# Numerical Simulation Analysis of Reinforced Geogrid Earth-rock Dam

**Abstract:** Using the general finite element software ADINA, the σ(stress)-ε(strain) state of wholesale uniaxial plastic geogrid-reinforced high-steep slope earth-rock dam and unreinforced earth-rock dam under the same load is compared and analyzed. The simulation results show that the uniaxial plastic geogrid manufacturers-reinforced high-steep slope earth-rock dam not only has a significant decrease in ε (strain) but also a relatively small σ (stress) compared with the unreinforced earth-rock dam. The application of the example shows that the reinforced high quality uniaxial plastic geogrid is used in the earth-rock dam, which not only makes the construction of the dam no longer restricted by the terrain but also is a practical and effective method.

**Keywords:** earth-rock dam; reinforced uniaxial plastic geogrid for sale; numerical simulation; finite element analysis

### introduction

With the development of society and the advancement of science and technology, the application of reinforced wholesale uniaxial plastic geogrid technology in water transport, water conservancy, and municipal engineering is becoming more and more common, and with the wide application of reinforced high quality uniaxial plastic geogrid technology, not only landfills The construction of earth-rock dams is not restricted by the topography, and it can reduce the ε (strain) of the dam and improve its stability, which provides a new guarantee for the safety of earth-rock dams.

The performance of reinforced soil mainly depends on the filler (such as physical and mechanical properties, hydraulic properties), the ribbed material (such as the deformation characteristics of the reinforcement, the layout scheme, the rib-soil interface characteristics), the panel (panel stiffness, panel, and ribs) Material connection method).

Although many experts have done a lot of research on reinforced materials, how to apply reinforced materials to earth-rock dams in landfills and the deformation state of reinforced materials under various loads has not been discussed. In this paper, the general finite element software ADINA is used to compare and analyze the uniaxial plastic geogrid for sale-reinforced high-steep slope earth-rock dam and the unreinforced earth-rock dam, which provides a theoretical basis for the application of reinforced materials in earth-rock dams.

**1. Theoretical model and method**

With the development of computer technology, the finite element method has become the mainstream in solving engineering problems. The finite element method mainly discretizes the analysis domain and then converts the boundary conditions of the control equation in the mechanical analysis into equivalent according to the variational principle. The algebraic equations are used to determine that the continuous field function problem in the solution domain is transformed into a solution to the field function value problem at finite discrete points. The finite element method is summarized as follows:

1.1 Discretization of the continuum. Discretization is the division of a given continuum into equivalent finite element combinations. The unit bodies are connected to each other only at the nodes to form a collection of units to replace the original structure.

1.2 Select the displacement mode. Make certain assumptions about the distribution of displacements in the element uniaxial plastic geogrid factory price. Assuming that the displacement is a simple function of the coordinates, ie, the displacement mode, the relationship between the displacement of any point in the element can be derived by the displacement of the node. The matrix form is:

Where: {f}—displacement array at any point in the unit;

{δ}ε—the node displacement array of the unit;

[N]—The shape function matrix whose elements are functions of the coordinates of the position of the node.

1.3 Using the variational method (or virtual work principle) to derive the element stiffness matrix, according to the geometric equation, derive the relational expression of the element strain by the node displacement from the expression (1) of the displacement.

Where: {ε}—displacement array of any point in the unit;

[B]—Unit strain matrix.

According to the physical equation, the relation expression of the unit stress expressed by the joint displacement is derived from the strain expression (2):

Where: {σ}—stress array at any point within the unit;

[k]—The elastic matrix associated with the unit material.

According to the variational principle, the relationship between the joint force acting on the element and the displacement of the joint uniaxial plastic geogrid factory price, that is, the equilibrium equation of the element is established, and the stiffness matrix of the element can be obtained:

Where: [δ]e—the element stiffness matrix;

{F}e—Unit node force array.

1.4 Calculate the equivalent junction load. Using the principle of virtual engineering, the boundary force, surface force, and volume force acting on the unit are converted into equivalent node loads and added to the nodes.

1.5 Perform a holistic analysis, synthesize the algebraic equations of the algebraic body of the entire discretized continuum, establish a balance equation, and integrate the stiffness matrix of each element into the overall stiffness matrix of the entire structure [k]; then the equivalent junction acting on each element The point force arrays are assembled into a total load array [k]. The overall equilibrium equation is obtained by aggregating the equilibrium equations of all the elements:

Where: [k] – the overall stiffness matrix;

[δ]—the overall node displacement array;

{F}—The overall load array.

1.6 Solve. The joint displacement is obtained by solving the global equilibrium equation, and the corresponding results are obtained according to the relationship between the above strain, stress and joint displacement.

