© The Author(s) 2025. Published by EDP Sciences and China Science Publishing & Media Ltd.

1 Introduction

Nuclear energy, acknowledged as a low-carbon energy source, is characterized by its high energy density, abundant reserves, and cost-effective operation, positioning it as a pivotal element in China’s energy strategy. To optimize the energy structure and enhance energy security, third-generation nuclear safety technologies are being actively advanced, and more stringent safety standards are being implemented for nuclear power plants.

Squat reinforced concrete shear walls, characterized by a Shear Span Ratio (SSR) of less than 0.5 and renowned for their high stiffness and strength, are widely utilized as major seismic lateral-force-resisting components in critical facilities such as nuclear power plants and industrial structures [1, 2]. Early studies, led by Benjamin and Williams [3], explored their deformation patterns and mechanical behavior, laying a theoretical foundation for subsequent research. However, existing design codes primarily address bending-dominated high SSR walls, whereas squat shear walls typically exhibit shear-dominated failure modes, necessitating unique design approaches. Cardenas et al. [4] observed that the shear strength of squat shear walls under specific conditions can exceed predictions by conventional codes [5, 6], with reinforcement configuration playing a critical role. Salonikios et al. [7, 8] validated the applicability of European and ACI standards for squat shear wall design and highlighted that diagonal reinforcement significantly enhances shear performance.

In recent years, advancements in high-strength materials and sophisticated modeling techniques have driven research into the behavior of squat shear walls under complex loading conditions. Kuang and Ho [9] demonstrated that optimized reinforcement configurations can significantly improve the ductility of non-seismic walls. Gulec [10] analyzed data from 434 experiments and proposed revised design formulas to address gaps in current standards. Additionally, the use of recycled concrete and Ultra-High-Performance Concrete (UHPC) is being actively explored. Peng et al. [11] found that recycled concrete squat shear walls exhibit acceptable seismic performance under specific conditions, offering a sustainable construction approach.

2 Squat reinforced concrete shear walls

2.1 Key features of shear walls

Squat shear walls, characterized by their high stiffness and superior shear performance, are extensively utilized in seismic design and structures requiring resistance to lateral loads. These walls transmit horizontal forces to the foundation through shear action, effectively resisting lateral displacements caused by external forces, thereby enhancing the stability and seismic performance of buildings. In regions with high seismic demands, squat shear walls are employed to ensure the functionality and safety of structures, preventing failures under strong earthquakes or extreme conditions [12].

The design of squat shear walls requires a comprehensive consideration of geometric dimensions, material properties, and load-bearing capacity. Key factors include shear strength, crack control, and seismic energy dissipation capacity to ensure overall stability and seismic performance. These walls hold a critical position in seismic design, making them an essential choice for improving structural safety [13].

2.2 Parameters influencing seismic performance

The seismic performance of reinforced concrete shear walls is governed by critical parameters such as the SSR, Axial Load Ratio (ALR), material properties, and reinforcement ratio. These factors directly affect the wall’s strength, stiffness, ductility, and energy dissipation capacity, which are fundamental considerations in seismic structural design.

The SSR plays a pivotal role in determining the performance of shear walls. Salonikios et al. [7] reported that walls with low SSRs exhibit superior shear performance compared to those with high SSRs but at the expense of reduced ductility. Hence, design strategies need to balance strength and deformation capacity. Wei et al. [14] experimentally demonstrated that with an increasing SSR, the failure mode transitions from shear-dominated to a combination of shear and flexure, accompanied by a significant improvement in ductility.

The ALR has a pronounced influence on seismic performance. Looi et al. [15] observed that a higher ALR enhances load-bearing capacity but decreases ductility and energy dissipation capacity while accelerating stiffness degradation. Li et al. [16] further noted that UHPC walls exhibit excellent shear strength under high ALR; however, their ductility requires further optimization. The selection of an appropriate ALR is especially critical for the design of shear walls in high-rise buildings.

Innovations in material properties have provided new opportunities for improving the performance of shear walls. Hung and Hsieh [17] demonstrated that the incorporation of steel fibers into high-strength concrete significantly improves shear strength and toughness. Li et al. [16] found that steel fibers can enhance the shear capacity and energy dissipation of UHPC walls. Similarly, Peng et al. [11] concluded that recycled concrete, when appropriately designed, can achieve seismic performance comparable to that of conventional concrete, offering a sustainable alternative for construction.

