Study on Rapid Repair Method of Earthquake Damaged Pier Column Based on Multi-Level Fortification

Abstract

As a critical component of lifeline engineering, bridges play a vital role in post-earthquake rescue and disaster relief efforts. The rapid repair of earthquake-damaged piers is essential to ensure the uninterrupted functionality of lifeline systems. This paper presents a novel method for the rapid repair of earthquake-damaged pier columns using steel sleeves, based on a multi-level fortification approach, integrating numerical simulation, structural design, and experimental research. In alignment with the multi-level fortification requirements, the structural form of the outer steel sleeves was designed, key influencing factors were analyzed, and a design scheme for the outer steel sleeve was proposed. Furthermore, a quasi-static test was conducted to evaluate the seismic performance of the pier columns before and after repair. The results indicate that the maximum horizontal load the pier can withstand after repair is approximately 40% higher than that before the damage. When the pier’s bearing capacity reaches its maximum value, the horizontal displacement increases from 29.15 mm to 95.65 mm, indicating a significant improvement in the seismic performance of the repaired pier. Failure initiates with the buckling of the brace, followed by the buckling of the steel sleeves, demonstrating a multi-stage failure mode. This mode satisfies the requirements of multi-level fortification, with enhanced ductility achieved while maintaining the pier column’s bearing capacity, thereby enhancing the protection of the foundation.

1. Introduction

Since the beginning of the 21st century, earthquake disasters have occurred frequently, causing significant damage to social development. As a critical lifeline infrastructure, bridges play a vital role in post-earthquake rescue and disaster relief efforts. The piers, being ductile components of the bridge, are designed to absorb and dissipate seismic energy when the bridge is subjected to an earthquake. Consequently, bridge piers are often subjected to substantial damage during seismic events [1,2].

In recent years, some scholars have conducted relevant research on the reinforcement of piers. Usually, the mechanical properties of piers are enhanced by wrapping different materials on the outside of the piers, including concrete, steel plates, carbon fiber cloth, and some new composite materials [3,4,5,6,7,8].

Chen Zheng-Chan et al. [9] found that the stiffness and overall bearing capacity of the reinforced piers were improved to a certain extent by adding longitudinal reinforcement and stirrups, and casting concrete with formwork or directly using shotcrete. Jiang Ji-Tong et al. [10] studied the stress hysteresis phenomenon of flexural members reinforced with enlarged cross-sections, and suggested that the reduction factor of the newly added steel bar strength in the reinforcement specification be changed from 0.9 to 1.0. However, the influence of shrinkage creep was not considered in this paper. At the same time, Montes O et al. [11] believed that the reinforcement efficiency of concrete for earthquake-damaged piers decreases with the increase in pier height, and its application is limited when the pier height is high. This method involves extensive wet work and prolonged construction periods, which significantly limits its applicability in emergency situations requiring the rapid resumption of traffic. Carbon fiber cloth reinforcement refers to the method of pasting carbon fiber cloth on the surface of the pier column or pasting the damaged pier column section on the surface after casting concrete with a support mold [12]. Chen X [13] repaired low-reinforcement gravity piers by adhesive steel and carbon fiber cloth. The test results showed that the lateral bearing capacity of the piers was increased by more than 100%, and further research is needed on the reasonable reinforcement thickness. With the rapid advancements in the engineering materials industry, numerous innovative materials, such as SMAs (shape memory alloys), have been utilized for pier reinforcement [14,15]. However, SMAs are relatively cost-prohibitive compared to conventional engineering materials. In pier reinforcement, balancing reinforcement effectiveness with associated engineering costs is essential. Careful evaluation of this balance can maximize the overall benefits. Some scholars [16,17] apply steel sleeves to the periphery of piers for reinforcement. Experimental studies have shown that the stiffness and bearing capacity of piers can be greatly improved. When reinforcing damaged piers, the steel sleeve can also play the role of a template, making it convenient to grout between the steel sleeve and the pier to repair the damaged concrete, greatly reducing the construction difficulty and construction period.

