Numerical simulation study on the structural stability of lattice retaining wall for gas pipeline in mountainous area

With the increasing demand for natural gas, the coverage of long-distance natural gas pipelines is also expanding, and the hydrogeological and climatic environments in the areas crossed by long-distance pipelines are also more complicated [1-2]. Pipeline through the mountainous areas, due to the complex and steep mountainous terrain, long-distance pipeline construction will inevitably cause damage to the original landscape of the mountainous areas, and in the filling of the pipeline, due to the compaction of the backfill soil is difficult to return to its original state, when encountered in the extreme rainfall weather is easily washed by the erosion of water erosion caused by soil erosion, resulting in the pipeline exposed or even overhanging, threatening the safe operation of the pipeline, so the pipeline project is very necessary to carry out hydraulic protection, so the pipeline project is very important. Hydraulic protection is very necessary [3-6].

Hydraulic protection of gas pipelines is to use various measures to avoid protecting the soil of the pipeline from being washed away and lost, of which retaining wall is the most commonly used one kind of hydraulic protection measures [7]. Although the current research and application of retaining walls are very mature, the most practical engineering applications are still slurry masonry retaining walls, which have the advantages of local materials, low cost, and strong supporting and retaining capacity [8-9]. However, as a kind of rigid retaining wall, it also has the shortcomings of poor deformation adaptability and high requirements for foundation bearing capacity [10-11]. Especially when used for gas pipeline protection in mountainous areas, due to the inconvenience of transportation in the mountains, the cement, sand and even construction water needed for the construction need to spend a huge amount of manpower and material resources to be transported to the work site [12-14]. Grid retaining wall is a new supporting structure, which can make full use of the stone at the work site to form the wall, and because the grid retaining wall is a kind of porous flexible structure, so it is adaptable to the deformation of the foundation, and it does not need cement mortar during the construction, which is very suitable for the construction of the water protection project of the gas pipeline in mountainous areas [15-18].

Grid cage is a kind of mesh box structure prepared by double twisted steel wire mesh with anti-corrosion treatment, which has the characteristics of high strength, high durability and good flexibility, etc. The bin cage protection technology has received wide attention and a series of successful experiences and theoretical results have been achieved. Literature [19] examined the role of gabion walls in hilly areas on road construction and flood control embankment building in terms of structural stability, flexibility and other engineering factors, and analyzed the retaining structure and load-bearing components of gabion cage walls to meet the design requirements such as high strength, high efficiency and stability. Literature [20] describes the design and construction process of the gabion water barrier structure, which can avoid the damage and impact on the environment under the strong water flow and play an important role in land and soil conservation. Literature [21] proposed a new type of quadruped-gabion-quadruped reinforced river channel model, which can effectively guide the water flow and reduce the scouring process, reducing the damage to the riverbanks under strong water flow. Literature [22] utilized gravel instead of sand and gravel filter material in the gabion retaining wall structure to enhance the drainage performance of the reservoir and separated the gravel material by geotextile wrapping to avoid clogging phenomenon, which provided a great help in mitigating the erosion inside the agricultural reservoir. Literature [23] showed that gabion gabions filled with filter material can significantly shrink the area of slope damage caused by heavy rainfall and prolong the duration of breaching, and that a suitable arrangement of filter gabions can increase the potential for slope stabilization. Literature [24] analyzed the hydrodynamic properties and geotechnical properties of gabion box sand-filled geotextile tubes for embankment design, and the gabion box as armor and filled with sand can avoid embankment damage caused by hydrodynamics, and the independent geotextile cylinder structure can also strengthen geotechnical stability. Most of the existing research on the structure of retaining wall of lattice is carried out for the road construction and water conservancy project, while the natural gas pipeline protection project in the terrain conditions, loading conditions, construction conditions and protection requirements, etc. There is a great deal of difference, and there is an urgent need for relevant research to provide a basis for the application and popularization of the retaining wall of lattice in the natural gas pipeline water protection project.

The safety of gas pipelines in mountainous areas is related to the rights and interests of thousands of households using gas. In this paper, we study the optimal value of the gabion retaining wall to maintain stability, so that it can better protect the gas pipeline in mountainous areas. The gabion retaining wall and its finite element theory and so on, and combined with the T city high pressure natural gas transmission project for the design of slope scour protection program and numerical settings, analysis. Based on the relevant setup, we further study the influence of elastic modulus of reinforcing body filler on the change of gabion retaining wall, and obtain the values of the influence of elastic modulus of reinforcing body on the horizontal displacement of gabion retaining wall wall surface, force of reinforcing material, and the structural stability of gabion retaining wall. Through the experimental study of four different natural conditions of different layers of the stability of the gabion mesh box changes, to obtain the best design value of the relevant parameters.

2

The basic theory of retaining wall of the gabion is explained

Before studying the values related to the lattice retaining walls in specific engineering projects, this section first elaborates on the concept of lattice retaining walls and finite element theory and unit analysis to clarify the basic connotation of the research object.