### 2. Analysis of numerical simulation results

**2.1 Establishment of a finite element model**

**2.1.1 Model prototype**

In this paper, a homogeneous earth dam is taken as the research object. The construction is restricted by the two sides of the mountain. The height of the dam is 30m, the slope of the upstream dam is 1:2, the slope of the downstream dam is 1:2, the width of the dam is 5m, and the reinforced wholesale uniaxial plastic geogrid The number of grid layers is 8 layers and the grid length is 20 m.

Figure 1 Model prototype

**2.1.2 Establishment of a finite element model**

The model is considered according to the plane strain problem, in which the two-dimensional solid element adopts four-node unit, the one-dimensional rod unit adopts beam unit, and the bottom of the dam is horizontal. In order to conform to the real situation, the vertical direction of freedom is fixed, and the two sides of the dam body extend downward by 30m respectively. In the simulated bedrock strata, the parameters of each component are as shown in the material parameter table of Table 1. The contact unit is set between the dam bottom and the bedrock, between the rib belt and the soil body, and the panel unit is arranged on the dam slope downstream of the dam body. Under the same load, the relationship between σ(stress)-ε(strain) of reinforced high quality uniaxial plastic geogrid high-steep slope earth-rock dam and unreinforced earth-rock dam is compared. (Figure 2, Figure 3)

Table 1 Material Parameter Table

**2.2 Analysis of deformation results**

2.2.1 Comparative analysis of displacement (horizontal displacement) of the uniaxial plastic geogrid for sale-reinforced earth-rock dam and unreinforced earth-rock dam

Figure 4 and Figure 5 show the horizontal displacement cloud map of two types of earth-rock dams. From the comparative analysis in the figure, the uniaxial plastic geogrid manufacturers make the downstream dam slope more stable by limiting the horizontal displacement of the soil. Figure 6 is the reinforced grille. Comparative analysis of horizontal deformation of dam slopes of dams and unreinforced earth dams, the x-axis is the distance from each point to the dam site, and the y-axis is the horizontal deformation of the dam slope downstream of the dam. Under the same load, no The displacement of the dam slope downstream of the gluten-type earth-rock dam gradually increases with the distance from the dam site, and the dam crest displacement reaches the maximum value ymax=-0.003m, while the horizontal displacement of the dam slope downstream of the reinforced wholesale uniaxial plastic geogrid-type earth dam Significantly reduced.

Figure 2 Finite element model of the reinforced uniaxial plastic geogrid manufacturers earth-rock dam

Figure 3 Finite element model of unreinforced earth and rock dam

Figure 4 Reinforced uniaxial plastic geogrid for sale earth-rock dam y-displacement

Figure 5 Unreinforced earth and rock dam y-displacement

2.2.2 Comparative analysis of displacement (horizontal displacement) of the high quality uniaxial plastic geogrid-reinforced earth-rock dam and unreinforced earth-rock dam

Figure 7 and Figure 8 are vertical displacement deformation cloud diagrams of two types of earth-rock dams. Under the same load, the displacement of the unreinforced earth dam slope gradually increases with the distance from the dam site, and the dam crest displacement reaches The maximum value of zmax=-0.016m and the vertical displacement of the dam slope downstream of the reinforced uniaxial plastic geogrid factory price-type earth dam are significantly reduced.

Fig.6 Comparative analysis of horizontal deformation of dam slopes of reinforced grid earth dam and unreinforced earth dam

Figure 7 Reinforced high quality uniaxial plastic geogrid earth-rock dam z-displacement

Figure 8 unreinforced earth and rock dam z-displacement

Fig.9 Comparison and analysis of vertical deformation of dam slope of reinforced grid earth dam and unreinforced earth dam

Figure 10 Reinforced wholesale uniaxial plastic geogrid earth-rock dam y-stress

Figure 11 Unreinforced earth and rock dam y-stress

**2.3 Analysis of stress results**

2.3.1 Comparative analysis of stress (horizontal stress) of the uniaxial plastic geogrid manufacturers-reinforced earth-rock dam and unreinforced earth-rock dam

