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Article(id=1243226200513036548, tenantId=1146029695717560320, journalId=1242798230522609684, issueId=1243226190786441246, articleNumber=null, orderNo=null, doi=10.7511/jslx20240508001, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1715097600000, receivedDateStr=2024-05-08, revisedDate=1717689600000, revisedDateStr=2024-06-07, acceptedDate=null, acceptedDateStr=null, onlineDate=1774337824227, onlineDateStr=2026-03-24, pubDate=1761580800000, pubDateStr=2025-10-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774337824227, onlineIssueDateStr=2026-03-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774337824227, creator=13701087609, updateTime=1774337824227, updator=13701087609, issue=Issue{id=1243226190786441246, tenantId=1146029695717560320, journalId=1242798230522609684, year='2025', volume='42', issue='5', pageStart='699', pageEnd='888', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774337821909, creator=13701087609, updateTime=1774338282025, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1243228120724128564, tenantId=1146029695717560320, journalId=1242798230522609684, issueId=1243226190786441246, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1243228120724128565, tenantId=1146029695717560320, journalId=1242798230522609684, issueId=1243226190786441246, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=772, endPage=779, ext={EN=ArticleExt(id=1243226201414811926, articleId=1243226200513036548, tenantId=1146029695717560320, journalId=1242798230522609684, language=EN, title=Study on the impact characteristics of dam-break flow based on the B-spline material point method, columnId=1243226193193971746, journalTitle=Chinese Journal of Computational Mechanics, columnName=Research Papers, runingTitle=null, highlight=null, articleAbstract=

Accurately simulating the impact characteristics of a dam break is of paramount significance for the prediction and mitigation of dam-break flow disasters. The B-spline material point method (BSMPM), as an improved algorithm of the material point method (MPM), effectively enhances computational accuracy and improves convergence. However, the BSMPM solves the governing equations based on a tensor grid rather than an Eulerian background grid. Moreover, its interpolation shape functions have a larger influence domain. Consequently, when solving problems involving fluid-structure coupling and contact, issues such as premature contact, difficulty in capturing contact interfaces, and challenges in calculating contact forces arise. Within the same tensor grid space of the BSMPM, accurate capture of contact interfaces is achieved based on the relative velocities and unit outward normals of the same nodes; employing the Greville Abscissa enables precise contact of contacting objects, thereby avoiding premature or spurious contact; through the Lagrange multiplier method, interface contact forces are accurately determined, thus constructing a high-precision contact algorithm for fluid-structure strongly coupled problems, facilitating research on the simulation of dam-break fluid impact with rigid and elastic obstacles, and enabling a comparison with existing experimental or simulated results. The results demonstrate that the simulated impact loads and structural deformation evolution patterns correspond well with existing experimental/simulated results. For rigid obstacles, the peak impact pressure exhibits concave parabolic growth and positive correlation exponential function growth with increasing water level and dam-break slope, respectively. For elastic obstacles, the peak impact pressure decreases exponentially with the increase in the height of the probing point. The feasibility and effectiveness of simulating dam-break flow impact problems using the BSMPM contact algorithm are validated, providing a new perspective for simulating dam-break flow impact problems.

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准确模拟溃坝的冲击特性对溃坝流灾害预测和防治具有重要意义。B样条物质点法作为物质点法的一种改进算法，有效提高了计算精度和改进了收敛性。然而，B样条物质点法基于张量网格而非欧拉背景网格进行控制方程的求解；同时，其插值形函数具有更大的影响域；因此，在求解流固耦合等接触问题时存在过早接触、接触界面不易捕捉、接触力难以计算等问题。在同一B样条物质点张量网格空间内，基于同一结点的相对速度以及单位外法线实现接触界面的准确捕捉；采用格列维尔公式（Greville Abscissa），实现接触物体的精准接触，避免过早或虚假接触；通过拉格朗日乘子法，准确判定界面接触力，构建采用流固统一描述的流固强耦合高精度接触算法，开展溃坝流体冲击刚性和弹性障碍物模拟研究，并与已有试验结果或模拟结果进行对比。结果表明，模拟所得冲击荷载及结构变形演化规律与已有试验结果/模拟结果吻合较好；对刚性障碍物，随水位高度和溃坝坡度的增大，冲击压力峰值分别呈现下凹型抛物增长和正相关指数函数增长；对弹性障碍物，冲击压力峰值随探测点高度的增大呈负相关指数函数递减。验证了基于B样条物质点法接触算法模拟溃坝流冲击问题的可行性和有效性，为模拟溃坝流冲击问题提供一种新视角。

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孙政*（1986-），男，博士，硕士生导师，副教授（E-mail：）.

