一个需要解决的技术难题。

    3、多物理场耦合问题:地质灾害过程通常涉及多种物理场的相互作用,例如流固耦合和热-力耦合。而物质点法通常较难实现多物理场的耦合。因此,需要进一步发展物质点法的流固耦合公式和三维建模技术,解决地质灾害中的多物理场耦合问题。

    物质点法在地质灾害领域的发展趋势主要有以下几个方面:

    1.多方法耦合:物质点法和有限元法(或其他方法)分别擅长不同类型的物理过程模拟。通过耦合可以同时考虑物质点的大变形和有限元网格的局部细节,从而使模拟更加全面和真实。此外,耦合后能够充分发挥两者的优势,实现高效的计算和准确的结果。

    2.多物理过程耦合模拟:未来的发展将更加注重多物理过程的耦合模拟,包括力学、水文和热学等。地质灾害往往是多种因素共同作用的结果,通过耦合模拟可以更全面地理解地质灾害的发生机制和演化过程。

    3.多尺度模拟与精细化分析:随着计算机技术的进步,基于物质点法的地质灾害模拟将更加注重多尺度模拟和精细化分析。通过多尺度模拟,可以更好地理解地质灾害的全过程,从微观粒子到宏观地形,为灾害防治和应急响应提供更准确的数据支持。

    4.数据驱动的模拟方法:随着遥感技术、地理信息系统和人工智能的发展,将机器学习与物质点法相结合,可实现数据驱动的地质灾害模拟方法。通过大数据分析和机器学习技术,可以更准确地模拟地质灾害的发生和演化过程,提高预测的准确性和实用性。

    综上所述,物质点法在地质灾害领域有广阔的应用前景,但也面临着诸多挑战和问题。不但需要物质点法自身的发展,还需要将其在地质灾害领域不断进行研究和探索,提高模型的准确性、可靠性和实用性,以更好地应对地质灾害带来的风险和挑战。

    1、物质点法是一种将拉格朗日法和欧拉法的优点兼具的模拟方法。物质点法适用于模拟材料的大变形和非线性行为;可以处理多相物质的相互作用,例如流体-结构相互作用、颗粒材料的动态行为;适用于模拟固体、液体和气体等不同性质的物质,涵盖了广泛的应用领域;能够有效模拟材料的破坏和断裂行为,适合于模拟地质岩土等颗粒材料的行为。然而粒子间的相互作用需要额外的处理以保证数值精度和数值稳定性;需要处理大量的计算和存储数据及考虑网格与颗粒的相互作用和穿透等问题,对计算、内存、初始网格的生成和处理要求较高;在处理边界条件和碰撞等问题时,需要额外的算法和技术支持。

    2、物质点法具有模拟滑坡与泥石流的触发、运动和平稳三个阶段的全过程能力。相较于有限元和有限差分等工具,物质点法能够实时分析模型整体的能量、速度和加速度等力学参数,从而全面了解地质灾害的动态过程,并为后续的防灾减灾工作提供实质性建议和更具体、有效的预防策略。

    3、物质点法通过不断尝试和发展流固耦合公式、动力边界条件以及多物理场综合模拟技术,使其能够模拟两项、多项以及多物理场耦合的地质灾害问题。由于物质点法处于发展阶段,随着算法的不断改进与发展,其在模拟地质灾害大变形问题具有非常光明的应用前景。未来,物质点法将应用于地质灾害大变形的各个研究方向。

  • 图  1   物质点离散示意图

    Figure  1.   Schematic diagram of material point discretization

    图  2   物质点法求解示意图(① 物质点信息映射 ②动量方程求解 ③更新物质点信息)

    Figure  2.   Schematic diagram of material point method solution (①Mapping of material point information, ②Solving the momentum equation, ③Updating material point information)

    图  3   固结程度和时间因子关系图(修改自Abe,2014)

    Figure  3.   Relationship diagram between degree of consolidation and time factor (Modified from Abe, 2014)

    图  4   不同摩擦系数下钢球质点位置随时间变化(修改自Lei,2022)

    Figure  4.   Variation of steel ball particle position over time under different friction coefficients (modified from Lei, 2022)

    表  1   模拟滑面与实际滑面对比信息表(王升,2022)

    Table  1   Comparison table of simulated slip surface and observed slip surface(Wang Sheng,2022)

    滑面对比 剪出口水平距
    /m(后缘)
    剪出口高差
    /m(后缘)
    滑面最大
    深度/m
    滑带角度
    /(°)
    模拟滑面 544.5 111.9 53.9 5.3
    实际滑面 457.0 92.1 49.7 2.2
    下载: 导出CSV
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  • 收稿日期:  2024-05-06
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