2.1

Overview of Grid Retaining Walls

Gabion retaining wall is a new type of layered gabion retaining wall, which is made of woven steel wire mesh with anti-corrosion treatment (coated with alum and high wear-resistant organic coating) into standard-sized mesh boxes, which are transported to the construction site and then assembled, and then fill the boxes with blocks or shards that are not easy to be weathered and disintegrated to form a retaining wall. Compared with the traditional gravity retaining wall, the gabion retaining wall is a kind of porous flexible structure with good integrity, durability, water permeability, adaptability to deformation and resistance to scouring, and it has a wide range of application and easy construction. When used for gas pipeline protection in mountainous areas, it can give full play to the advantages of more construction stones in the mountains and low cost, and at the same time, in terms of material transportation, only the packaged gabion mesh box needs to be transported to the project, avoiding the transportation of cement, sand and other materials, and solving the problem of difficult to fetch water from the top of the mountain.

2.2

Finite element theory and unit analysis

2.2.1

Planar isotropic cell analysis

1)

Problem formulation

In the finite element method of the plane problem, the most commonly used is the triangular unit and rectangular unit, these two types of unit shape is simple, regular, the unit of the various basic matrices of the solution is relatively easy and have to show the representation of the characteristics of the unit is also good to grasp, the programming is relatively easy. But the precision of the triangle unit is low, the stress results are not easy to organize, in the nonlinear analysis of soil, soil unit stress value in thousands of iterations will cause a large error in the correction. Although the rectangular unit overcomes the above shortcomings, it is not adapted to the curve boundary, nor can it adapt to the arbitrary requirements of meshing. If the arbitrary quadrilateral unit is used instead, and the displacement function of the rectangular unit is still used, the above shortcomings of the rectangular unit can be overcome to maintain the advantages of its high accuracy. However, this destroys the displacement continuity between neighboring cells on the common boundary, because in the right-angle coordinate system xy , the displacement function of the rectangular cell varies nonlinearly along any straight line inclined to the x - or y -axis. For this reason, it can be solved by means of a coordinate transformation. The above problem is solved by selecting a coordinate system ξη and transforming the coordinate system so that any quadrilateral cell in the right-angle coordinate system xy becomes a rectangular cell in the coordinate system ξη . In other words, the quadrilateral in the xy -plane is transformed into a square in the ξη -plane centered at the origin with side length 2 by the coordinate transformation from the independent variable (x, y) to the independent variable (ξ,η) , and the nodes 1, 2, 3, 4 in the xy -plane correspond to the nodes 1, 2, 3, 4 in the ξη -plane, respectively. This coordinate transformation is not performed on the whole structure, but on each unit separately, so that ξη belongs to the local coordinate system, while xy is called the overall coordinate system.

2)

Displacement function

In order to realize the above coordinate transformation, given that the quadrilateral under the local coordinate system ξη is a square, its displacement function can be completely modeled after the displacement function of a rectangular cell. It is taken as: (1) $\begin{array}{l} u = N_{1} u_{1} + N_{2} u_{2} + N_{3} u_{3} + N_{4} u_{4} = \sum_{i = 1}^{4} N_{i} u_{i} \\ V = N_{1} V_{1} + N_{2} V_{2} + N_{3} V_{3} + N_{4} V_{4} = \sum_{i = 1}^{4} N_{i} V_{i} \end{array}$

where the form function Ni is: (2) $N_{i} (ξ, η) = \frac{1}{4} (1 + ξ_{i} ξ) (1 + η_{i} η) (i = 1, 2, 3, 4)$

From Eqs. (1) and (2), it can be seen that the displacement function is a linear function of ξ or η on each side of the quadrilateral cell, and its value can be completely determined by the displacement values of the two nodes on that side. Therefore, in the local coordinate system, the displacement function expressed in Eq. (2) reflects the continuity of the displacements on the common boundary of neighboring cells.

3)

Coordinate transformation

The next step is to establish the transformations between the local coordinates and the overall coordinates. Along any line where ξ is equal to a constant, x and y vary linearly with η . Similarly, along any line where η is equal to a constant, x and y vary linearly with ξ . Thus, the relationship between the two coordinate systems can be described in a form similar to the displacement function equation (1) and equation (2). Therefore, the coordinate transformation equation is also taken as: (3) $\begin{array}{l} x = N_{1} x_{1} + N_{2} x_{2} + N_{3} x_{3} + N_{4} x_{4} = \sum_{i = 1}^{4} N_{i} x_{i} \\ y = N_{1} y_{1} + N_{2} y_{2} + N_{3} y_{3} + N_{4} y_{4} = \sum_{i = 1}^{4} N_{i} y_{i} \end{array}$

The form function N_i in Eq. (2) is the same as that in Eq. (2), and this displacement mode and coordinate transformation equation using the same form function of the unit is called the equal reference unit.

