Study on the mechanical characteristics and impact resistance improvement of substation masonry wall under flood load

2.1. Masonry wall finite element model

Fig. 1 displays the finite element model of the masonry wall with foundation structural columns, simulated using ABAQUS software. Solid element C3D8R is used to simulate the blocks, structural columns, and foundations, while beam element B31 is used to simulate the reinforcement. To simplify the simulation of masonry walls, each block is extended in six directions in space to include 1/2 of the thickness of the surrounding vertical and horizontal mortar joints, forming a “composite block” and modeled as an isotropic continuous element [18]. The reinforcement adopts a double-line material model, and the mechanical behavior of concrete is simulated using a damage plasticity model. The concrete material parameters are shown in Tables 1 and 2, and Table 3 displays the parameters of the reinforcement material.

Fig. 1Masonry wall finite element model

a) Overall model

b) Wall model

The interaction between the combined blocks is set and all degrees of freedom of the foundation are constrained. The simplified separated modeling method for block walls simulates the failure of mortar joints by the failure of contact behavior between composite blocks, and their contact behavior needs to be set in the normal and tangential directions respectively [19]. The normal behavior adopts “hard” contact to prevent mutual intrusion between adjacent component elements. For tangential behavior, the “penalty” contact property (Coulomb friction property) is set, with a friction coefficient of 0.5. Viscous behavior is handled using the non-coupled traction separation criterion, which assumes that pure normal separation will not cause changes in tangential traction stress, and pure tangential slip will not cause changes in normal traction stress. In addition, binding constraints are used between the composite block and the construction column, as well as between the composite block and the foundation, and built-in constraints are used between the reinforcement skeleton and the construction column. The hexahedral meshing method is employed to achieve good simulation accuracy.

2.2. Flood load calculation method

Since most of the substation enclosures are subject to flooding caused by heavy rainfall, the flooded area is relatively shallow. Therefore, it can be assumed that the coupling effect between the water flow and waves of the flood can be ignored. When considering the total water flow pressure, the total water flow pressure is composed of wave load, dynamic water load, and static water pressure.

The static water pressure that varies along the height of the wall can be expressed as:

where: $F_G$ is the hydrostatic pressure, $\rho$ represents the water density, $g$denotes gravitational acceleration, and h represents the water depth. Hydrostatic pressure and flood water depth are directly proportional. Horizontally, at the same water depth, the hydrostatic pressure is equal; at different water depths, the hydrostatic pressure at the bottom is large.

The wave pressure calculation method of Ryoji [20] was used to calculate the wave load force. In this project, $d/L$ is determined from the given data to meet the condition of shallow water wave area, i.e.$\text{0.135}\le d/L<\text{0.35}$. Consequently, the maximum wave load beneath the static water surface can be expressed as follows:

where: $k$ is the wave number, which can be calculated as $\text{2}\pi /L$, $L$ is the average wavelength; $\gamma$ is the flood heaviness; $H$ is the wave height of the incident wave; the $\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}(\bullet )$function is the hyperbolic cosine function; is the flood depth; $z$ is the vertical coordinate that is positive upwards from the static water surface. The mean wavelength $L$ can be determined according to Appendix C Wave Calculation Lookup Table of Levee Engineering.

In this study, based on the experimental results of Danel, the incident wave height $H$ is selected as the limiting incident wave height Hlim [21] in front of the wall, which can then be expressed as:

The primary load acting on the enclosure surface is the dynamic water load [22], which can be expressed as follows:

where: $F_w$ is the standard value of water flow force; $K_w$ is the integrated impact coefficient of water flow resistance, when the opening rate is 0, $K_w$ is 2.32; $A$ is the gross area of the wall on the flow-facing surface; $v$ is the velocity of the water flow, which can be calculated as:

where: the Xie Cai coefficient $C=R^{1/6}/n$; the hydraulic radius $R=S/x$; $i$ is the slope of the river section, taken as 0.005; $n$ is the roughness coefficient of the riverbed, taken as 0.03; $S$ is the cross-sectional area of the riverbed; and $x$ is the wet perimeter of the cross-section of the riverbed.