Most existing studies have focused on bridge piers with inadequate seismic performance, and fewer studies have explored the reinforcement and repair of earthquake-damaged bridge piers, particularly via rapid reinforcement methods. Rapid reinforcement and repair of earthquake-damaged bridge piers facilitate timely restoration of traffic, ensure the swift progression of emergency rescue efforts, and are crucial for safeguarding lives and property. This paper addresses the multi-level seismic fortification and rapid reinforcement requirements of bridges and introduces an innovative external steel sleeve rapid reinforcement method. Leveraging existing technological advantages, multi-level fortification and rapid reinforcement are achieved through the optimization of structural measures, detailed design, simplification of external steel sleeve forms, and improved construction processes. The seismic performance of the repaired earthquake-damaged reinforced concrete piers is validated through low-cycle reciprocating tests.

2. Design of New Jacket Steel Casing Structure

According to the Specifications for Seismic Design of Highway Bridges [18], bridge seismic design follows a two-stage design approach. Under E1 earthquake conditions, the structural strength and stiffness largely remain unchanged. Under E2 earthquake conditions, localized damage is permissible. In line with this, this paper proposes a new type of outer steel sleeve structure designed to achieve multi-level defense, as illustrated in Figure 1. In addition to meeting the two-stage fortification requirements, the proposed design addresses potential impacts of more severe earthquakes. The outer steel sleeve is designed to be restorable and replaceable in the event of auxiliary structure damage, ensuring functional recovery.

The system consists of two semicircular steel sleeves (“1” in Figure 1), diagonal bracing, and a bottom plate. Flanges (“2” in Figure 1) on both sides of the semicircular steel sleeves include bolt holes for assembly, with bolts connecting the two semicircular jackets into a unified structure. Preloading the pier column enhances the restraint effect of the steel sleeve. The damaged concrete is restored using grout between the steel sleeve and the earthquake-damaged pier column, strengthening their connection. A bottom plate is included at the base of the steel sleeve, with ground anchor holes provided for securing the sleeve to the cap using ground anchor screws (“3” in Figure 1). Diagonal braces are welded between the steel sleeve and the bottom plate (“4” in Figure 1) to provide additional stability.

The new type of outer steel sleeve achieves the concept of multi-level defense after the pier column is repaired and satisfies the requirements of a stepped failure mode. The specific analysis is as follows:

• (1). Under an E1 earthquake, the outer steel sleeve and the pier column remain elastic, with no structural damage.

• (2). Under an E2 earthquake, the diagonal brace on the steel sleeve experiences tension or compression, yielding to absorb seismic energy. The rest of the steel sleeve and the pier column remain intact and operational. Additionally, the diagonal brace buckles but can be efficiently replaced to restore its functionality.

• (3). For earthquakes exceeding the E2 level, the bottom of the pier column sustains partial damage; however, the overall bridge structure remains stable.

Thus, the stepped failure mode—diagonal brace buckling followed by partial damage to the pier column—is achieved, satisfying the criteria for multi-level defense.

The new type of outer steel sleeve rapid construction process is as follows:

• (1). After the bridge is damaged by an earthquake, the damage information is obtained in time, and the site measurement is carried out to determine the damage status and repair plan.

• (2). Unload the superstructure, straighten the piers and restore their elevation.

• (3). Clean the broken concrete at the bottom of the pier and clean the surface dust.

• (4). Drill and clean the holes according to the design of the outer steel sleeve, and then install the outer steel sleeve to ensure that the bolts are installed in the correct position.

• (5). Install the chemical anchors into the holes to ensure that the chemicals are fully cured, and then grouting is carried out, and early-strength self-compacting grouting material is selected.

• (6). Within 6 h after grouting, prestress the high-strength bolts on the outer steel sleeve through equipment, and enter the maintenance state after completion. The entire repair process can be completed within one day.

After the pier is repaired, if the diagonal brace is damaged due to aftershocks, it is necessary to weld the diagonal brace to meet the seismic performance target of the pier under the action of aftershocks.

Currently, most domestic bridge reinforcement measures address the presence of cracks in existing bridges or deficiencies in the reinforcement design of old bridges. There is little research and practical implementation concerning the reinforcement and repair of earthquake-damaged bridges in China. The construction technology used to repair pier columns with this structure enables the rapid repair and reinforcement of earthquake-damaged pier columns, minimizing traffic interruption and ensuring cost-effectiveness. This structure can be repaired post-earthquake and is capable of withstanding frequent aftershocks. A notable feature is its ability to achieve multi-level fortification in repaired pier columns, meeting the requirements of the stepped failure mode. It meets ductility targets at both material and structural levels, thereby enhancing the ductility of repaired piers. The reinforcement and repair of bridges after earthquakes hold significant social importance.