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孙政*（1986-），男，博士，硕士生导师，副教授（E-mail：）.

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孙政*（1986-），男，博士，硕士生导师，副教授（E-mail：）.

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Statistical analysis of dam failure and its loss of life in China[J]. Hydro-Science and Engineering, 2023(1): 1-15. 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Model parameters and value

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ParametersValuesParametersValues
H584 mm h2 mm×2 mm
L146 mmnppc2×2
h080 mm E11 MPa
b012 mm ρ11000 kg•m－3
g9.81 m•s－2 υ0.0
μ0.001 pa•s E21.4 MPa
Time step10 μs ρ22500 kg•m－3
CPU time0.517 s T0.5s
), ArticleFig(id=1243226258629312747, tenantId=1146029695717560320, journalId=1242798230522609684, articleId=1243226200513036548, language=CN, label=表1, caption=

模型参数及对应值

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ParametersValuesParametersValues
H584 mm h2 mm×2 mm
L146 mmnppc2×2
h080 mm E11 MPa
b012 mm ρ11000 kg•m－3
g9.81 m•s－2 υ0.0
μ0.001 pa•s E21.4 MPa
Time step10 μs ρ22500 kg•m－3
CPU time0.517 s T0.5s
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溃坝流冲击特性的B样条物质点法模拟研究
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华云军 1 , 周晓敏 1, 2 , 徐云卿 1 , 孙政 1, 2
计算力学学报 | 研究论文 2025,42(5): 772-779
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计算力学学报 | 研究论文 2025, 42(5): 772-779
溃坝流冲击特性的B样条物质点法模拟研究
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华云军1, 周晓敏1, 2, 徐云卿1, 孙政1, 2
作者信息
  • 1.江西理工大学　土木与测绘工程学院，赣州　341000
  • 2.江西理工大学　河流源头水生态保护江西省重点实验室，赣州　341000

    • 孙政*（1986-），男，博士，硕士生导师，副教授（E-mail：）.

Study on the impact characteristics of dam-break flow based on the B-spline material point method
Yunjun HUA1, Xiaomin ZHOU1, 2, Yunqing XU1, Zheng SUN1, 2
Affiliations
  • 1.School of Civil and Surveying Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
  • 2.Jiangxi Provincial Key Laboratory of Water Ecological Conservation at Headwater Regions, Jiangxi University of Science and Technology, Ganzhou 341000, China
出版时间: 2025-10-28 doi: 10.7511/jslx20240508001
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摘要
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准确模拟溃坝的冲击特性对溃坝流灾害预测和防治具有重要意义。B样条物质点法作为物质点法的一种改进算法，有效提高了计算精度和改进了收敛性。然而，B样条物质点法基于张量网格而非欧拉背景网格进行控制方程的求解；同时，其插值形函数具有更大的影响域；因此，在求解流固耦合等接触问题时存在过早接触、接触界面不易捕捉、接触力难以计算等问题。在同一B样条物质点张量网格空间内，基于同一结点的相对速度以及单位外法线实现接触界面的准确捕捉；采用格列维尔公式（Greville Abscissa），实现接触物体的精准接触，避免过早或虚假接触；通过拉格朗日乘子法，准确判定界面接触力，构建采用流固统一描述的流固强耦合高精度接触算法，开展溃坝流体冲击刚性和弹性障碍物模拟研究，并与已有试验结果或模拟结果进行对比。结果表明，模拟所得冲击荷载及结构变形演化规律与已有试验结果/模拟结果吻合较好；对刚性障碍物，随水位高度和溃坝坡度的增大，冲击压力峰值分别呈现下凹型抛物增长和正相关指数函数增长；对弹性障碍物，冲击压力峰值随探测点高度的增大呈负相关指数函数递减。验证了基于B样条物质点法接触算法模拟溃坝流冲击问题的可行性和有效性，为模拟溃坝流冲击问题提供一种新视角。