Both the on-site damage and finite element simulation indicate that the middle and lower parts of the enclosure wall experience the most displacement, gradually decreasing from bottom to top. The highest tensile stress is observed at the junction of the wall and the structural column. Therefore, measurement points P1-P6 are selected at the center of the span of the wall to study the displacement changes at different heights of the wall, and measurement points P7-P12 are chosen to investigate stress variations at different heights of the wall where they connect to the structural column. To verify the reasonableness of the numerical model, a comparison between the actual damage of the wall in the field in Fig. 3(a) and the numerical simulation damage in Fig. 3(b) is carried out. The area damaged by the substation enclosure wall under the flood impact is the upper wall, and it is out-of-face impact damage. The results of the numerical simulation and the location and form of the actual substation enclosure wall damage are basically in line with each other, which indicates that the numerical simulation can simulate the actual engineering force characteristics to a certain extent, and the subsequent dynamic response analysis is combined.

Fig. 2Distribution of flood load on masonry walls

a) Load diagram

b) Mapping of wall measurement points.

Fig. 3Damage situation of masonry walls

a) Physical damage on site

b) Model simulation of destruction

3.1. Project overview

This study is based on the Xinyang, Henan 500 kV substation project. The substation is situated in a hilly and low-lying region, with the wall's north side exposed to flooding. In 2021, Henan Province encountered a rare extremely heavy rainstorm in history. The flood level exceeded the original design standard, and the substation wall is flooded. The masonry wall collapsed over a large area due to water scouring, after the local walls on the upstream face overturned from the bottom of the superstructure wall. Fig. 4 shows the actual engineering layout and construction of the masonry walls, which mainly consist of structural columns and walls made of A3.5 autoclaved aerated concrete blocks using MD7.5 mixed mortar. The wall height is 2.3 meters. The block size is 600 mm × 300 mm × 300 mm, with mortar between the blocks. C30 concrete and reinforcements are used to construct columns on both sides of the block wall. The cross-sectional size is 300 mm × 300 mm, with a centerline spacing of 3 meters between adjacent structural columns. Expansion joints are placed every 6 meters on the wall. For numerical modeling and stress analysis, this article focuses on the wall between two expansion joints.

Fig. 4Layout and construction information of masonry wall (Unit: mm)

a) Wall elevation view

b) Wall plan

3.2. Force characteristics analysis

The stress characteristics of the substation’s masonry wall are examined based on engineering monitoring measurements of a flood depth of 1 m and a flood velocity of 2 m/s. The compressive stress distribution of the masonry wall under flood loading is shown in Fig. 5, where the stress cloud of the masonry wall on the flood side outside the substation station (referred to as the “outer side”) is shown in Fig. 5(a), and the stress cloud of the masonry wall on the facility side (referred to as the “inner side”) is shown in Fig. 5(b).

Fig. 5Cloud chart of wall pressure stress under flood load

a) Outer side

b) Inner side

The flood pressure causes an increase in compressive stress at the center of the bottom of the outer wall, exhibiting a relatively uniform stress distribution ranging from –2.43 MPa to 4.74 MPa. Notably, the inner wall experiences significant stress concentration. The compressive stress in the structural column gradually increases with height, reaching its maximum value at the connection with the foundation.

The distribution of tensile stress in the masonry wall under flood load is shown in Fig. 6. The connection area between the wall and the structural column experiences the highest tensile stress. The outer connection between the structural column and the foundation shows greater tensile stress with notable variations compared to the inner side. Moreover, due to block interaction, several regions on the wall show prominent tensile stresses, primarily near the structural columns, indicating the force transfer mechanism between the blocks and the structural columns.