3. Analysis of Main Influencing Factors of New Outer Steel Sleeve

The circular single-column reinforced concrete pier is used as a case study for analysis. Based on the reinforcement test model detailed in Part 3, the main parameters of the pier are as follows: the cross-sectional diameter is 450 mm, and the pier height is 1800 mm. The concrete is classified as C40, and the longitudinal reinforcement consists of HRB400-grade steel bars with a diameter of 18 mm, totaling 8 bars, resulting in a longitudinal reinforcement ratio of 1.28%. The stirrups are HRB400-grade steel bars with a diameter of 10 mm, densely distributed within the bottom 600 mm of the pier, with a spacing of 60 mm and a stirrup ratio of 1.28%. Outside the densified region, the stirrup spacing is 120 mm, with a stirrup ratio of 0.64%. The dimensions of the component base (pedestal) measure 1900 mm in length, 900 mm in width, and 600 mm in height. The dimensions of the top loading area measure 600 mm in length, 600 mm in width, and 500 mm in height. The specimen dimensions and reinforcement are illustrated in Figure 2.

3.1. Analysis of the Influence of Steel Casing Structure

The comparative analysis is mainly conducted on several different structural forms, including the steel sleeve alone, the steel sleeve with a bottom plate, and the steel sleeve, bottom plate, and diagonal brace. The thickness of the steel sleeve, bottom plate, and diagonal brace is 5 mm, and the height is 650 mm, as shown in Table 1. The material of the steel sleeve is Q235 steel.

As illustrated in Figure 3, the ABAQUS (CAE 2016) finite element model of the pier column and repair steel sleeve was established. The concrete was simulated using solid elements, the longitudinal reinforcement and stirrups were simulated using truss elements, and the outer steel sleeve was simulated using shell elements. The ground anchor bolt was simulated using connection elements, with the other end fixed after coupling with the bottom plate of the steel sleeve. The bearing capacity was set according to the ground anchor bolt’s design capacity determined during the actual test. The concrete material constitutive model employs the CDP model provided by ABAQUS, with uniaxial compression and tension formulas as specified in the standards [19]. The CDP model, full name Concrete Damaged Plasticity, is designed for applications in which concrete is subjected to monotonic, cyclic, and/or dynamic loading under low confining pressures. The concrete constitutive structure is shown in Figure 3. The steel bar material constitutive model utilizes the reload stiffness degradation bilinear hysteresis model proposed by Clough [20], which can simulate the bond between ordinary steel bars and concrete in reinforced concrete piers. The hysteresis rule is shown in Figure 4. The outer steel sleeve material constitutive model employs a bilinear model [21], with the plastic stiffness taken as 1/1000 of the initial elastic modulus. The specific constitutive relationship of the outer steel sleeve is shown in Figure 5.

Completely fixed constraints are applied on both sides of the pier base loading. For the anchor bolt, a connector is used for simulation, and a fixed constraint is applied at the lower end of the connection.

To simulate the test process of the external steel sleeve repair, penalty function friction was employed to model the interaction between the steel sleeve and the concrete. The steel sleeve was temporarily deactivated during the initial loading pre-damage of the pier column using the life and death unit. Once the pier column reached the damaged condition following initial loading, the external steel sleeve and its contact with the pier column concrete were activated. Finally, the finite element model shown in Figure 6 is established.

A vertical load is applied to the center of the top of the pier in order to simulate the effect of the superstructure on the pier. A horizontal load is applied to the side of the cap beam, and the loading system refers to the low-cycle reciprocating test in Section 3.1 of this paper.

To verify the accuracy of the finite element model, Figure 7 compares the experimental hysteresis curve with the finite element results before and after the pier column repair. The hysteresis curve of the pier column simulated by the finite element model before repair aligns closely with the experimental results. From the horizontal loading phase to the peak load phase, the finite element model accurately replicates the stiffness changes in the pier column. However, during the phase from the peak bearing capacity to the bearing capacity limit, the finite element results exhibit a more rapid decline in bearing capacity compared to the experimental data. In the unloading phase, the stiffness degradation simulated in the finite element model during the latter half of the unloading phase is less pronounced than observed in the test. Overall, the ABAQUS finite element software effectively simulates the bearing capacity changes before the pier column repair, enhancing the reliability of simulating the repair of earthquake-damaged pier columns.