溃坝流  /  冲击特性  /  B样条物质点法  /  接触算法

Accurately simulating the impact characteristics of a dam break is of paramount significance for the prediction and mitigation of dam-break flow disasters. The B-spline material point method (BSMPM), as an improved algorithm of the material point method (MPM), effectively enhances computational accuracy and improves convergence. However, the BSMPM solves the governing equations based on a tensor grid rather than an Eulerian background grid. Moreover, its interpolation shape functions have a larger influence domain. Consequently, when solving problems involving fluid-structure coupling and contact, issues such as premature contact, difficulty in capturing contact interfaces, and challenges in calculating contact forces arise. Within the same tensor grid space of the BSMPM, accurate capture of contact interfaces is achieved based on the relative velocities and unit outward normals of the same nodes; employing the Greville Abscissa enables precise contact of contacting objects, thereby avoiding premature or spurious contact; through the Lagrange multiplier method, interface contact forces are accurately determined, thus constructing a high-precision contact algorithm for fluid-structure strongly coupled problems, facilitating research on the simulation of dam-break fluid impact with rigid and elastic obstacles, and enabling a comparison with existing experimental or simulated results. The results demonstrate that the simulated impact loads and structural deformation evolution patterns correspond well with existing experimental/simulated results. For rigid obstacles, the peak impact pressure exhibits concave parabolic growth and positive correlation exponential function growth with increasing water level and dam-break slope, respectively. For elastic obstacles, the peak impact pressure decreases exponentially with the increase in the height of the probing point. The feasibility and effectiveness of simulating dam-break flow impact problems using the BSMPM contact algorithm are validated, providing a new perspective for simulating dam-break flow impact problems.