Fig. 6Cloud chart of wall tensile stress under flood load

a) Outer side

b) Inner side

Fig. 7 shows the displacement cloud of the masonry wall under flood load. The red part of the displacement is larger and concentrated in the lower region, and the blue part of the displacement is smaller and concentrated in the upper region, indicating that the wall deformation is smaller above and larger below. Under similar working conditions, when the flood load is low, the wall has no vertical deformation, with displacement and deformation primarily occurring perpendicular to the wall. However, under higher flood loads, the wall exhibits significant displacement and deformation. The deformation pattern of the wall follows a decreasing trend from the centerline to the edges, with larger deformation observed below and smaller deformation above. The rigidity of the structural columns on both sides of the masonry wall is large, the deformation is small on the top and small on the bottom, and a certain degree of twisting phenomenon occurs. The deformation of the masonry wall is not uniform, because the wall is composed of multiple blocks interacting with each other by setting, and the flood load at different heights varies greatly, resulting in differences in deformation between the blocks distributed along the height of the wall. In addition, the deformation decreases with increasing height, which is because the flood height for this condition is 1.0 m and the lower area is directly subjected to flooding.

Fig. 7Displacement cloud map of masonry wall

4.1. Influence of flood depths

The flood depth parameters selected for analysis are 0.5 m, 0.6 m, 0.75 m, 0.8 m, 1.0 m, and 1.25 m. A comparative analysis of stress distribution and displacement changes of masonry enclosure walls under different flood depths was conducted to study the stress and deformation change patterns of masonry enclosure walls with varying flood depths.

Fig. 8 displays the displacement and stress response of the masonry wall at various measurement points during flooding. As depicted in Fig. 8(a), when the flood depth ranges from 0 to 0.8 m, the displacement at different measurement points is small, with values below 0.05 m. When the flood depth is increased to 0.8 m, the displacement changes at the wall measurement points P1, P2, and P3 are very significant, while the displacement changes at the other measurement points are small. As the flood depth continued to increase, the displacements at points P1 and P2 are 0.085 m and 0.029 m, respectively, when the depth reached 1.0 m, which increased by 0.043 m and 0.028 m, respectively, compared with the depth of 0.5 m. In addition, the displacements at point P1 are consistently the largest at different flood depths, which indicates that this point is the most unfavorable location for the wall. At a flood depth of 1.25 meters, the middle block at the lower end of the wall experiences its highest stress, resulting in wall collapse without recorded simulation data.

Fig. 8(b) illustrates the stress variation of the masonry wall under flood loading. The stresses at measurement points P9, P10, P11, and P12 do not change much when the flood depth increases from 0.5 m to 1.0 m. The stresses at measurement points P9, P10, P11, and P12 do not change much. However, the stresses at measurement points P7 and P8 changed significantly, and when the flood depth increased from 0.5 m to 1.0 m, the stresses at measurement point P7 are 0.30 m and 1.96 m, respectively, which increased by 553.3 %.

Fig. 8The impact of flood depths on fences

a) Changes in displacements with flood depths

b) Variation of stress with flood depths.

Fig. 9 illustrates the evolution of stress cloud diagrams for the masonry enclosure wall as the flood depth reaches 1.0 m. It is evident that the application of flood load results in intricate stress patterns on both sides of the wall, and the stress values in the lower part of the wall are always greater than those in the upper part of the wall; the stresses in the wall are greater at the ends and the bottom of the outer wall, which satisfy the results obtained from the stress analysis section.

Fig. 9The change process of wall stress cloud map at a flood depth of 1.0 m

a) Initial application of loads

b) Progressive change of loads

c) Continuing changes in loads

d) End of load application

4.2. Influence of water velocity

The water velocity parameters selected for this study are 1 m/s, 2 m/s, 3 m/s, 4 m/s, and 5 m/s. The objective is to investigate the stress distribution and displacement changes of the masonry enclosure wall. The comparative analysis aims to identify the relationship between flood velocity, stress, and deformation of the masonry enclosure wall.