According to the finite element calculation results, the resulting skeleton curve is presented in Figure 8. As can be seen from the figure, when the steel sleeve alone is applied, the horizontal bearing capacity of the repaired component RA1 is 150.58 kN, which is only 9.05% higher than that of the original column A1. Upon the addition of the bottom plate, the bearing capacity of the repaired pier column RA2 is 21% higher than that of the pier column RA1 without the bottom plate, and 32.4% higher than that of the original column. Upon the addition of the diagonal brace, the bearing capacity increases by 1.44% compared to the case without the diagonal brace, but the degree of improvement is small. It can be seen that the effect of adding the diagonal brace on the bearing capacity is limited; however, the diagonal brace provides energy dissipation after yielding.

In terms of stiffness, the initial stiffness of the repaired pier RA2 was 41.8% higher than that of the pier RA1. After further setting the diagonal brace, the initial stiffness of RA3 was 36.5% higher than that of RA2. Upon setting both the diagonal brace and the bottom plate simultaneously, a higher level of ductility was observed. Since the grouting filling after the concrete damage was not taken into account, the initial stiffness of the pier after repair was lower than that of the pier before repair. In actual tests and engineering, due to the implementation of subsequent grouting, the stiffness recovery of the pier will improve to some extent compared to the finite element results.

Through the above comparative analysis, after adopting the structural form of the steel sleeve, bottom plate, and diagonal brace, the bearing capacity and stiffness of the repaired bridge pier are significantly improved; therefore, this structural form is selected for further analysis.

3.2. Analysis of the Influence of Steel Sleeve Thickness

The RA3 repair scheme proposed in the above analysis emphasizes the significant impact of steel sleeve thickness on the stress distribution within the pier column. Therefore, this section primarily analyzes the influence of steel sleeve thickness on the pier column’s performance. The main parameters used in the analysis are listed in Table 2. The height is set at 650 mm, with a thickness of 5 mm for both the bottom plate and diagonal brace. Chemical anchors are used for anchoring. The skeleton curves for different steel sleeve thicknesses are shown in Figure 9, while the stress distribution is illustrated in Figure 6.

From the skeleton curve shown in Figure 5, it can be observed that the peak bearing capacity of the repaired pier column increases with the thickness of the steel sleeve. For steel sleeve thicknesses of 2 mm, 3.5 mm, 5 mm, and 10 mm, the peak bearing capacities are 158.38 kN, 174.34 kN, 180.04 kN, and 188.70 kN, respectively. These values correspond to 117.28%, 128.14%, 131.37%, and 136.69% of the original pier column’s peak horizontal bearing capacity of 135.05 kN, before repair.

As the steel sleeve thickness increases, the initial stiffness of the repaired pier column improves. However, it is still lower than the initial stiffness of the pier column before repair. This is because the finite element simulation does not consider the grouting, which restores the bottom concrete’s function after damage. From the perspective of the horizontal bearing capacity, the repaired pier column’s bearing capacity increases as the steel sleeve thickness increases.

Figure 10 shows the stress distribution on the steel sleeve at different thicknesses. When the thickness of the steel sleeve is less than 5 mm, the stress distribution is uniform, and the stress levels are higher, enabling the steel sleeve to perform well. However, when the steel sleeve thickness reaches 10 mm, the stress becomes concentrated at the upper side of the steel sleeve and the middle position of the loading side. Additionally, as the steel sleeve thickness increases, the maximum stress on the steel sleeve begins to decrease, and the rate of decrease gradually slows down. This is because the increased stiffness of the repaired pier column leads to the upward movement of a plastic hinge when the steel sleeve reaches a certain thickness. Therefore, when repairing a pier column, it is crucial to balance the pier column’s bearing capacity and calculate an appropriate steel sleeve thickness to meet the seismic performance requirements after repair.