4)

Jacobi matrix and transformation determinant

In the finite element method for planar problems, the equations for determining the strain, stress and stiffness matrices of a rectangular cell are: (4) ${ε} = [\begin{matrix} \frac{\partial u}{\partial x} \\ \frac{\partial v}{\partial y} \\ \frac{\partial u}{\partial y} + \frac{\partial v}{\partial x} \end{matrix}] = [B] {δ}^{e}$ (5) ${σ} = [D] {ε} = [D] [B] {δ_{e}}$ (6) $[K_{e}] = \iint {[B]}^{T} [D] [B] d x d y$

The geometric matrix [B] in the above equation can be easily found by equation (3): (7) $[B] = [\begin{matrix} B_{1} & B_{2} & B_{3} & B_{4} \end{matrix}]$ (8) $[B_{i}] = [\begin{matrix} \frac{\partial N_{i}}{\partial x} & 0 \\ 0 & \frac{\partial N_{i}}{\partial y} \\ \frac{\partial N_{i}}{\partial y} & \frac{\partial N_{i}}{\partial x} \end{matrix}] (i = 1, 2, 3, 4)$

Since the differentiation of the form function with respect to the overall coordinates is to be used in [B] , but the form function expressed in Eq. (2) is expressed in local coordinates (ξ,η) . So the coordinate transformation is to be carried out so that all calculations are carried out in the local coordinate system, and from the formula for the derivation of the composite function, there is: (9) $\begin{matrix} \frac{\partial N_{i}}{\partial ξ} = \frac{\partial N_{i}}{\partial x} \frac{\partial x}{\partial ξ} + \frac{\partial N_{i}}{\partial y} \frac{\partial y}{\partial ξ} \\ \frac{\partial N_{i}}{\partial η} = \frac{\partial N_{i}}{\partial x} \frac{\partial x}{\partial η} + \frac{\partial N_{i}}{\partial y} \frac{\partial y}{\partial η} \end{matrix}$

written in matrix form: (10) ${\begin{array}{l} \frac{\partial N_{i}}{\partial ξ} \\ \frac{\partial N_{i}}{\partial η} \end{array}} = [\begin{array}{l} \frac{\partial x}{\partial ξ} & \frac{\partial y}{\partial ξ} \\ \frac{\partial x}{\partial η} & \frac{\partial y}{\partial η} \end{array}] {\begin{array}{l} \frac{\partial N_{i}}{\partial x} \\ \frac{\partial N_{i}}{\partial y} \end{array}} = [J] {\begin{array}{l} \frac{\partial N_{i}}{\partial x} \\ \frac{\partial N_{i}}{\partial y} \end{array}}$

where [J] is the transformation matrix, also known as the Jacobi matrix, which is expressed as: (11) $[J] = [\begin{array}{l} \frac{\partial x}{\partial ξ} & \frac{\partial y}{\partial ξ} \\ \frac{\partial x}{\partial η} & \frac{\partial y}{\partial η} \end{array}] = [\begin{array}{l} \sum_{i = 1}^{4} \frac{\partial N_{i}}{\partial ξ} x_{i} & \sum_{i = 1}^{4} \frac{\partial N_{i}}{\partial ξ} y_{i} \\ \sum_{i = 1}^{4} \frac{\partial N_{i}}{\partial η} x_{i} & \sum_{i = 1}^{4} \frac{\partial N_{i}}{\partial η} y_{i} \end{array}]$

Rewriting equation (11), so the derivative of the form function with respect to x , y can be expressed as: (12) ${\begin{array}{l} \frac{\partial N_{i}}{\partial x} \\ \frac{\partial N_{i}}{\partial y} \end{array}} = {[J]}^{- 1} {\begin{array}{l} \frac{\partial N_{i}}{\partial ξ} \\ \frac{\partial N_{i}}{\partial η} \end{array}} (i = 1, 2, 3, 4)$

where [J]⁻¹ is the inverse matrix of the Jacobi matrix. Substituting Eq. (12) into Eq. (4) yields the geometric matrix [B] in the local coordinate system, and thus the strains and stresses.

Eq. (6) is the formula to find the unit stiffness matrix in general coordinates, and now the unit stiffness matrix is to be formed in the local coordinate system, therefore, dx and dy must be replaced by dξ and dη , and the limit of integration is correspondingly replaced by $\iint_{v}$ and ${\int^{}}_{- 1}^{1} {\int^{}}_{- 1}^{1}$ , which can be obtained by vector algebra: (13) $d x d y = [J] d ξ d η$

where [J] is the determinant of the Jacobi matrix. Substituting Eq. (13) into Eq. (6) gives: (14) $[K_{e}] = \iint {[B]}^{T} [D] \cdot [B] d x d y = \int_{- 1}^{1} \int_{- 1}^{1} {[B]}^{T} [D] \cdot [B] \cdot [J] d ξ d η$

With Eq. (13) and Eq. (14) the requirement of unit stiffness matrix calculation in local coordinate system can be realized.

5)

Gaussian integration method

It is noted that in Eq. (14), the product function is difficult to be expressed as an explicit formula, and even if its explicit formula is found, it is quite difficult to perform integration. Therefore, numerical integration is mostly used in finite element analysis, i.e., certain points (called integration points) are selected in the cell, the function values of the product function at these integration points are calculated, and then these function values are multiplied by the corresponding weighting coefficients, and then the sum is calculated as the approximate integral value. The two-dimensional Gaussian integral formula for a planar isoparametric cell can be written as: (15) $\begin{matrix} I = \int_{- 1}^{1} \int_{- 1}^{1} f (ξ, η) d ξ d η \\ = \int_{- 1}^{1} [\sum_{i = 1}^{n} H_{i} f (ξ_{i}, η)] d η \\ = \sum_{j = 1}^{n} H_{j} [\sum_{i = 1}^{n} H_{i} f (ξ_{i}, η_{j})] \\ = \sum_{j = 1}^{n} \sum_{i = 1}^{n} H_{j} H_{i} f (ξ_{i}, η_{j}) \end{matrix}$

Where: n - the number of integration points in the ξ direction and η direction, in the number of taken integration points;

i , j - the code number of the same integration point in the ξ and η directions;

f(ξ_i,η_i) - the value of the function of the product function f at the integration points i , j (coordinates ξ_i , η_i);

H_i , H_j - one-dimensional weighting coefficients of the integration points in the ξ and η directions.