Fig. 10 displays the displacement and stress response of the masonry wall at different measurement points during flooding. Fig. 10(a) presents the displacement changes in the masonry enclosure under flood loading. As the water velocity increases from 0 m/s to 3 m/s, the wall displacement increases slowly due to the low inertia of the water body, and the change rule of the displacement at different control points is the same, in which the displacement of the wall measuring point P2 is the largest. When the water velocity increases from 3 m/s to 4.0 m/s, the displacements of measuring points P1 and P2 increase rapidly to 0.12 m and 0.070 m, which are 118.18 % and 573.07 % larger compared with that when the water velocity is 1 m/s.

Fig. 10The impact of flood velocity on the fence

a) Changes in displacements with flood velocity

b) Variation of stress with flood velocity

The stress variation in the masonry enclosure under flood loading is given in Fig. 10(b). There is no significant change in stress values at the measurement points along the wall as the water velocity increases from 0 m/s to 2 m/s, where the maximum stress is applied to the measurement point P8, with a profit of 0.072 MPa. The change in stress at the measurement point P8 is very significant when the water velocity increases from 2 m/s to 4 m/s. The stress at the measurement point P8 at a water velocity of 4 m/s is 4.43 MPa, which is 4.43 MPa, compared to that at the water velocity of 1 m/s increased by 376.34 %, and the stress change at the rest of the measurement points is small.

Fig. 11 depicts the stress cloud diagram changes of the masonry wall under a flow water velocity of 5 m/s. The flood load increases due to the velocity rise, resulting in large displacement and deformation of the wall. The lower wall experiences severe deformation, including being washed away, while the upper wall undergoes relatively small deformation. However, damage occurs along the through joint in the lower wall, leading to the collapse of the upper wall. The connection between the wall and the structural column exhibits relatively small deformation.

Fig. 11The change process of wall stress cloud map when flood speed is 5 m/s

a) Initial application of loads

b) Progressive change of loads

c) Continuing changes in loads

d) End of load application

4.3. Effect of erosion depth

The erosion depth parameters selected for analysis are 0.1 m, 0.2 m, 0.3 m, 0.4 m, and 0.5 m. A comparative analysis of stress distribution and displacement changes of the masonry enclosure wall was conducted under various erosion depths to investigate the deformation and stress change patterns of the masonry wall concerning erosion depth.

Fig. 12 presents the displacement and stress response of the masonry wall at various measurement points during flooding. Fig. 12(a) shows that when the erosion depth is less than 0.4 m, the displacement at the measuring points of the wall does not change significantly with the increase of erosion depth, and the increase is small. When the erosion depth gradually increases from 0.4 m to 0.5 m, the displacements at measuring points P2 and P3 increase significantly, and the displacements at the rest of the measuring points change less. When the erosion depth is 0.5 m, the displacements at measuring points P2 and P3 are 0.12 m and 0.074 m, which are 104.09 % and 305.14 % larger compared to the erosion depth of 0.1 m. The displacements at measuring points P2 and P3 are 0.12 m and 0.074 m, respectively.

The stress variation of the masonry enclosure under flood load is given in Fig. 12(b). When the erosion depth is less than 0.4 m, there is no significant change in the stress at the wall measurement points. When the erosion depth exceeds 0.4 m, the stress change at measurement point P8 is very significant, and the stress change at other measurement points is small. When the erosion depth reaches 0.5 m, the stress at measuring point P8 is 3.41 MPa, which increases by 193.09 % compared with the erosion depth of 0.1 m. The stress at measuring point P8 is 3.41 MPa, which is 193.09 % higher than the stress at measuring point P8.

Fig. 12The impact of different erosion depths on the wall

a) Changes in displacements with erosion depths

b) Variation of stress with erosion depths

Fig. 13 gives the process of stress cloud changes in the masonry enclosure wall at an erosion depth of 0.5 m. As the depth of erosion increases, the static water load on the upper wall remains unchanged, while the wave load remains largely unchanged, and the dynamic water load increases. The displacements at control point 1, which is most significantly impacted by the flood, are relatively large. Wall panel tensile stresses are then distributed more to the blocks below.

Fig. 13Change process of stress cloud map of the wall when the erosion depth is 0.5 m

a) Initial application of loads

b) Progressive change of loads

c) Continuing changes in loads

d) End of load application