3.3. Steel Sleeve Design

Through the analysis in the previous section, it is finally determined that the thickness of the outer steel sleeve bottom plate in this test is 10 mm, and the thickness of both the semicircular steel sleeve and the diagonal brace is 5 mm. Ref. [22] recommends the reinforcement height $l_j\ge 0.25L$ of the outer steel sleeve for reinforcing the pier column $l_j\ge D$, where D is the diameter of the pier column and L is the height of the pier column. In the US standard [23], it is mentioned that the predicted height of the plastic hinge area is the larger value of 1.5 times the height of the pier column in the bending direction, the height of the area where the bending moment exceeds 75% of the maximum plastic bending moment, and 0.25 times the distance from the maximum bending moment point to the inflection point. Based on the finite element results and the actual height of the pier column damage, the height of the outer steel sleeve is determined to be 675 mm. At the same time, in order to facilitate grouting during the later reinforcement of the pier column, the diameter of the steel sleeve is designed to be 500 mm, which is slightly larger than the diameter of the earthquake-damaged pier column. In terms of the bottom plate design, holes are pre-drilled at the chemical anchor bolt position on the bottom plate with a hole diameter of 50 mm. Each semicircular bottom plate has four anchor holes that are ground later. The specific structure of the outer steel sleeve is shown in Figure 11.

In order to enable the assembly of the two semicircular steel sleeves into a unified structure and ensure sufficient restraint during the grouting of the pier column, they are fixed using bolts. Small flanges are welded on both sides of each semicircular steel sleeve, with pre-drilled bolt holes provided on each flange. The diameter of each bolt hole is 20 mm, as shown in Figure 12.

In this test, the gap between the steel sleeve and the pier column, as well as the crushed concrete at the bottom of the pier, were grouted with H60 ultra-fine grouting material. This material is known for its ultra-fine composition and early strength development. The compressive strength of this grouting material is provided in Table 3 below.

4. Experimental Study on Strengthening Pier Columns

In order to verify the difference between the mechanical properties of the repaired pier and the initial pier, a low-cycle reciprocating test was carried out on the pier. The test model used in the reinforcement test is shown in Figure 2.

4.1. Experimental Plan

1. Test equipment

The component is subjected to low-cycle repeated loading under a constant axial force. Based on the concrete material test, the vertical axial pressure corresponding to a 10% axial pressure ratio is calculated to be 570.96 kN. A vertical force is applied to the top of the pier using a 1000 kN hydraulic jack, with the axial force distributed to the pier via a distribution beam. The horizontal force is applied by the Moving Target Simulator (MTS) actuator with a maximum thrust of 960 kN. The test loading setup is illustrated in Figure 13 and Figure 14.

The displacement of the loading end at the top of the pier is automatically collected by the MTS actuator control system. In order to avoid the error of the control system and the error caused by the slight relative slip between the pier base and the rigid ground, a wire displacement meter is also arranged at the top and base of the pier, as shown in Figure 15.

• 2.. Measurement point arrangement

In order to study the damage of stirrups and longitudinal reinforcement after pier column damage, 8 and 9 resistance strain gauges are arranged on one side of the longitudinal reinforcement and stirrup, respectively, in this test, and both sides of the loading side are arranged. Considering the difference in positive and negative loading, the specific arrangement of strain gauges is shown in Figure 16.

When designing the steel sleeve, diagonal braces were added. In order to measure the stress distribution and changes of the steel sleeve diagonal braces, strain gauges were also arranged on the diagonal braces as a measurement method. Resistive strain gauge measuring points were arranged on the steel sleeve. The specific arrangement of strain gauges and the actual on-site pasting are shown in Figure 17.

• 3.. Loading system

To ensure the comparability of subsequent test data, the loading regime for the piers before and after repair remains consistent. According to the Specification for Seismic Testing of Buildings [24], each load level is repeated once before yielding and three times after yielding, continuing until the horizontal bearing capacity reduces to 85% of the maximum load or the specimen exhibits significant damage and becomes unsuitable for further loading. Due to test constraints, loading was displacement-controlled, with displacement applied by the MTS actuator while maintaining an axial compression ratio of 10%. To prevent accidents caused by test uncertainties, loading was terminated upon longitudinal reinforcement failure or a sudden change in bearing capacity. The specific loading regime is illustrated in Figure 18.