In the finite element analysis program for reinforced soils, the number of integration points is taken as n = 3 , i.e., there are 3 × 3 = 9 Gaussian integration points in an isoparametric unit.

6)

Formation of isoparametric cell stiffness matrix

From the above discussion, the formula for forming the stiffness matrix of plane equal parameter unit can be written as: (16) $\begin{matrix} [K_{e}] = {\int^{}}_{- 1}^{1} {\int^{}}_{- 1}^{1} {[B]}^{T} [D] [B] | J | d ξ d η \\ = {\sum^{}}_{j = 1}^{n} {\sum^{}}_{i = 1}^{n} H_{i} H_{j} ([B] T [D] [B] | J |) \end{matrix}$

where [B] and |J| are calculated values for Gaussian integration points. Finding [B] and |J| are done by the corresponding subroutines.

7)

Overall Balance Equation and Nodal Loads

According to the principle of virtual work and the principle of virtual displacement, the equilibrium equations are obtained: (17) $[K_{c}] {δ} = {R}$

In order to effectively save memory, the wavefront method, which does not require the formation of the overall stiffness matrix, can be used in solving the finite element overall balance equation (17). According to the actual stress situation of the reinforced soil retaining wall, only the self-weight effect and the vertically distributed load at the top of the wall are considered, then the nodal loads are relatively simple and can be formed directly according to the principle of load displacement.

8)

Unit stress calculation

After solving the overall equilibrium equation and obtaining the four-node displacement of each equal reference unit, the stresses at each Gaussian point inside the unit can be obtained according to equation (18).

(18)

\begin{matrix} {ε_{i}} = [B_{i}] {δ_{e}} \\ {σ_{i}} = [D] {ε_{i}} \end{matrix} (i = 1, 2, 3, 4)

where [B_i] is the geometric matrix at the i nd Gaussian integration point, which is given in Eq. (8). {ε_i} and {δ_e} are the strain and stress column matrices corresponding to this integration point.

2.2.2

Contact units

1)

Contact state

The interface (contact surface) between the reinforcement band and the soil body is divided into the same mesh so that the node coordinates are relative one to the other to form one-to-one corresponding node pairs. It is assumed that in the discretized case, the action between the reinforcement band unit and the soil unit on the interface is transmitted through the contact node pairs. The contact state of each localized region on the contact surface is judged by the node pairs: normal contact without tangential movement (bonding), normal contact with tangential movement (slipping), or no contact (disengagement).

Let the distance of the k st node pair (nodes i and j ) on the contact surface in the vertical interface direction be g₀ and the relative distance in the tangential direction be s₀ (in the initial state the reinforcement strip is bonded to the soil: g₀ = s₀ = 0 ), and the displacements in the vertical interface direction under the incremental load be g_ni and g_nj , and the slips in the parallel interface direction be g_si and g_sj . The clearance and relative slip of the k th node pair on the contact surface be equal to: (19) $g_{n} = g_{n j} - g_{n i} - g_{0}$ (20) $g_{s} = g_{s j} - g_{s i} - s_{0}$

Boundary conditions where contacting bodies are in contact with each other can be categorized as:

Disengagement: gap g_n remains positive;

Bonding: gap g_n = g_s = 0 , i.e. no gap in the normal direction, no slip in the direction of the initial line at the beginning and end of one load incremental step;

Slip: clearance g_n remains zero, there is slip in the direction of the parallel interface, and g_s is not zero.

The law of friction in contact, and the intrinsic relationship of the contact surface currently most of the use of Cullen’s law of friction, that is, the coefficient of friction μ in the process of solving for a constant value, in this paper, also use Cullen’s law.

2)

Contact unit stiffness matrix

There are two ways to deal with the contact boundary conditions, one method is to assume that there is a special unit on the contact surface of the two objects, whose unit stiffness matrix is consistent with the given contact boundary conditions; the other is to directly substitute the contact boundary conditions into the equilibrium equations. In this paper, the contact unit method is used.