Dam-break flow  /  impact pressure characterization  /  B-spline material point method  /  contact algorithm
华云军, 周晓敏, 徐云卿, 孙政. 溃坝流冲击特性的B样条物质点法模拟研究. 计算力学学报, 2025 , 42 (5) : 772 -779 . DOI: 10.7511/jslx20240508001
Yunjun HUA, Xiaomin ZHOU, Yunqing XU, Zheng SUN. Study on the impact characteristics of dam-break flow based on the B-spline material point method[J]. Chinese Journal of Computational Mechanics, 2025 , 42 (5) : 772 -779 . DOI: 10.7511/jslx20240508001
正文
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1　引言
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大坝工程是一项对人类社会发展起到了重要保障作用的水利工程，但同时也存在着巨大安全隐患。受全球气候变化和人类活动的影响，水库大坝溃坝事件时有发生，不仅造成了人员伤亡和财产损失，也给周边地区的生存环境造成严重破坏。如海河流域63.8特大溃坝事件，河南驻马店75.8特大溃坝事件，以及1993年青海沟后水库溃坝事件[1]，以上事故都给水库下游群众造成不可挽回的损失。因此，开展溃坝流体冲击特性模拟研究对溃坝流灾害防治及重建具有重要意义。
溃坝流是一个复杂的自由表面流动问题。目前，对于溃坝流问题的研究主要有理论研究[2,3]、物理试验[4,5]、数值模拟[6,7]三类方法，由于物理试验耗费大量的人力、物力、财力，模拟周期较长，缺点较为明显；随着科技发展，数值模拟更多地应用于溃坝流问题的研究，数值方法主要包括两类，一类是有网格法，如有限差分法（FDM）[8]、有限体积法（FVM）[9]、有限元法（FEM）[10]等方法，在模拟大变形问题时会出现网格畸变而引起误差；另一类是无网格法，如光滑粒子流体动力学（SPH）[11]、无网格伽辽金法（EFG）[12]和移动粒子半隐式法（MPS）[13]。
物质点法结合了拉格朗日粒子和欧拉背景网格双重描述，既具有拉格朗日粒子型无网格算法的优势，又避免网格畸变和求解非线性对流项；在传统物质点法中，当物质点穿越背景网格边界时，会产生网格穿越误差，引起数值振荡；B样条物质点法[14]将线性插值形函数用B样条基函数替换，有效消除了网格穿越误差，提高了计算精度和收敛性。廉艳平等[15]在B样条物质点法中引入接触算法研究了冲击侵彻问题，验证了此法在求解复杂问题时的有效性。
本文基于B样条物质点法接触算法模拟溃坝流体冲击刚性/弹性障碍物动力全过程，分析冲击压力峰值随水位高度及坡度的演化规律，并与已有实验结果进行对比[16]；同时，研究弹性障碍物结构变形和溃坝流体压力的分布规律；旨在验证B样条物质点法接触算法在模拟溃坝流流体冲击特性的可行性和有效性，以期为研究溃坝流问题提供技术支撑。
2　计算方法
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2.1　B样条物质点法
相较传统物质点法，B样条物质点法采用高阶B样条基函数实现背景网格节点和物质点之间的信息映射和节点内力的求解。B样条物质点法具体算法实现过程如下。
（1）划分参数网格、将研究对象离散成一组物质点。
（2）初始化物质点的位置、质量、动量等物质信息。
（3）采用B样条基函数，在第k个计算时间步，将物质点上的质量和动量信息映射到节点自由度空间的节点自由度上。
式中　上标k为计算时间步，下标p为物质点的变量，xp为物质点p的位置矢量，m为质量，v为速度矢量。
（4）计算节点自由度上的内力和外力为
式中为B样条插值基函数的梯度，σ为柯西应力张量，b和t分别为体力和表面力矢量，V为体积，h为面力边界厚度。
（5）计算节点自由度上的加速度和速度
式中a为加速度矢量。
（6）在节点自由度空间，施加本质边界条件。
（7）将各节点自由度的加速度和速度信息通过B样条基函数映射回各物质点，得到第k+1个时间步上物质点的速度和位置。
（8）将更新后的各物质点速度重新映射回各节点自由度上，并计算物质点第k+1个时间步上的应变增量Δε。
（9）更新物质点的密度、应力应变、位置等信息，开始下一计算步。
2.2　接触算法
考虑两个接触的物体r和s，如图1所示。其中Ωr和Ωs分别为体r和体s的当前构型，ns和nr是向外的单位向量，Γr和Γs是边界，且Γc是接触面，在接触面处，物体r和s向外的法向单位矢量相反，即ns=－nr。
2.2.1　接触探测准则
如图1所示，接触的两个物体满足以下不可穿透性准则。
式（15）可改写为
即两个物体要么保持接触，要么彼此分离。由式（16）可知，当满足该准则时，两个物体在网格节点I处（如图1所示）接触并可能相互穿透。当满足式（17）时，表明两个物体有穿透的可能性。
式中是物体r在节点I沿其边界的单位向外法向量。为保持接触过程中的动量守恒，和必须满足共线条件。为此，首先计算物体b在节点I处的单位向外法向量为
两个物体的单位向外法向量可确定为两个法向量的平均值[17]，即