4.2. Analysis of Test Results

1. Failure form of specimen

   • (1). Original column failure form

     The specimen was subjected to horizontal displacement loading. When the loading displacement reached 6 mm, two transverse cracks appeared on the loading side of the specimen, located 10 cm and 40 cm from the pier bottom, as shown in Figure 19a. As the horizontal displacement at the pier top increased to 10 mm, the horizontal cracks propagated toward the non-loading side. When the displacement reached 20 mm, a distinct crushing sound was observed at the bottom of the pier. At a displacement of 40 mm, the horizontal bearing capacity of the component reached 140.42 kN, marking the peak horizontal bearing capacity. At 50 mm displacement, significant peeling of concrete occurred on both sides of the loading side of the pier bottom. As the displacement continued to increase, the peeling surface expanded upward and laterally. When the displacement reached 60 mm, the concrete was crushed, as shown in Figure 19b. At 100 mm displacement during the second loading cycle, longitudinal reinforcement fractured, resulting in a sharp decline in bearing capacity, and the test was terminated. The specimen exhibited bending failure. The concrete crushing area of the pier column was primarily concentrated within 500 mm of the pier base, extending downward in a fan-shaped pattern, as shown in Figure 19c. After removing the crushed concrete, it was observed that a longitudinal reinforcement bar on the loading side was broken, as shown in Figure 19d.

   • (2). Damage form of pier column after repair

     The damaged pier column was repaired with an outer steel sleeve, with the main parameters identical to those described in Section 3.3. After the repair, the pier column underwent pseudo-static loading using the same method as the original column. At horizontal displacements of 3 mm and 6 mm, no cracks or other observable phenomena occurred. At a displacement of 10 mm, fine cracks emerged in the tensile zone of the concrete at the upper end of the steel sleeve. When the displacement increased to 30 mm, cracks appeared in the bonding zone between the steel sleeve and the grouting material, as shown in Figure 20a. At a displacement of 80 mm during the first loading cycle, buckling of the diagonal brace at the bottom of the steel sleeve was observed, as shown in Figure 20b. At 100 mm displacement, the protective layer of the pier column’s upper section began to peel off, as shown in Figure 20c. When the displacement reached 120 mm, crushing of the concrete above the external steel sleeve was observed. Simultaneously, it was noted that the displacement of the pier column below the top of the steel sleeve decreased. At a horizontal displacement of 140 mm, the bearing capacity dropped sharply, accompanied by the distinct sound of internal steel bar failure, leading to the termination of the test.

2. Hysteresis performance

The hysteresis performance reflects the seismic performance of the component by recording the entire process from elasticity to destruction. Through the hysteresis curve of the component, the skeleton curve, stiffness degradation, energy dissipation and displacement ductility of the component can be indirectly obtained, thus reflecting the seismic performance of the component from all aspects.

Figure 21 shows the displacement-load hysteresis curves of the original pier and the repaired pier. From the load-displacement hysteresis curve of the original pier in Figure 15, it can be seen that the hysteresis loop is shuttle-shaped and has a good pinching effect during the entire process of the pier from being elastic to elastoplastic to plastic. In the initial stage of loading, the component is in an elastic state with a large stiffness. As the loading displacement increases, the horizontal bearing capacity of the component reaches the maximum value. As the displacement continues to increase, the stiffness decreases until a longitudinal reinforcement in the pier breaks, the horizontal bearing capacity drops sharply, and the loading stops.

The hysteresis curve of the repaired pier is a full shuttle shape. Compared with the original pier, it has good seismic performance. The component reaches the extreme value of bearing capacity under a larger loading displacement, and the reinforced component has a slower bearing capacity growth rate than the prototype pier in the process of reaching the extreme value of bearing capacity. When the displacement of the prototype component reaches the ultimate load of 100 mm, the bearing capacity of the repaired component is still greater than that before the repair.

• 3.. Skeleton curve

In order to intuitively see the ultimate bearing capacity of the component, the skeleton curve comparison diagram before and after the repair of the component is given, as shown in Figure 22. As can be seen from Figure 22, the maximum positive horizontal load of the repaired pier is 190.42 kN, which is 135.6% of the maximum horizontal load of the prototype pier of 140.42 kN. The maximum negative horizontal load is 172.26 kN, which is 146.9% of the maximum negative horizontal load of the prototype pier of 117.28 kN. After the use of the outer steel sleeve for repair, the horizontal bearing capacity of the pier can be effectively restored and improved to a certain extent. When the bearing capacity of the repaired pier reaches the maximum value, the horizontal displacement is 95.65 mm, which is significantly improved compared with the displacement of 29.15 mm when the prototype pier reaches the maximum horizontal bearing capacity. It can be seen from the structural skeleton curve diagram before and after the repair that the initial stiffness of the repaired pier is greater than that of the unrepaired pier, which is more obvious during the process of negative displacement loading, and the yield strength of the structure is also improved to a certain extent compared with before the repair.

