Two-dimensional analysis of strain stress in rock environments around the tunnel with nonlinear elasto-plastic behavior under shear loads by finite element method

Master's thesis in the field of civil engineering, soil and foundation

Today, due to the progress of the tunneling industry, the need to analyze and design underground structures in rocky environments is felt more than in the past. Although there are many numerical and practical software available in this field, none of them are complete and perfect in all fields, and each of them has the best application in specific environments and conditions. As a result, programming in this field can be justified. In this thesis, we will program and create software by using finite element method and MATLAB. In the first step, using linear regression, the best coefficients are selected for the desired rock sample. By using this software, a comparison has been made between the rupture areas around the circular tunnel in two-dimensional elastic and elasto-plastic environment under Beniawski and Hook-Brown criteria. This software has the ability to draw rupture areas around the tunnel and calculate stresses and strains at all points. At the end, the results obtained from the elastic analysis have been compared with the analytical results obtained from the shock relations and the results obtained from the elasto-plastic analysis have been compared with the results of ADINA software. By comparing the results, the accuracy of the developed software is evaluated and it can be concluded that the results of the Hook-Brown analysis are closer to the analytical results. Chapter 1 Introduction 1-1 Preface: Today, rock mechanics and underground structures engineering have become one of the most important branches of geotechnical engineering. software for analyzing underground structures and rock slopes. The most important requirement of a tunnel designer in the analysis of underground structures is to obtain the area of ??rupture, stress and displacement in different points around this structure. These results are very important. Using these results, you can determine the areas that need to be strengthened. Although many accurate solutions for the analysis of rock environments have been provided so far, but due to the limitations of analytical methods in modeling environments with elasto-plastic, heterogeneous, non-isotropic behavior, complex boundary conditions, complex tunnel shapes, etc. The interest in using numerical methods is expanding day by day. Among all the numerical methods, the finite element method [1] has received a lot of attention due to its simplicity and greater flexibility.

Although in most of the researches, the behavior of stone is considered to be linear elastic, but triaxial resistance tests show that the behavior of most stones is nonlinear elasto-plastic. Considering the ability of the finite element method, modeling the rupture of this work behavior does not seem to be a problem. In addition to the method of analysis, the criterion used for analysis is also very important. The rupture criterion should be able to model well the behavior of the rock environment under different loading conditions. Many empirical criteria have been presented so far, but the most important and effective of them are Hook-Brown's criterion [2] and Beniawski's criterion [3], both of which are widely used in executive works.

Today, there are many softwares for the analysis of underground spaces, each of which relies on an analytical or numerical method. But with all the interpretations, no specific software can be found that can comprehensively and completely meet all the demands of a tunnel engineer. These demands include

1- Drawing the rupture areas around the tunnel clearly and clearly

2- Covering all existing criteria, both theoretical and experimental

3- Modeling all behavioral models, including linear elastic, nonlinear elasto-plastic, nonlinear elastic.

4- Behavioral modeling of heterogeneous, non-isotropic, sealant rock environments.

5- The effect of reinforcing elements such as rockbolt and the design of internal protective cover

The author's intention in presenting this discussion is that no comprehensive and complete software can be found that can have all the criteria required for all types of analysis. As a result, with all these possibilities, programming is still done a lot in the discussion of tunnels and rock slopes, for specific purposes that the software is not able to cover.

In this research, several goals are considered, which are

1- a graphical comparison between the fracture areas of an underground structure under the same loading conditions, under the two criteria of Hooke-Brown and Beniaevsky in a rock environment with elastic behavior; and its comparison with the provided analytical solutions

2- The effect of shear load on the rupture areas around the tunnel

3- Presenting the non-linear elasto-plastic behavior model with Hooke and Brown criteria and comparing its results with one of the commercial software

(images are available in the main file)

It should be mentioned that all the programming steps were done in MATLAB [4] environment.

1-2- An overview of the conducted researches:

It is safe to say that a brief description of the conducted researches on underground structures with the finite element approach would require as much work and time as several researches. Anyway, in this chapter, we will try to point out the conclusions of these researches and their results.

In 2002, in a research conducted by Sin [5] and colleagues, they conducted an analysis with the finite element method approach on the Kuina tunnel [6] in India [1]. They modeled a model resulting from several underground spaces, as shown in Figure 1-1, both in 2D and 3D in a heterogeneous environment and obtained the distribution of stress and displacement around the tunnel and compared them with the results obtained on site. They considered the resulting environment to be caused by 23 types of rocks with different resistance properties. Some of them had elastic behavior and some of them had Druckerpraeger elasto-plastic behavior. They performed this analysis by Solvay [7] software developed by Solvay Engineering Group in Sweden. This software is based on the finite element method and can be used for all non-linear elastic and Drucker-Prager elasto-plastic behaviors for stone and concrete. In this thesis, a series of indicators were installed to measure the change of location and tension around the existing spaces, and through them, they obtained the actual tension and change of locations in certain places of this environment. The results show the fact that the 3D analysis is closer to the real values ??in terms of accuracy, but the results of the 2D analysis are more conservative. In 1993, a research was conducted by Fama [8], Duncan [9] and others [2]. In this research, the underground structure has been analyzed in heterogeneous rock environments (horizontally layered type, of course). The basis of the work is the use of Caserat theory[10]. In this theory, with a series of simplifying assumptions, the layered rock environment becomes a homogeneous environment and then it is analyzed by the finite element method. The obtained results show a much closer and more accurate convergence to the analytical answers.

In 2008, Salim Benshamdi[11] and colleagues analyzed a part of an underground chamber in a research [3]. In this research, due to the symmetry of the shape, only half of it was analyzed and the result was shown in Figure 1-2. The analysis of this sample is very similar to the analysis of underground rock foundations. The behavior of non-linear stone materials was considered as softening [12]. Using nonlinear finite element analysis and Mohr-Columb criterion, the plastic zone around the underground space was obtained by plotting the yielded Gauss points. As shown in Figure 1-2, the plastic zone around the tunnel is represented by the yielding Gauss point plot. In another part of this research, they analyzed the environment in three different heterogeneous states and obtained the effect of different heterogeneities in the development of the plastic zone. In another part, a comparison was made between the rupture area in elastic behavior and the plastic area in elasto-plastic behavior, the result shows the more accurate elasto-plastic analysis and the greater proximity of the stresses and changes in the resulting locations with the results measured at the site and location. In another part of this comprehensive research, in different percentages of the final loading, 20, 40, 60, 80 percent, the plastic area around this stone column was obtained and compared.

In the field of rock plastic analysis, the work done in Iran is very limited. One of these limited researches was done by Morteza Ahmadi and Mohsen Meshari [4]. In this article, the two-dimensional stress-strain analysis around the rock of underground excavations has been investigated in the case that the environment around the underground excavations also shows elasto-plastic behavior under the applied load. To analyze the stress in this case, a software called Finite Element Program [13] has been prepared, which is based on the Finite Element Method. In this regard, the use of the finite element method for stress analysis has been stated and it has been used in solving the basic equations of solid mechanics (principle of total potential energy) and the final relations for analysis have been presented.