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1、离心加载有限元方法在边坡稳定离心加载有限元方法在边坡稳定分析中的应用分析中的应用报告人报告人: :曹建建曹建建 河海大学岩土工程研究所 Geotechnical Institute of Hohai University坡坡某某边边滑滑坡坡事事故故边坡稳定分析方法边坡稳定分析方法pp极限平衡法极限平衡法极限平衡法极限平衡法pp极限分析法极限分析法极限分析法极限分析法pp有限元法有限元法有限元法有限元法pp有限元强度折减法有限元强度折减法有限元强度折减法有限元强度折减法pp 离心加载有限元方法离心加载有限元方法离心加载有限元方法离心加载有限元方法提纲提纲一、一、RFPA方法介绍方法介绍二、离心加
2、载有限元方法基本原理二、离心加载有限元方法基本原理三、边坡破坏模拟三、边坡破坏模拟四、总结四、总结RFPARFPA方法介绍方法介绍 RFPA是由东北大学岩石破裂与失稳研究中心唐春安唐春安教授建立的一种用于分析岩石等脆性材料破坏的数值计算方法。 单元在应力达到破裂准则时发生破坏,并对破坏单元进行刚度退化刚度退化处理。这样就可以用连续介质力学方法处理物理非连续介质问题,研究裂缝的发生和发展过程。 本构关系本构关系t0- ft0- ftrtuc0fc0fcrConstitutive law of element (Compressive stresses are positive)Mohr-Coul
3、omb criterion is met.Maximum tensile strain criterion is met. 通过修改RFPA程序的参数值如残余强度、拉压应变等，从而使该法可以考虑土体的理想弹塑性应力应变关系。 由于目前土体不考虑其受拉破坏，因而忽略RFPA程序中原有的拉伸单元采用最大拉应变准则进行损伤判别的判据。随着单元应力的增加，对压剪单元采用摩尔库仑准则作为判别依据：离心加载有限元方法基本原理离心加载有限元方法基本原理 RFPA离心加载有限元方法考虑在抗剪强度指标粘聚力和内摩擦角不变的前提下，逐渐增加岩土体的重力加速度（增加容重），反复进行有限元迭加计算，直至边坡达到临界破
4、坏状态。 其工作原理如同边坡的离心模型试验，随着离心机施加的重力加速度增加，最终使边坡达到破坏。 破坏标准破坏标准有限元静力平衡计算不收敛滑动面塑性区贯通安全系数定义安全系数定义破坏时的重力加速度土体固有加速度边坡破坏模拟边坡破坏模拟土质边坡尺寸如图所示，土体粘聚力，内摩擦角采用平面应变模型，四边形单元，单元数目为32014044800个，离心加载系数0.01。 ，泊松比，土体容重，坡角为。土质边坡土质边坡Step026001Step030002Step032017Step032023离心加载有限元方法极限平衡法 极限分析有限元法 随着土体容重的增加，破坏面由坡底向坡顶推进；同时，坡顶逐渐出现
5、张裂缝，张裂缝自上而下扩展与向上推进的滑动面贯通，于是边坡发生失稳破坏。 表1 不同方法求得的稳定安全系数方法稳定安全系数计算值极限平衡法（Spencer法）极限分析有限元法离心加载有限元法1.301.301.311.311.281.28 按照安全系数的定义公式，求得土坡的稳定安全系数为1.28，与表1中列出的安全系数数值接近。土岩边坡尺寸示意图（单位：cm） 离心机试验结果 与离心机试验比较与离心机试验比较数值模拟结果（加载到14g ） 离心加载有限元法是边坡稳定分析的新尝试，通过与已有研究成果对比，由数值模拟试验和分析结果可得到以下结论： 运用RFPA离心加载有限元方法可以很好地模拟出边坡
6、由局部破坏逐渐扩展贯通的整个渐进破坏过程，稳定安全系数的定义简单、明确。 应用离心加载有限元方法分析边坡稳定性时，无需假定滑动面的具体形状和位置；在计算过程中，不需假定 、 参数的比例关系，岩土体的强度指标在计算过程中保持常量。 总结总结存在问题：存在问题：本构关系；土体的非均匀性 感谢东北大学唐春安教授提供软件支感谢东北大学唐春安教授提供软件支持及相应指导！持及相应指导！谢谢指导谢谢指导! !gSjVmYq!t&w-z1D4G7JbMePhTkWoZr$u(x+A2E5H9KcNfRiUlXp#s&v)y0C3F6IaLdPgSjVnYq!t*w-z1D4G8JbMeQhTkWoZr%u(x
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28、0B3F6IaLdOgSjVmYq!t*w-z1D4G7JbMeQhTkWoZr$u(x+B2E5H9KcNfRiUlXp#s&v)y0C3F6IaLdPgSjVnYq!t*w-A1D4G8JbMeQhTlWoZr%u(x+B2E6H9KcOfRiUmXp!s&v)z0C3F7IaMdPgSkVnYq$t*x-A1D5G8JbNeQhTlWo#r%u(y+B2E6H9LcOfRjUmXp!s&w)z0C4F7IaMdPhSkVnZq$t*x-A2D5G8KbNeQiTlXoXo#r%v(y+B3E6I9LcOgRjUmYp!t&w)z1C4F7JaMdPhSkWnZq$u*x-A2D5H8Kb
29、NfQiTlXo#s%v(y0B3E6I9LdOgRjVmYp!t&w-z1C4G7JaMePhTkWnZr$u*x+A2E5H8KcNfQiUlXp#s%v)y0B3F6I9LdOgSjVmYq!t&w-z1D4G7JbMePhTkWoZr$u(x+A2E5H9KcNfRiUlXp#s&v)y0C3F6IaLdPgSjVnYq!t*w-A1D4G8JbMeQhTkWoZr%u(x+B2E5H9KcOfRiUmXp#s&v)z0C3F7IaLdPgSkVnYq$t*w-A1D5G8JbNeQhTlWo#r%u(y+B2E6H9LcOfRjUmXp!s&w)z0C4F7IaMdPgSkVnZq$