• 4.. Stiffness degradation

According to the Building Seismic Test Specification [24], the stiffness of a component is represented by the secant stiffness. The secant stiffness K_i is determined using the following equations:

(1)$K_i={\displaystyle \frac{\left|+F_i\right|+\left|-F_i\right|}{\left|+X_i\right|+\left|-X_i\right|}}$

where +Fi, −Fi are the loads at the ith positive and reverse peak points; and +Xi, −X_i are the displacements at the ith positive and reverse peak points.

Figure 23 is a comparison of the stiffness degradation of the bridge piers. As can be seen from Figure 23, the stiffness degradation curve of the repaired piers has a similar overall profile to that of the original piers. The stiffness of the repaired piers is generally greater than that before the repair. At the same time, the stiffness of the repaired piers has a slower degradation process than that of the original piers. The piers can effectively restore their seismic performance after repair.

In the early stage of loading, the stiffness of the repaired pier is slightly greater than that of the original pier, and the stiffness of the pier can be effectively restored. As the displacement load increases, the repaired pier shows greater stiffness. This is because the outer steel sleeve plays the role of stirrups, which can produce effective restraint stress on the grouting material between the repaired pier and the steel sleeve, improve the deformation capacity of the concrete, and enable the concrete to still participate in the earthquake resistance after being compressed. At the same time, the steel sleeve can vertically provide a part of the bending resistance lost after the yielding and rupture of the longitudinal reinforcement.

• 5.. Displacement ductility

Ductility reflects the plastic deformation capacity of the structure and reflects the seismic performance of the structure. The ductility coefficient is generally defined as follows:

(2)$\mu ={\mathsf{\Delta }}_u/{\mathsf{\Delta }}_y$

where Δy is the load value when the structure reaches yield, and Δu is the ultimate deformation of the component. In this paper, the deformation of the component corresponding to the load value on the hysteresis curve dropping to 85% of the maximum load value is taken as the ultimate deformation. The yield displacement, ultimate displacement and displacement ductility coefficient obtained from the hysteresis curve of the repaired pier are shown in Table 4.

As can be seen from Table 4, the ultimate displacement of the repaired pier is 120 mm, which is larger than that of the original pier, and is 120% of the original pier limit. The displacement ductility coefficient of the repaired pier is 7.06, which is 112.96% of that of the original pier. The repaired pier can effectively improve the ultimate displacement of the pier and improve the displacement ductility coefficient of the pier to a certain extent.

• 6.. Energy consumption capacity analysis

Energy dissipation capacity refers to the ability of a structure to dissipate seismic energy when it is subjected to an earthquake. It is an important indicator for evaluating seismic performance. When a bridge is subjected to an earthquake, plastic hinges are generated at the bottom of the pier and energy is dissipated. This paper uses the energy dissipation coefficient E and the equivalent viscosity coefficient ζ_eq to evaluate the energy dissipation capacity of components, which can be calculated according to the following formula:

(3)$E={\displaystyle \frac{S_{(ABC+CDA)}}{S_{(OBE+ODF)}}}$

(4)${\zeta }_{eq}={\displaystyle \frac{1}{2\pi }}\cdot {\displaystyle \frac{S_{(ABC+CDA)}}{S_{(OBE+ODF)}}}$

where: S_(ABC+CDA)—the area enclosed by the hysteresis curve in Figure 24;

S_(OBE+ODF)—sum of the areas of triangles OBE and ODF in Figure 24.

As can be seen from Figure 25, the energy dissipation coefficient and viscous damping coefficient of the repaired pier are generally smaller than those of the prototype pier, indicating that the energy dissipation performance of the repaired pier is worse than that of the original specimen, but it still basically restores the energy dissipation performance of the prototype pier.