Figure 10 and Figure 11 show the horizontal stress cloud diagram of two types of earth-rock dams. The reinforced earth-rock dams have significantly lower horizontal stresses than the unreinforced earth-rock dams. Figure 12 shows the reinforced grid-type earth dams and The horizontal stress analysis of the dam slope downstream of the reinforced earth dam, the x-axis is the distance from each point to the dam site, the y-axis is the horizontal stress of the dam slope downstream of the dam, and the dam slope stress of the reinforced earth-rock dam under the same load As the distance from the dam site increases first and then decreases, the tensile stress appears in the horizontal direction of the downstream dam slope, and its maximum value σymax=-600kPa and the reinforced uniaxial plastic geogrid manufacturers-type earth dam downstream dam slope, due to the rib belt— The interaction between the soil and the panel, the horizontal stress is significantly reduced σymax=-20kPa, the vertical stress after reinforcement is reduced by 580kPa compared with the unreinforced earth dam, the stability increase effect is obvious, and the dam is The displacement of the top has a certain area of compressive stress and the maximum compressive stress σymax=50kPa. It can be concluded that the reinforced uniaxial plastic geogrid factory price-type earth dam has not only reduced the displacement of the downstream dam slope, but also the stress is reduced.

2.3.2 Comparative analysis of stress (vertical stress) between the wholesale uniaxial plastic geogrid-reinforced earth-rock dam and unreinforced earth-rock dam

Figure 13 and Figure 14 show the vertical stress cloud diagram of two types of earth-rock dams. It can be seen from the figure that the reinforced earth-rock dam has a larger difference in vertical-direction stress than the unreinforced earth-rock dam. The x-axis is the point. The distance from the dam site, the y-axis is the vertical stress of the dam slope downstream of the dam. It can be seen from Figure 15 that the vertical stress of the dam slope exists under the same load with the dam site without reinforcement. A large range of tensile stress, the maximum tensile stress is vertical σzmax=-150kPa, and the dam after the reinforced earth dam has vertical compressive stress, and the compressive stress is vertical σzmax=100kPa, which will make the dam slope downstream of the dam more stable.

### 3. Conclusion

The general finite element software ADINA is used to compare the stress and strain of uniaxial plastic geogrid for sale-type refuse earth dam and unreinforced garbage earth dam under the same load. The numerical simulation can be used to obtain the following conclusions:

Fig.12 Comparative analysis of horizontal stress of dam slope downstream of reinforced grid earth dam and unreinforced earth dam

Figure 13 Reinforced uniaxial plastic geogrid manufacturers earth-rock dam z-stress

Figure 14 Unreinforced earth and rock dam z-stress

Fig.15 Comparative analysis of vertical stress of dam slope of reinforced grid type earth dam and unreinforced earth dam

1 The horizontal and vertical displacements of the reinforced grid type earth dam and the unreinforced earth dam are reduced under the same load. The horizontal displacement of the unreinforced earth dam slope is the distance from the dam site. Increase and gradually increase, the displacement of the dam crest reaches the maximum value ymax=-0.003m, and the horizontal displacement of the dam slope downstream of the reinforced high quality uniaxial plastic geogrid-type earth dam is significantly reduced due to the rib-belt-belt between the panels. Interaction, the horizontal displacement of the dam slope downstream of the reinforced uniaxial plastic geogrid factory price-type earth dam is almost zero.

2 The vertical deformation and horizontal deformation of the dam slope downstream of the reinforced grid earth dam and the unreinforced earth dam are the same, and the displacement of the dam top reaches the maximum vertical displacement zmax=-0.016m, while the reinforced uniaxial plastic geogrid factory price The vertical displacement of the dam slope downstream of the grid earth dam is significantly reduced.

3Comparative analysis of the horizontal stress of the dam slope downstream of the reinforced grid earth dam and the unreinforced earth dam. Under the same load, the displacement of the untyped earth dam slope increases first with the distance from the dam site. Decrease, there is obvious tensile stress in the horizontal direction of the downstream dam slope, the maximum value σymax=-600kPa and the dam slope of the uniaxial plastic geogrid for sale-type earth dam downstream, and the reinforced earth dam due to the rib belt-soil-panel The interaction between the horizontal stress and the horizontal stress is obviously reduced by σymax=-20kPa. The vertical stress after reinforcement is reduced by 580kPa compared with the unreinforced earth dam. The stability increase effect is obvious, and the displacement at the top of the dam appears. The compressive stress maximum compressive stress σymax of a certain area is 50 kPa.

Comparing and analyzing the horizontal stress of the dam slope of the reinforced dam and the unreinforced dam, it can be seen that under the same load, the vertical stress of the unreinforced dam slope is along with the dam site. In the case of unreinforced, there is a large range of tensile stress, and the maximum tensile stress is vertical σzmax=-150 kPa, and the dam after the reinforced earth dam has vertical compressive stress, and the compressive stress is vertical σzmax=100 kPa, which will make The dam slope downstream of the dam is more stable.

All in all, the reinforced grid technology not only improves the σ (stress)-ε (strain) relationship of the dam but also provides a reliable method for the construction of related buildings in water transportation and municipal engineering.