如果物体r比物体s更硬，或者物体r和物体s的碰撞面分别为凸面和凹面，则可以确定两个物体的法向量为
在BSMPM架构中，式（17）给出的接触探测准则是探测接触的不可穿透性准则。仅采用式（17）可能导致接触过早发生，如图2所示。随着基函数增加后，这个问题变得更加明显。如以三次基函数为例，其支持范围是参数单元（dc）大小的四倍。在这种情况下，即使两个物体之间的实际距离（记为）等于4dc，即没有发生物理接触，也满足式（17）。需要注意的是，为负值表明两个体之间有重叠和穿透。因此，接触发生的判据可以表示为
其中引入λdc以考虑颗粒尺寸，当在初始参数网格单元的每个方向上放置两个物质点时，通常建议λ为0.5。如图3所示，节点I处两个物体之间的距离为
其中为物体b与计算网格节点I之间的距离在物体b法向量上的投影。
其中和xI分别为粒子p和计算网格节点I的位置。
2.2.2　张量网格节点位置
B样条物质点法的接触探测是在张量网格空间进行的。然而，张量网格空间并非真实的物理网格划分，为准确判定是否接触，需要确定张量网格空间的真实空间位置。基于Greville Abscissa公式[18]确定张量网格空间中节点的空间位置xiI：
其中下标i表示方向，ξi，I+J是第（I+J）个结点的坐标分量，p为B样条基函数阶次。
2.2.3　接触力的计算
根据牛顿第三定律，两个物体在接触节点处的接触力满足
对于研究的问题，计算网格节点I处的法向接触力（记为）不能为拉力，因此，其取值不大于0。依赖于物体b的单位向外法线矢量，可表示为
为了计算节点接触力，接触算法采用预估校正的方式实现。首先，在不考虑任何接触的情况下，对物体的节点动量方程进行独立积分，得到不考虑接触的试验解。如果没有满足式（21）的接触网格节点，则试验解成为最终的理论解。但是，如果存在接触节点，则这些特定网格节点处的接触力计算如下，计算网格节点I处物体b的试验动量由式（28）确定，节点的试验速度由式（29）确定。
然后，通过加入接触力对物体的试验解进行修正，确定为
在粘性接触情况下，节点速度必须符合连续性条件。
将式（31）代入式（32），得到节点接触力为
法向接触力和切向接触力可表示为
在滑移接触的情况下，接触面的摩擦用库仑摩擦模型来描述。根据这个模型，如果由式（34）得到的切向接触力超过最大静摩擦力，会受到最大静摩擦力的约束。最后节点接触力表示为
式中μ为库仑摩擦系数。
3　溃坝流冲击刚性障碍物问题
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首先开展溃坝流冲击刚性障碍物模拟研究，计算模型如图4所示，其中水箱模型的长度L为1610 mm，高度D为600 mm；H为溃坝流模型初始水位高度；在刚性障碍物上分别取高度h1=30 mm和h2=80 mm两个标记点；背景网格尺寸h=2 mm，初始溃坝坡度θ=0°；整个溃坝模型受重力g=－9.81 m/s2作用，水的密度ρ=1000 kg/m3，模拟过程中将左右边界、底边界以及障碍物边界均视为对称边界条件。冲击压力P可由式（36）计算得到；同时，将时间t进行无量纲化为T*，冲击压力P无量纲化为P*。
图5给出了水位高度H=300 mm时，在不同时刻下溃坝水体自由表面及水体压力分布云图。可以看出，在T*=1时刻，溃坝流体开始坍塌，各分界面水体压力分布均匀，属于静水压力，在自由表面处出现两个不连续的液面；在T*=2时，自由表面也出现了两个不连续的液面，水体前端冲击角度变小，并且前端运动较快，后端运动较慢，水体压力分布均匀；在T*=3时，水体达到障碍物瞬间，水体压力集中在冲击点，自由表面不连续液面消失，整个液面分布较为光滑；在T*=4~6时，压力分布不均，冲击到障碍物的水体经过向上飞溅、翻转、下落等过程。
图6和图7分别比较了初始水位H=300 mm和H=600 mm时，标记点h1=30 mm和h2=80 mm处模拟和试验所得冲击压力的演化规律。可以看出，模拟结果与实验结果吻合较好；在四种不同工况下，当水流冲击到障碍物时，冲击力瞬间增至峰值，后以不完全相同的形式开始下降；从曲线走势上来看，图6（a）和图7整体趋势基本一致，在水流达到障碍物后，冲击力以开口向上的抛物线形式开始减弱；而图6（b）在达到峰值后，冲击力并未一直衰减，而是呈现出一小段锯齿状的运动轨迹，说明该标记点来回受到流体的冲击，符合溃坝流冲击障碍物的冲击特性。
进一步分别研究初始水位高度H和溃坝坡度θ对冲击压力的影响规律，分别如图8和图9所示。图8在水平冲击下，随水位高度增大，无量纲化冲击压力峰值增大，无量纲冲击压力峰值与水位高度满足下凹型抛物线增长规律；在水位高度300~600 mm、600~900 mm、900~1200 mm三个阶段，无量纲化冲击压力峰值增长幅度基本一致。图9在水位高度为300 mm时，无量纲化冲击压力峰值随溃坝坡度变化呈正相关指数函数增长规律。
4　溃坝流冲击弹性障碍物问题
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基于B样条物质点法接触算法继续对溃坝流冲击弹性障碍物进行数值模拟，溃坝模型初始状态如图10所示。数值模型由两部分组成，分别是溃坝流模型和弹性障碍物模型，溃坝流模型的初始高度H=292 mm，宽度为L=146 mm；弹性障碍物初始模型高度h0=80 mm，宽度是b0=12 mm，压力探测标记点h1=20 mm，h2=40 mm，h3=60 mm；整个溃坝模型受重力g=－9.8 m/s2作用，具体模型参数列入表1。