Let F_n be the pressure at the perpendicular boundary, F_s be the slip force at the parallel interface, the stiffness of the perpendicular interface is k₀ and the slip stiffness is k_s . F_n = k_n (g_nj – g_ni – g₀), F_s = k_s (g_sj – g_si – s₀). Under the localized coordinate system xyz , defining z axes of the perpendicular contact surfaces, with the interface lying in the xy -plane, and the F_s , g_sj , and g_si components in the x - and y -directions are set to be the displacement and force matrices of the junction pairs (i, j) for F_sx , g_sxj , g_sxi , and F_sy , F_sy , g_syj , g_syj: (21) $[g_{e}] = {\begin{matrix} g_{n j} \\ g_{s x j} \\ g_{s y j} \\ g_{n i} \\ g_{s x i} \\ g_{s y i} \end{matrix}}, [F_{e}] = {\begin{matrix} F_{n} \\ F_{s x} \\ F_{s y} \\ - F_{n} \\ - F_{s x} \\ - F_{s y} \end{matrix}}$

Has the following differential relationship: (22) $[K_{e}] {d g_{e}} = {d F_{e}}$

[K_e] is the contact cell stiffness matrix, determined from the contact state as follows:

When μ|F_n|>|F_s|, the interface node pair is in the bonded state: (23) $[K_{e}] = [\begin{matrix} k_{n} & 0 & 0 & - k_{n} & 0 & 0 \\ 0 & k_{s} & 0 & 0 & - k_{s} & 0 \\ 0 & 0 & k_{s} & 0 & 0 & - k_{s} \\ - k_{n} & 0 & 0 & k_{n} & 0 & 0 \\ 0 & - k_{s} & 0 & 0 & k_{s} & 0 \\ 0 & 0 & - k_{s} & 0 & 0 & k_{s} \end{matrix}]$

When μ|F_n|=|F_s|, the interface node pair is in the slip state: (24) $[K_{e}] = [\begin{matrix} k_{n} & 0 & 0 & - k_{n} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ - k_{n} & 0 & 0 & k_{n} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{matrix}]$

When the interface is in the detached state, the contact unit stiffness matrix is zero matrix.

In Eq. (23) and Eq. (24), the stiffness k_n and slip stiffness k_s of the vertical interface can be determined with reference to the compression modulus and shear modulus of the contact body, while the amount of penetration between the contact surfaces should be limited to avoid mutual penetration of the contact bodies or an infinite increase in the number of iterations. The contact stiffness values that give satisfactory results will be different due to different cell grid densities, relative positions, material properties and geometries. For example, if the grid density increases, the number of contact cells will also increase and the load on each cell will decrease. If the number of contact cells is tripled, a suitable contact cell stiffness value should be half of the original. Therefore, there is no universal method to determine the optimum value of contact cell stiffness before solving. Therefore, the only way is to try different values until the correct value is found. It is safer to start with a smaller value and then steadily increase it until there is no more change in the analysis. Then for this particular analyzed problem, this point is the desired proper value.

2.2.3

Gabion wire units

Since gabion wire is a high-strength, high-modulus tensile material, which is mainly used to make mesh boxes for filling stones and tying adjacent gabion units, it is mainly subjected to tensile forces without considering its compression as well as bending, and thus can be treated as a one-dimensional linearly elastic rod unit.

The stiffness matrix of the rod unit is: (25) $[k] = [\begin{matrix} k_{i i} & k_{i j} \\ k_{j i} & k_{j j} \end{matrix}]$

Among them: (26) $k_{i j} = k_{j i} = \frac{E A}{l} [\begin{array}{l} b_{i} b_{j} & b_{i} c_{j} \\ c_{i} b_{j} & c_{i} c_{j} \end{array}]$

In the formula: (27) $l = \sqrt{{(x_{i} - x_{j})}^{2} + {(y_{i} - y_{j})}^{2}}$ (28) $b_{i} = - b_{j} = \cos θ = \frac{x_{j} - x_{i}}{l}$ (29) $c_{i} = - c_{j} = \sin θ = \frac{y_{j} - y_{i}}{l}$

where θ is the angle formed by the rod with the X axis; A is the cross-sectional area of the rod; and E is the modulus of elasticity of the rod.

3

Engineering background and program setting

Combined with the specific geographic location of the project, the design of the slope scour protection program, and the selection and analysis of the relevant parameters of the gabion retaining wall. The following section will expand the design and analysis and other corresponding content in detail.

3.1

Introduction to the City of T High Pressure Natural Gas Transmission Project

T city is located in the southeast coast, is a typical subtropical monsoon climate zone, warm and humid climate, four distinct seasons, plenty of light, the Pacific Ocean monsoon brings abundant rainfall, the basin of the multi-surface average precipitation is generally between 1600 ~ 2200mm, precipitation is not only spatial distribution is not uniform, inter-annual changes are also large, and the distribution within the year there are obvious differences. July, August and September in the survey area is the typhoon season, the maximum wind exceeds 11 levels, and is accompanied by heavy rainfall and very heavy rainfall, which is very likely to cause flash floods, resulting in house collapses and highway washouts.