The reinforcement ratio and its configuration are critical factors influencing the seismic behavior of shear walls. Through machine learning analysis of 393 experimental datasets, Mangalathu et al. [18] identified boundary element reinforcement ratios and the wall length-to-thickness ratio as key parameters affecting failure modes. Beyer et al. [19] emphasized that changes in the proportion of shear to flexural deformation influence stiffness degradation and energy dissipation capacity, highlighting the importance of rational reinforcement design in enhancing seismic performance.

Incorporating these key factors into the design process is essential for developing shear walls that exhibit optimal performance under seismic loading conditions.

2.3 Failure mechanisms

The failure modes of squat shear walls are significantly influenced by geometric shape, SSR, reinforcement characteristics, and loading conditions, typically exhibiting shear failure, shear-flexural failure, and flexural failure. In Reference [20], shear wall specimens with SSRs of 1.0, 1.5, and 2.0 exhibited distinct failure modes. Specimen SW1-1 (SSR = 1.0) failed in shear-compression, characterized by “X”-shaped diagonal cracks extending to the top and concrete crushing at the base. Specimen SW2-1 (SSR = 1.5) experienced flexural-shear failure, with inclined cracks in the web and a major horizontal crack at the base, showing moderate capacity loss. Specimen SW3-1 (SSR = 2.0) demonstrated flexural failure, featuring horizontal cracks at the bottom and fewer, gentler diagonal cracks, indicating good ductility. These results illustrate the transition from shear-dominated to flexure-dominated failure as SSR increases, as shown in Figure 1.

Fig. 1 Failure mode of shear wall specimen with different SSR: (a) Shear failure, (b) Shear-flexural failure, and (c) flexural failure [20].

The SSR is a key factor in determining the failure mode, with low SSR walls being prone to shear-dominated failures, including diagonal tension failure, diagonal compression failure, and shear sliding failure [21], as shown in Figure 2. Diagonal tension failure is characterized by horizontal steel yielding and the development of primary diagonal cracks, which are more prominent under high constraint conditions. Diagonal compression failure is primarily caused by the crushing of the web concrete, with widespread cracks but no distinct primary cracks, often resulting in brittle failure. Shear sliding failure is characterized by the yielding of longitudinal steel and the formation of a sliding surface due to bending cracks at the bottom, leading to local concrete crushing and overall failure. These failure modes are closely related to SSR, reinforcement ratio, and material properties.

Fig. 2 Failure modes of squat walls: (a) Diagonal tension, (b) Diagonal compression, and (c) Sliding shear [21].

Although low SSR walls predominantly fail in shear, optimized reinforcement configurations or the use of high-performance materials can result in some degree of shear-flexural failure or flexural failure. In shear-flexural failure, the wall initially exhibits flexural cracking, followed by the gradual expansion of diagonal cracks that lead to shear failure. When the shear capacity is lower than the flexural capacity, the failure mode of the structure shifts from shear-dominated to flexure-dominated. The change in SSR directly influences the transition of the wall from shear failure to shear-flexural or flexural failure [22]. At the same time, the ALR also has a significant impact on the seismic performance of the wall. Under high ALRs, the wall’s ductility and energy dissipation capacity are significantly reduced, and the failure mode of high-performance concrete (such as UHPC) walls may shift from shear-flexural to shear-sliding failure [16].

In recent years, improvements in material properties have provided new possibilities for optimizing shear wall design. The introduction of steel fibers into high-strength concrete or the reasonable use of recycled concrete can significantly enhance shear strength, ductility, and energy dissipation capacity [11, 17]. Additionally, the reinforcement ratio and configuration are also important factors affecting the failure mode. For instance, a high reinforcement ratio at the boundary elements can effectively improve the wall’s bending capacity, while adjusting the shear-flexural deformation ratio can mitigate stiffness degradation [18, 19].

Research on shear wall failure mechanisms has deepened under complex environmental conditions and cyclic loading. Environmental factors, such as acid rain erosion [23], can weaken shear strength, causing the failure mode to shift from shear-flexural to diagonal tension failure. The length of the plastic hinge and the changes in the section compression zone are key control factors for shear-sliding failure [24]. Furthermore, modern research leveraging cyclic softening membrane models and machine learning technologies has explored failure modes from the perspectives of nonlinear hysteretic performance and data-driven approaches, providing more flexible and accurate tools for seismic design [18, 24].