• 7.. Stress and strain

  1. (1). Strain before repair

     Figure 26 illustrates the variation in longitudinal reinforcement strain with height in the damaged original pier column, with the pier bottom height set as the zero point. When the horizontal displacement of the pier top is between 3 mm and 6 mm, the strain values of the longitudinal reinforcement at various heights are relatively low, with a gradual increase in strain. At a loading displacement of 6 mm, the strain in the longitudinal reinforcement at a height of 400 mm above the pier bottom reaches 9.96 με. This is due to the fact that the pier remains in an elastic state initially during loading. As the loading displacement of the pier top increases, the longitudinal reinforcement strain value rises significantly, although the strain change remains confined within the 0 mm to 400 mm height range of the pier. The strain increase at 280 mm above the pier bottom is particularly pronounced, indicating that the longitudinal reinforcement is under significant tensile stress at the pier bottom, where the concrete is severely damaged by compression. The longitudinal reinforcement strain along the height of the pier column changes less compared to during the early stages of loading, with the exception of the pier bottom, and the maximum value remains within 1000 με. It can be concluded that, apart from the plastic hinge area, the damage to other parts of the pier column is minimal or negligible. In actual comparison, the damage to the prototype pier is primarily concentrated at the bottom of the pier column, and only cracks appear at other locations along the height of the pier, with no concrete crushing. The strain in the longitudinal reinforcement further confirms the damage to the pier column. Therefore, the primary focus should be on the plastic hinge region at the bottom of the pier during the repair process.

  2. (2). Strain changes after repair

     The stress variation in the outer steel sleeve reflects the strength of the restraint it provides to the core concrete, thereby evaluating the working performance of the steel sleeve. Figure 27 illustrates the stress variations in the steel sleeve under varying loading displacements after the pier was repaired with the external steel sleeve. As can be seen from the figure, in the early stage of loading displacement, when the horizontal displacement is small, the strain in the steel sleeve increases rapidly. As the loading displacement gradually increases, the rate of strain increase in the steel sleeve gradually decreases. This is due to the fact that the damage to the pier occurs on the upper side of the steel sleeve, and the effectiveness of the steel sleeve is diminished. The strain in the longitudinal reinforcement of the pier before repair shows that the tensile stress of the longitudinal reinforcement is mainly concentrated within 600 mm above the bottom of the pier, which is consistent with the crushing area of the concrete at the bottom of the pier. The repair height of the pier can be effectively controlled during the repair process.

5. Conclusions

• (1). A design scheme for the outer steel sleeve structure that enables stepped damage, multi-level defense, and rapid reinforcement is proposed. A new outer steel sleeve rapid construction process is presented. The key influencing factors, such as the steel jacket structure and thickness, are analyzed, and an improved optimal design scheme for the outer steel sleeve parameter combination is proposed.

• (2). The test results indicate that, after repair, failure initially occurred in the diagonal brace, followed by a transfer of failure to the pier, demonstrating a stepped failure mode. Before repair, the hysteresis curve of the pier was full with more noticeable pinching; after repair, the hysteresis curve exhibited a shuttle shape, demonstrating improved seismic performance. After repair, the horizontal peak bearing capacity of the pier was restored to its pre-repair level. The ductility coefficient increased by 12%, and stiffness degradation was slower, indicating improved ductility.

• (3). The rapid repair method for earthquake-damaged piers proposed in this paper is applicable to a wide range of concrete bridge types, including simply supported beam bridges, continuous beam bridges, and rigid frame bridges. Additionally, the appropriate steel plate thickness, reinforcement height, and prestressing force can be tailored to meet the seismic requirements of bridges in different seismic fortification intensity zones, ensuring compatibility with reinforcement needs across varying seismic zones and demonstrating significant potential for widespread application.

Author Contributions

Conceptualization, X.X. and X.L.; Methodology, S.X.; Validation, L.Y. and S.X.; Formal analysis, L.Y. and S.X.; Investigation, L.Y. and X.C.; Data curation, H.W.; Writing—original draft, X.X., L.Y. and X.L.; Writing—review & editing, X.X., L.Y., H.W., X.C., S.X. and X.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures and Tables

Table 1

Main structural form.

Serial Number	Thickness/mm	Height/mm	Structural Form
A1	0	0	Original column
RA1	5	650	Steel sleeve only
RA2	5	650	Steel sleeve and base plate
RA3	5	650	Steel sleeves, braces and base plates

Table 2

Main parameter values.

Model Number	Steel Sleeve Thickness/mm	Repair Height/mm
B1	0	0
RB1	2	650
RB2	3.5	650
RB3	5	650
RB4	10	650

Table 3

Material parameters of grouting material.

Design Value of Compressive Strength (MPa)	Compressive Strength (MPa)
45	44.95

Table 4

Comparison of displacement ductility.

Specimen Type	Yield Displacement Δy (mm)	Limit Displacement Δu (mm)	Displacement Ductility Factor	Yield Load (kN)	Ultimate Load (kN)
Original column	16	100	6.25	117	119
Repair column	17	120	7.06	136	190

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