在h=1 mm，h=2 mm，h=4 mm背景网格尺寸下，研究溃坝流流体冲击障碍物左上端X方向的前缘位置变化，获得在不同背景网格尺寸下弹性障碍物左上端X方向的前缘位置的动态演化规律。如图11所示，在大于0 s小于0.15 s时，溃坝流体未能触碰到障碍物，弹性障碍物未变形；在0.15 s左右，坍塌流体在冲击到弹性障碍物的瞬间都存在小幅度的回弹趋势；在大于0.2 s小于0.25 s时，溃坝流冲击弹性障碍物左上端前缘位置达到峰值，并且随背景网格尺寸的增大，峰值也随之增大。
基于上述研究，基于B样条物质点法接触算法模拟溃坝流冲击弹性障碍物，在背景网格尺寸h=2 mm时，将模拟结果与文献[19-21]采用不同有限元方法模拟结果进行比较，从图12可知，整个过程可包括以下三个阶段，第一阶段大于0 s小于0.15 s时，溃坝开始坍塌，但水锋未与弹性障碍物接触；第二阶段是在大于0.15 s小于0.25 s时，此时塌陷的溃坝流体接触到弹性障碍物，弹性障碍物一直沿着水流运动方向变形，直到t=0.25 s左右，此时弹性障碍物的挠度达到最大值；第三阶段在大于0.25 s到小于0.5 s时，此阶段溃坝流体坍塌接近结束，弹性障碍物的变形逐渐恢复，水流继续向右侧壁面前进。综上所述，基于B样条物质点法接触算法分析在弹性障碍物左上端X方向前缘位置随时间变化与文献[19]模拟结果基本吻合。证明了B样条物质点法接触算法在模拟流固耦合问题中的可行性和准确性。
图13是在背景网格尺寸h=2 mm时，左侧压力云图是Idelsohn等[19]采用其他数值方法模拟得到的压力云图与右侧基于B样条物质点法接触算法所得在不同时刻形态演化的对比。从图13可以看出，两者在不同时刻的压力轮廓基本一致，开始时刻压力分布均匀，在撞击到障碍物时液体冲击角度由向右变为向右上，少部分液体开始飞溅，最后当液体撞击到水箱边界后，液体回弹，一部分液体向上扩散，另一部分液体向下扩散，落地后回弹撞击弹性障碍物。表明基于B样条物质点法接触算法能够很好地分析溃坝流冲击弹性障碍物等问题。
图14模拟在h=2 mm的背景网格尺寸下，溃坝流冲击弹性障碍物不同标记点的压力变化，随着探测点高度增大，冲击压力峰值呈减弱趋势；在溃坝流冲击标记点h1位置时，溃坝流冲击到障碍物的一瞬间，冲击压力迅速达到峰值，之后呈抛物线形下降趋势；而在冲击标记点h2、h3位置时，在达到冲击压力峰值后，下降过程存在一个波谷段，而溃坝流冲击刚性障碍物时不存在波谷段。
图15是无量纲化冲击压力峰值随探测高度变化的拟合曲线，从阶段分析可知，在探测高度20 mm到40 mm阶段，冲击压力递减较为缓慢，在40 mm到60 mm阶段，冲击压力衰减趋势更为明显；总体上看，随探测高度的增大，无量纲化冲击压力峰值减小，二者呈负相关指数函数递减规律。
5　结论
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本文基于B样条物质点法，采用格列维尔公式实现接触物体的精准接触，并通过拉格朗日乘子法准确判定界面接触力，模拟溃坝流冲击刚性障碍物和弹性障碍物，分析溃坝流冲击特性，得出以下结论。
（1）基于B样条物质点法接触算法分别对溃坝流冲击刚性障碍物和弹性障碍物进行模拟，模拟所得冲击荷载演化规律及结构变形与已有试验结果/模拟结果吻合较好。
（2）当溃坝流冲击刚性障碍物时，在水平冲击下，随初始水位高度的增大，无量纲化冲击压力峰值增大，无量纲化冲击压力峰值与水位高度变化满足下凹型抛物线增长规律；在水位高度一定时，随溃坝坡度的增大，无量纲化冲击压力峰值增大，两者满足正相关指数函数增长规律。
（3）当溃坝流冲击弹性障碍物时，在水平冲击下，弹性障碍物自由端前缘位置变化与其他数值方法模拟结果吻合较好；随着压力探测高度的增大，无量纲化冲击压力峰值减小，无量纲化冲击压力峰值与探测高度的变化呈负相关指数函数递减规律。
基金
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  • 国家自然科学基金(12262013; 11902127)
  • 江西省自然科学基金杰出青年基金(20232ACB211005)
  • 江西省主要学科学术和技术带头人培养计划(20225BCJ23022)
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2025年第42卷第5期
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doi: 10.7511/jslx20240508001
  • 接收时间：2024-05-08
  • 首发时间：2026-03-24
  • 出版时间：2025-10-28
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  • 收稿日期：2024-05-08
  • 修回日期：2024-06-07
基金
国家自然科学基金(12262013; 11902127)
江西省自然科学基金杰出青年基金(20232ACB211005)
江西省主要学科学术和技术带头人培养计划(20225BCJ23022)
作者信息
    1.江西理工大学　土木与测绘工程学院，赣州　341000
    2.江西理工大学　河流源头水生态保护江西省重点实验室，赣州　341000
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