The design pressure of the main gas transmission line of the high-pressure natural gas transmission project in T city is 4.5MPa, the diameter of the main pipe is DN550, and the diameter of the branch pipe is DN350.The total length of the pipeline of this project is 102.56km, among which the length of the main line DN500 is about 95.98km, and the length of the branch line DN300 is 7.53km.The main part of the pipeline project is situated in the hilly area of the southeast coast, and the main geomorphological units are hilly and plains. The main geomorphologic units are hills and plains. The test section is set in the hilly and mountainous area, generally the ground elevation is below 105m, and most of the mountainous area is gentle, with developed vegetation and less exposed foundation. The slope of the terrain is generally 15°-35°, and the steeper part can reach 35°-45°. The geology of the project is as follows: the surface soil of hilly mountainous area is clay soil gravel and gravel-containing pulverized clay, brownish-yellow, medium dense, gravel accounts for about 15-25%, 2-5cm in diameter, the constituents of medium-weathering bedrock, gravel accounts for about 15-25%, and the rest is clay soil and sand, the soil quality is not uniform. The standard value of foundation bearing capacity is [f_ak] = 240kPa . The engineering geological properties are good, and the soil and stone grade is class II.

3.2

Design of Scour Protection Program for Slopes

Referring to the actual working condition of K1+650-K1+800 section of high-pressure natural gas pipeline in T city, a scale-down model test with a scale-down ratio of 1:10 was carried out. Due to the size limitation of the test device, only the slope length of 38m in this section was intercepted for the same slope ratio scaling model test. A total of seven soil slopes were filled with a slope ratio of 1:1.55, with a slope width of 1.3 m, a slope length of 3.8 m, a slope height of 2.2 m, and a fill thickness of 10.4 cm. Among them, except for one bare soil slope used for comparison, a total of six types of protective slopes were designed and fabricated, which are as follows:

1) Installation of a slurry schist retaining wall. In order to investigate the scour protection effect of the traditional slurry schist retaining wall, a slurry schist retaining wall located in the position of Fig. 1(a) was installed to protect the slope.

2) Installation of a gabion retaining wall. In order to investigate the scour protection effect of the gabion retaining wall, set up a gabion retaining wall located in the position of Fig. 1 (a) to protect the slope, and the position of the gabion retaining wall is the same as the position of the slurry schist retaining wall.

3) Setting two gabion retaining walls. In order to investigate the effect of the number of retaining walls on the erosion of the slope, two gabion retaining walls located in the position of Fig. 1 (b) are set up on the slope.

4) Installation of three gabion retaining walls. In order to explore the relationship between the number of retaining walls and the amount of slope erosion, three gabion retaining walls located in the position of Figure 1 (c) are set to protect the slope.

5) Installation of three-dimensional geonet. In order to investigate the anti-erosion effect of three-dimensional geonet, the three-dimensional mesh is spread flat to cover the whole slope.

6) Setting a gabion retaining wall + 3D geonet. To investigate the anti-erosion effect of the combination of gabion retaining wall and 3D geonet, the slope is covered with 3D geonet on the basis of a gabion retaining wall at the location of Fig. 1(a).

3.3

Parameter selection and numerical analysis

The slope geotechnical body is simulated using plane strain units, the constitutive relation is based on an ideal elastic-plastic model, and the yield criterion is the Mohr - Coulomb yield criterion. The voids between the gabion fillings are not considered, and they are regarded as a continuous medium. The lattice mesh is simulated separately from the filler, the lattice filler is modeled by Mohr - Coulomb model, and the lattice mesh is simulated by linear elastic unit. Table 1 shows the determined physico-mechanical parameters of the slope geotechnical body and the supporting structure. The interface parameters between the gabion box and the slope surface are automatically calculated by the property assistant in the software according to the properties of the neighboring units, and Table 2 shows the interface parameters between the gabion box. In this paper, the slope is a permanent slope with one level of safety, and the stability coefficient F_st=1.35 under general working condition and F_st=1.15 under seismic working condition.Table 3 shows the stability coefficients of the slopes and the stability evaluation results of the construction phases obtained from the calculation. The evaluation results in Table 3 show that the slope is in a basic stable state when it is not supported, and support measures should be taken in time to ensure the safety and stability of the slope.

Table 1.

Mechanical parameters of rock and soil mass and supporting structure

Name	Cell type	Modulus of elasticity E/M Pa	Poisson’s ratio μ	Heavy gamma γ/(k N·m^-3)	Saturation weight γ _sat/(k N·m^-3)	Cohesion c/k Pa	Angle of internal friction φ/(°)
Fully weathered granite	Plane strain	25	0.305	20.8	22.3	5.5	35
Heavily weathered granite	Plane strain	550	0.266	25.5	26.4	56	36
Moderately weathered granite	Plane strain	19043	0.227	25.9	26.5	83	37
Anchor rope	The implantable truss	210006	0.302	77.5
Lattice beam	Beam	31007	0.203	25.2
Lattice network	Geotechnical grid	1404	0.301	25.6
Gubbin packing	Plane strain	2008	0.305	25.1	27.6	21	46

Table 2.

Interface parameters between gabion cages and the slope surface

Screen	Normal stiffness modulus kn/(k N·m^-3)	Shear stiffness modulus kt/(k N·m^-3)	cohesion c/k Pa	Angle of internal friction φ/(°)
Gabin cage - Slope	5.5×10⁸	4.7×10⁷	3.5	21.4
Gabion cage - Gabion cage	3.5×10⁸	3.1×10⁸	31	35.2

Table 3.