To more accurately predict wall performance and reveal the stress distribution patterns during the failure process, scholars have proposed new analytical methods, such as the truss-arch model [25]. These methods, combining experimental and numerical simulations, provide theoretical support and practical guidance for the design of walls under complex loading conditions. Overall, research on the failure modes of squat shear walls is evolving towards higher performance and more complex environmental conditions, based on SSR, ALR, and reinforcement optimization, offering valuable insights for modern seismic design.

3 RC shear walls with openings

3.1 Advances in research on walls with openings

Shear walls with openings have become a critical focus in structural engineering research in recent years due to the challenge of balancing architectural functionality and structural safety. As primary lateral force-resisting components, the design of openings in shear walls is often necessary to accommodate architectural features such as doors and windows. However, these openings significantly reduce the load-bearing capacity and seismic performance of the walls [26, 27]. Studies have demonstrated that the geometric shape, size, location, and number of openings are key factors affecting the mechanical behavior of shear walls.

Early investigations utilized experimental and theoretical approaches to explore the mechanical behavior of shear walls with openings. Saheb and Desayi [26] experimentally analyzed the effects of openings on the cracking patterns and ultimate loads of shear walls and proposed corresponding predictive formulas. Guan et al. [27] employed nonlinear finite element analysis to study the stress distribution and mechanical performance of walls with various opening configurations, confirming that openings weaken both axial strength and stiffness.

Recent studies have focused on the mechanical performance of shear walls under complex opening configurations and diverse loading conditions. Mosoarca [28] demonstrated that staggered openings accelerate stiffness degradation and significantly reduce wall ductility, proposing a classification of failure modes based on different opening arrangements. Wang et al. [29] experimentally evaluated the shear behavior of shear walls with eccentric openings under cyclic loading, highlighting that stress concentrations caused by eccentric openings accelerate localized damage, leading to premature failure, as shown in Figure 3. Di Trapani et al. [30] investigated the cyclic performance of infill walls with openings and found that the shape and position of openings significantly influence failure modes and deformation capacity. For instance, regular-shaped openings cause less reduction in wall performance compared to irregular-shaped openings.

Fig. 3 Scheme of crack propagation [29].

Current design standards for predicting the strength and stiffness of shear walls with openings are often conservative. Studies by Fares [31] and Mohamed El-Beshlawy [32] indicate that empirical formulas in existing codes do not adequately reflect the actual performance of shear walls with openings in practical applications. They recommend modifying current design models based on experimental data to enhance both safety and economic efficiency. For example, incorporating influence coefficients or correction factors can more accurately quantify the weakening effects of openings.

In summary, research on shear walls with openings spans foundational experiments, numerical simulations, and design standard optimization. Future studies should focus on the integration of complex opening arrangements with realistic loading conditions to develop more precise predictive models and design methodologies, providing effective and safe guidance for engineering practice.

3.2 Influence of opening size on wall performance

The size of openings is a critical parameter affecting the performance of shear walls, as it determines their strength, stiffness, and seismic behavior [33–36]. Studies indicate that the ratio of the opening area to the total wall area directly influences wall performance. When the opening ratio exceeds 20%, a significant reduction in wall stiffness is observed [34, 37]. Li et al. [33] developed a method for analyzing the initial stiffness of shear walls with openings and experimentally validated the nonlinear stiffness degradation trend for walls with large openings.

Experimental results also show that an increase in the opening area significantly impacts the hysteretic behavior and energy dissipation capacity of the walls. Tafheem et al. [35] found that while additional reinforcement can partially restore wall strength, its effect on stiffness improvement is limited. Furthermore, Liu et al. [37] investigated the performance of walls with post-formed openings reinforced with steel plates. Their findings reveal that reinforcement measures significantly enhance wall ductility, achieving a 58% improvement in ductility.

For small openings (with an opening ratio below 10%), Yu et al. [38] found that their impact on the flexural behavior of slender walls is limited, and deformation is primarily controlled by flexure. In contrast, large openings substantially reduce the seismic capacity of walls. Stress concentrations caused by openings accelerate crack propagation, adversely affecting the cumulative energy dissipation capacity of the walls [39].

3.3 Impact of opening layout and position

The position and arrangement of openings are critical factors determining the performance of shear walls, as they directly influence stress distribution, crack propagation, and failure modes [28, 29, 40, 41]. Central openings in shear walls significantly reduce shear strength, while edge-near openings have a comparatively smaller impact on strength [28, 36]. For instance, Hosseini et al. demonstrated that eccentric openings substantially alter wall ductility and energy dissipation capacity, leading to premature local failures [42].

