# FEMSL-python

**Repository Path**: atlas999/femsl-python

## Basic Information

- **Project Name**: FEMSL-python
- **Description**: 超静定反应法python版本
- **Primary Language**: Python
- **License**: BSD-3-Clause
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 1
- **Forks**: 0
- **Created**: 2023-06-27
- **Last Updated**: 2023-09-22

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

## 欢迎关注公众号：知岩智隧

![欢迎关注公众号：知岩智隧](./images/qrcode.jpg)


为了找到一种能够快速高效地进行结构参数化计算的方法，了解了相关的研究，以下是HRM方法（超静定反应法），原文献中使用matlab编写，并且相关的研究论文基本上都是基于该matlab代码写的。亲自推导了一遍论文中描述的原理，对照matlab代码使用用python复现了该方法并做了一些简单的扩展（我们没有matlab....,不过matlab有个web online试用的，不用安装）。

## HRM原理（节选）
参考原文献

## 复现的结果
原代码包含注释有一部分冗余代码，共差不多900行。用python优化删减后，仅600多行（含注释），包含绘图。主要核心点是刚度矩阵的组装和迭代计算，源代码有较多冗余的地方，原理不复杂，但该代码仅适用于圆形隧道、对称均布荷载，其它形状和荷载情况需重新修改代码，最大的优点是可以进行参数化的分析，该方法考虑了结构参数、地层参数、接头参数、连续结构和分块结构、所以进行不同工况的分析可以很轻松（见该课题组发的论文），地层弹簧的考虑与现在盾构隧道设计规范的相似。

![原代码-matlab-只有绘制曲线](./images/origin.jpg)


![python-重写结果](./images/python.jpg)


围绕这个方法Dias教授等人做了很多探索，主要是隧道衬砌的设计分析，如下：

一些相关的文献：
（最早的文献2007,Oreste提出）一种基于HRM的隧道支护尺寸数值计算方法[1]

一种分析隧道分段衬砌性能的新数值方法[2, 3]

基于HRM的隧道衬砌设计可靠性分析[4, 5]

基于HRM的隧道设计方法[6]（Du.Dianchun博士论文）

基于HRM的类矩形隧道衬砌性能分析[7]

基于HRM分析马蹄形隧道衬砌结构-仰拱的影响分析[8]

基于HRM的超载对饱和软岩中马蹄形隧道开挖的影响分析[9]

基于HRM的穿越多地层情况下的隧道衬砌设计[10]

基于HRM的隧道施工喷混衬砌的性能分析[11]

使用梁-弹簧法和力法的隧道分段衬砌结构分析[12]

使用梁-弹簧法和固体界面法的隧道分段衬砌数值分析[13]

基于HRM的地震荷载作用下的隧道管片衬砌结构分析[14]

一种用于隧道衬砌设计的变分连续HRM（VHRM）[15]

盾构隧道掘进从数字模型到数值模型的全自动化分析流程[16]（Jelena Ninic博士关于从数字模型到数值模型的自动化仿真分析研究，其中使用VHRM，VHRM是基于Kratos扩展的，基本原理也是使用HRM）

一种新拟静力加载方案的超静力反应法分析地震条件下的类矩形隧道实例[17]

参考文献：

 [1] Oreste P P. A numerical approach to the hyperstatic reaction method for the dimensioning of tunnel supports[J]. Tunnelling and Underground Space Technology. 2007, 22(2): 185-205.
 
 [2] Do N A, Dias D, Oreste P, et al. A new numerical approach to the hyperstatic reaction method for segmental tunnel linings[J]. International journal for numerical and analytical methods in geomechanics. 2014, 38(15): 1617-1632.
 
 [3] Do N, Dias D, Oreste P, et al. The behaviour of the segmental tunnel lining studied by the hyperstatic reaction method[J]. European Journal of Environmental & Civil Engineering. 2014, 18(4): 1-22.
 
 [4] Kroetz H M, Do N A, Dias D, et al. Reliability of tunnel lining design using the Hyperstatic Reaction Method[J]. Tunnelling and Underground Space Technology. 2018, 77: 59-67.
 
 [5] D. C. Du D D N A. Hyperstatic Reaction Method for the Design of U-Shaped Tunnel Supports[J]. International Journal of Geomechanics. 2018.
 
 [6] Du D. Design of Tunnels using the Hyperstatic Reaction Method[D]. 2019.
 
 [7] Du D, Dias D, Do N. Lining performance optimization of sub-rectangular tunnels using the Hyperstatic Reaction Method[J]. Computers and Geotechnics. 2020, 117: 103279.
 
 [8] Du D, Dias D, Do N, et al. U-shaped tunnel lining design using the Hyperstatic Reaction Method – Influence of the invert[J]. Soils and Foundations. 2020, 60(3): 592-607.
 
 [9] Du D, Dias D, Do N. Effect of surcharge loading on horseshoe-shaped tunnels excavated in saturated soft rocks[J]. Journal of Rock Mechanics and Geotechnical Engineering. 2020, 12(6): 1339-1346.
 
[10] Do N, Dias D. Tunnel lining design in multi-layered grounds[J]. Tunnelling and Underground Space Technology. 2018, 81: 103-111.

[11] Oreste P, Spagnoli G, Luna Ramos C A, et al. The Hyperstatic Reaction Method for the Analysis of the Sprayed Concrete Linings Behavior in Tunneling[J]. Geotechnical and Geological Engineering. 2018, 36(4): 2143-2169.

[12] Nikkhah M, Mousavi S S, Zare S, et al. Evaluation of structural analysis of tunnel segmental lining using beam-spring method and force-method (Case study: Chamshir water conveyance tunnel)[J]. Journal of Mining and Environment. 2017, 8: 111-130.

[13] Rashiddel A, Hajihassani M, Kharghani M, et al. Numerical analysis of segmental tunnel linings - Use of the beam-spring and solid-interface methods[J]. Geomechanics and Engineering. 2022, 29(4): 471-486.

[14] Do N, Dias D, Oreste P, et al. Behaviour of segmental tunnel linings under seismic loads studied with the hyperstatic reaction method[J]. Soil Dynamics and Earthquake Engineering. 2015, 79: 108-117.

[15] Bui H G, Ninić J, Do N A, et al. A variationally consistent hyperstatic reaction method for tunnel lining design[J]. International journal for numerical and analytical methods in geomechanics. 2022, 46(1): 205-217.

[16] Ninic J, Alsahly A, Vonthron A, et al. From digital models to numerical analysis for mechanised tunnelling: A fully automated design-through-analysis workflow[J]. Tunnelling and Underground Space Technology. 2021, 107: 103622.

[17] Do N A, Pham V V, Dias D. A new pseudo-static loading scheme for the hyperstatic reaction method - case of sub-rectangular tunnels under seismic conditions[J]. Sustainable and Resilient Infrastructure. 2023, 8(3): 340-356.