Stability coefficient and evaluation results of slope at each stage

Construction phase	Construction procedure	Stability coefficient F _s	Evaluation result
1	Untimbering	1.29	Basically stable
2	Prestressed anchor cable and lattice beam support	1.56	Stable
3	Gabion cage excavation, step construction	1.86	Stable
4	Gabion cage support	1.67	Stable

4

Analysis of the conditions affecting the gabion retaining wall

After setting up the corresponding gabion retaining wall in the slope, the following experiments and results of different conditions affecting the gabion retaining wall are analyzed to verify the stability of the gabion retaining wall set up in this paper.

4.1

Effect of changes in reinforcing body fill on gabion retaining walls

4.1.1

Effect of Changes in Modulus of Elasticity of Reinforced Body Fill on Horizontal Displacement of Walls

In order to investigate the changes of different modulus of elasticity of reinforcing body filler on the deformation and tendon strain of the interconnected single-stage reinforced gabion retaining wall, six cases of 30 MPa, 40 MPa, 50 MPa, 60 MPa, 70 MPa and 80 MPa were set up respectively.

Figure 2 shows the effect of the change in the modulus of elasticity of the reinforcing body filler on the horizontal displacement of the wall. As can be seen from Figure 2, DDK6+142.64 single-stage reinforced gabion retaining wall wall horizontal displacement along the wall height presents the phenomenon of “bulging belly”, in the middle position of the wall appeared the largest horizontal displacement; with the gradual increase in the modulus of elasticity of the reinforced body filler, section of the retaining wall at all levels of the wall horizontal displacement gradually decreased, but with the gradual increase in the modulus of elasticity, the wall horizontal displacement gradually decreased, but with the gradual increase in the modulus of elasticity, the wall horizontal displacement gradually increased. With the gradual increase of the modulus of elasticity of the reinforced filler, the horizontal displacement of the wall surface gradually decreases, but with the gradual increase of the modulus of elasticity, the rate of reduction of horizontal displacement of the wall surface gradually becomes smaller, which is mainly due to the fact that the larger the modulus of elasticity of the reinforced filler is, the stronger the integrality of the retaining wall, and the stronger the resistance to horizontal deformation.

4.1.2

Effect of different filler modulus of elasticity on tendon strain

Figure 3 shows the effect of different filler elastic modulus on the strain of tendon material. In order to facilitate the study of retaining wall reinforcement deformation, the 2nd, 10th and 17th layers of grids of DDK6+142.64 single-stage reinforced gabion retaining wall were selected. From the figure, it can be seen that with the gradual increase of the modulus of elasticity, the strain of each layer of reinforcing material along the laying direction roughly shows an increasing trend, in which the single-level wall reinforcing material strain change is very small, and the trend of strain change along the direction of reinforcing material laying is basically the same. Indicates that: the elastic modulus of the reinforced body filler has a small influence on the force of the reinforcement.

4.1.3

Changes in the horizontal displacement of the wall due to changes in the cohesion of the reinforcing body packings

Table 4 shows the variation of the horizontal displacement of the wall face by the variation of the cohesion of the reinforced body filler. From the table, it can be seen that the maximum horizontal displacements of the wall face of the single-stage reinforced soil barrier wall are 3.28-61.20 mm, which is about 0.042%-0.766% of the wall height. When the cohesion of the filler is 5-15 kPa, the single-stage retaining wall is 247.74%, 0 and -57.28%, respectively, and the horizontal deformation rate of the wall is larger, especially when the cohesion is 5 kPa, the horizontal displacement of the wall reaches the maximum, which shows that the friction angle in the reinforced filler has a great influence on the horizontal deformation of the wall. When the cohesion is 15-30 kPa, the single-level retaining wall is -77.28%, -81.37% and -81.37%, respectively, and the horizontal displacement rate of the wall surface has almost no change, and the horizontal displacement of the wall surface changes approximately linearly along the wall height. It can be seen that when the cohesion is 5 kPa, the rate of change of the retaining wall is larger, when the cohesion grows to more than 20 kPa, the rate of change of the retaining wall is very small, the horizontal displacement of the retaining wall at all levels changes less, and the retaining wall structure gradually tends to be stabilized. This is mainly due to the shear strength of the soil body according to the formula: F=tanϕ/tan∂ can be seen, with the increase of filler cohesion, soil body shear strength is also gradually increased, can effectively reduce the back of the wall surface horizontal earth pressure, so that the horizontal deformation of the wall surface is reduced. In the actual project can be appropriate to increase the cohesive force of the filler to ensure the stability of the structure, but when the cohesive force is too large, the role played is not large.

Table 4.

Influence of cohesive force of packing on horizontal displacement of wall

C/k Pa	C Rate of change/%	Single stage retaining wall D m_ax/mm	Single stage retaining wall (d m_ax/H)/%	Single stage retaining wall (d m_ax/H)Rate of change/%
5	-50	61.20	0.766	+247.74
10	5	17.62	0.221	0
15	+50	7.49	0.095	-57.28
20	+100	4.01	0.048	-77.28
25	+150	3.28	0.042	-81.37
30	+200	3.30	0.042	-81.37

4.2

Stability analysis of gabion retaining wall under complex conditions

In addition to analyzing the impact of the change of reinforcement filler on the gabion retaining wall, this section further analyzes the stability of the gabion mesh box support structure under more complex conditions to verify the effectiveness of the gabion retaining wall designed in this paper. In this paper, the slope gradient of the gabion box support structure ∂ = 28°, the friction coefficient between the gabion box and the slope is 0.65, the seismic intensity is set at 7.5 degrees, C_i is 1.8, K_h is 0.15, the role of rainfall is considered according to the saturation of the gabion filler by strong rainfall, t_w approximation is taken as 0.35 m. Fig. 4 shows the structural stability coefficients of the structure itself for the different layers of the gabion box under the natural conditions, earthquakes, rainfall, and the common effect of earthquakes and rainfall. Figure 4 shows the coefficient of stability of the structure itself under natural conditions, earthquake, rainfall and the combined effect of earthquake and rainfall for different layers of gabions.