30、t*x-A1D5G8KbNeQiTlWo#r%v(y+B3E6H9LcOgRjUmYp!s&w)z1C4F7JaMdPhSkWnZq$u*x-A2D5H8KbNfQiTlXo#r%v(y0B3E6I9LcOgRjVmYp!t&w)z1C4G7JaMePhSkWnZr$u*x+A2D5H8KcNfQiUlXo#s%v)y0B3F6I9LdOgSjVmYq!t&w-z1C4G7JbMePhTkWnZr$u(x+A2E5H8KcNfRiUlXp#s%v)y0C3F6IaLdOgSjVnYq!t*w-z1D4G8JbMeQhTkWoZr%u(x+B2E5H9KcOfRiUmXp#s&v)y0C3F7I
31、aLdPgSjVnYq$t*w-A1D4G8JbNeQhTlWoZr%u(y+B2E6H9KcOfRjUmXp!s&v)z0C4F7IaMdPgSkVnZq$t*x-A1D5G8JbNeQiTlWo#r%u(y+B3E6H9LcOfRjUmYp!s&w)z0C4F7JaMdPhSkVnZq$u*x-A2D5G8KbNfQiQiTlXo#r%v(y0B3E6I9LcOgRjVmYp!t&w)z1C4G7JaMePhSkWnZq$u*x+A2D5H8KbNfQiUlXo#s%v(y0B3F6I9LdOgRjVmYq!t&w-z1C4G7JbMePhTkWnZr$u(x+A2E5H8KcNfRiUl
32、Xp#s%v)y0B3F6IaLdOgSjVmYq!t*w-z1D4G7JbMeQhTkWoZr$u(x+B2E5H9KcNfRiUmXp#s&v)y0C3F7IaLdPgSjVnYq$t*w-A1D4G8JbNeQhTlWoZr%u(x+B2E6H9KcOfRiUmXp!s&v)z0C3F7IaMdPgSkVnYq$t*x-A1D5G8JbNeQiTlWo#r%u(y+B3E6H9LcOfRjUmYp!s&w)z0C4F7IaMdPhSkVnZq$t*x-A2D5G8KbNeQiTlXo#r%v(y+B3E6I9LcOgRjUmYp!t&w)z1C4F7JaMePhSkWnZq$u*x+A2
33、D5H8KbNfQiTlXo#s%v(y0B3E6I9LdOgRjVmYp!t&w-z1C4G7JaMePhTkWnZr$u*x+A2E5H8KcNfQiUlXp#s%v)y0B3F6IaLdOgSjVmYq!t*w-z1D4G7JbMePhTkWoZr$u(x+A2E5H9KcNfRiUlXp#s&v)y0C3F6IaLdPgSjVnYq!t*w-A1D4G8JbMeQhTlWoZr%u(x+B2E6H9KcOfRiUmXp#s&v)z0C3F7IaLdPgSgSkVnYq$t*w-A1D5G8JbNeQhTlWo#r%u(y+B2E6H9LcOfRjUmXp!s&w)z0C4F7IaMdP
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35、)z0C3F7IaLdPgSkVnYq$t*w-A1D5G8JbNeQhTlWoZr%u(y+B2E6H9KcOfRjUmXp!s&v)z0C4F7IaMdPgSkVnZq$t*x-A1D5G8KbNeQiTlWo#r%v(y+B3E6H9LcOgRjUmYp!s&w)z0C4F7JaMdPhSkVnZq$u*x-A2D5G8KbNfQiTlXo#r%v(y0B3E6I9LcOgRjVmYp!t&w)z1C4G7JaMePhSkWnZr$u*x+A2D5H8KcNfQiUlXo#s%v(y0B3F6I9LdOgRjVmYq!t&w-z1C4G7JbMePhTkWnZr$u(x+A2E5H8Kc
36、NfRiUlXp#s%v)y0C3F6IaLdOgSjVnYq!t*w-z1D4G4G8JbMeQhTkWoZr%u(x+B2E5H9KcNfRiUmXp#s&v)y0C3F7IaLdPgSjVnYq$t*w-A1D4G8JbNeQhTlWoZr%u(y+B2E6H9KcOfRjUmXp!s&v)z0C4F7IaMdPgSkVnYq$t*x-A1D5G8JbNeQiTlWo#r%u(y+B3E6H9LcOfRjUmYp!s&w)z0C4F7JaMdPhSkVnZq$u*x-A2D5G8KbNfQiTlXo#r%v(y+B3E6I9LcOgRjUmYp!t&w)z1C4F7JaMePhSkWnZ
37、q$u*x+A2D5H8KbNfQiUlXo#s%v(y0B3F6I9LdOgRjVmYq!t&w-z1C4G7JbMePhTkWnZr$u*x+A2E5H8KcNfQiUlXp#s%v)y0B3F6IaLdOgSjVmYq!t*w-z1D4G7JbMeQhTkWoZr$u(x+B2E5H9KcNfRiUmXp#s&v)y0C3F6IaLdPgSjVnYq!t*w-A1D4G8JbMeQhTlWoZr%u(x+B2E6H9KcOfRiUmXp!s&v)z0C3F7IaMdPgSkVnYq$t*x-A1D5G8JbNeQiTlWo#r%u(y+B2E6H9LcOfRjUmXp!s&w)z0C4F
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