As can be seen from Fig. 4, with the increase of the number of stacked layers of the grid box, its own anti-slip stability coefficient curve is gradually decreasing and then tends to flatten out, in the number of layers of the grid box from 1 to 4, the stability coefficient decreases significantly; when the number of layers increased from 5 to 7, the decrease is relatively slow; when more than 7, with the increase in the number of layers, the curve changes gently, and ultimately converge to a fixed value. Further analysis of the reasons can be seen, without considering the rainfall, earthquakes and other complex conditions, with the increase in the number of layers, the self weight of the gabion support structure system increases, the slip force generated also increases, while the bottom layer of the gabion provides the same slip resistance, and when the number of layers is enough, the slip resistance provided is basically negligible.

The law between the number of layers and the stability coefficient shows that the retaining wall made of seven layers of gabions stacked on top of each other can be safe and stable under natural conditions, 7.5 degree earthquake, and strong rainfall, and the minimum stability coefficient is 0.97, which is slightly less than 1 under the joint action of earthquake and strong rainfall, thus indicating that the gabion retaining wall designed in this paper has better stability.

5

Conclusion

In this paper, the basic values to keep the stability of the gabion retaining wall are obtained through the study. Through the study of 30 MPa, 40 MPa, 50 MPa, 60 MPa, 70 MPa, 80 MPa six cases of elastic modulus of reinforced body filler changes for the impact of the gabion retaining wall, get DDK6+142.64 single-stage reinforced gabion retaining wall wall in the middle of the wall in the position of the maximum horizontal displacement. And with the gradual increase of the modulus of elasticity of the reinforced filler, the horizontal displacement of the wall at all levels of the section gradually decreases, but with the gradual increase of the modulus of elasticity, the rate of reduction of the horizontal displacement of the wall gradually becomes smaller. Selection of appropriate modulus of elasticity of reinforced filler is conducive to enhancing the integrity of retaining wall.

Study the strain of tendons of the 2nd, 10th and 17th layers of grids of DDK6+142.64 single-stage reinforced gabion retaining wall in the change of elastic modulus of different fillers, and the results show that the modulus of elasticity of reinforcing body filler has a small influence on the force of tendons. The study of the influence of the change of the viscosity cohesion of the reinforced body filler on the change of the horizontal displacement of the wall surface learns that when the viscosity cohesion is 5 kPa, the horizontal displacement of the wall surface reaches the maximum and the rate of change of the retaining wall is large, while when the viscosity cohesion grows to more than 20 kPa, the rate of change of the wall is small, and the change of the horizontal displacement of the wall at all levels is small, and the structure of the retaining wall gradually tends to be stabilized. Therefore, it is possible to choose to select the cohesive force of the reinforced body filler around 25 kPa, so that the gabion retaining wall maintains a stable structure.

By studying the coefficient of structural self-stability of different layers of gabion mesh box under natural conditions, earthquake, rainfall, and the combined effect of earthquake and rainfall, it is learned that when the number of gabion mesh box reaches 7 layers, it can make the gabion retaining wall keep a better stability in all the 4 conditions. Therefore, in order to maintain the stability of the gabion retaining wall for a longer period of time in practical application scenarios, this paper suggests that the number of layers of the gabion mesh box should be increased to about 7 layers.

Funding:

1) Science and Technology Research project of Chongqing Municipal Education Commission: Stability analysis and protection design of Dougbin retaining wall in mountain gas pipeline (KJQN202404710).

2) Science and Technology Research project of Chongqing Municipal Education Commission: Infrared thermal imaging detection of liquid pipe network leakage in complex background (KJQN202404713).

Sprache:: Englisch

Zeitrahmen der Veröffentlichung:: 1 Hefte pro Jahr
Fachgebiete der Zeitschrift:: Biologie, Biologie, andere, Mathematik, Angewandte Mathematik, Mathematik, Allgemeines, Physik, Physik, andere

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Numerical simulation study on the structural stability of lattice retaining wall for gas pipeline in mountainous area

Zibin Li

Online veröffentlicht: 19. März 2025

Eingereicht: 17. Okt. 2024

Akzeptiert: 07. Feb. 2025

DOI: https://doi.org/10.2478/amns-2025-0526

SchlüsselwörterGabion retaining wall, Finite element simulation, Reinforced body filler, Modulus of elasticity, Gas pipeline

© 2025 Zibin Li, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
Gabion retaining wall, Finite element simulation, Reinforced body filler, Modulus of elasticity, Gas pipeline