Different opening layouts also have distinct effects on wall performance. The crack propagation patterns observed in squat shear walls are significantly influenced by the presence of openings, as highlighted by Saheb and Desayi [26] and Guan et al. [27]. Initially, microcracks form at regions of high stress concentration, particularly around the corners of openings, due to the redistribution of stresses caused by the discontinuity in the wall panel. As loading increases, these microcracks coalesce into major diagonal cracks, which typically extend from the corners of the openings toward the compression zones at the wall base. This diagonal cracking is a hallmark of shear-dominated behavior, as openings disrupt the load path, resulting in localized stress concentrations and modified crack patterns, as shown in Figure 4. Mosoarca [28] investigated staggered openings and highlighted that cracks primarily concentrated around the openings hinder the formation of plastic hinges. Zhang et al. [36] found that horizontally distributed multiple openings result in lower ductility and energy dissipation capacity, whereas vertically distributed multiple openings better maintain overall stiffness and seismic resistance.

Fig. 4 Wall panels and failure mode [27].

Research has further shown that the symmetry of openings significantly impacts wall performance. Ou et al. [39] observed through experiments that openings located in the central web area have the greatest adverse effect on lateral resistance, while openings near the edges or sides better preserve wall performance. Additionally, Xu et al. [43] experimentally verified that cracks in multi-opening walls primarily concentrate around the junctions of openings, suggesting that the influence of openings on stress behavior should be carefully considered in practical design.

Future studies should focus on optimizing opening layouts and enhancing designs under complex loading conditions. For example, Sabau et al. [40] and Khan and Srivastava [41] indicated that adjusting the position of openings and incorporating rigid elements can optimize stress distribution, thereby improving the overall seismic performance of shear walls.

4 Advanced numerical analysis of shear walls

4.1 Overview of numerical simulation techniques

Numerical simulation techniques provide essential tools for studying the behavior of reinforced concrete shear walls under complex loading conditions. Early research focused primarily on material mechanical properties and foundational mechanical models. For instance, Scott et al. [44] analyzed the effects of load eccentricity and strain rates on reinforced concrete elements through experimental studies and proposed a stress-strain curve for confined concrete under high strain rates, laying a foundation for understanding concrete behavior under seismic conditions. Subsequently, Gomes and Appleton [45] introduced an improved Menegotto-Pinto model, accounting for the inelastic buckling effects of reinforcement, offering a novel numerical method for simulating cyclic characteristics of steel materials.

With the increasing scale of buildings and the complexity of loads, researchers have developed modeling methods suitable for complex shear wall structures. Lu and Chen [46] proposed a nonlinear macro-model for coupled shear walls, which successfully simulated the interaction of bending, shear, and axial forces validated through experimental data. Additionally, Wallace [47] emphasized that the coupling effect of shear and bending in core walls and shear walls of high-rise buildings significantly influences overall performance, highlighting the importance of detailed treatment in modeling.

In recent years, numerical simulation has become central to studying the seismic performance of high-rise buildings. Lu et al. [48, 49] developed a finite element-based model that simulated building collapse under extreme seismic actions for the first time, as shown in Figure 5. Their subsequent research on the OpenSees platform developed new shear wall element models [50], effectively simulating seismic behavior in super high-rise buildings while significantly improving computational efficiency and prediction accuracy.

Fig. 5 (a) Multi-layer shell element and (b) Distribution of the rebar layer [48].

4.2 Simulation of shear wall behavior and performance

Shear walls exhibit complex behaviors under seismic loads, and researchers have explored key factors influencing their performance through numerical models. Hallinan and Guan [51] used the layered finite element method to study the performance of walls with openings, finding that side constraints and openings significantly influence wall strength, providing parameters for optimized design. Ding et al. [52] employed a mixed beam-shell model to capture shear deformation in reinforced concrete coupled walls, demonstrating the model’s reliability in predicting complex wall deformations.

Regarding the shear performance of walls, Kolozvari et al. [53] evaluated five finite element models in detail, concluding that they performed well in capturing yield and peak loads but showed variations in predicting crack distributions. Additionally, Isaković and Fischinger [54] introduced a force-displacement multi-vertical line element model capable of accurately simulating shear transfer mechanisms and nonlinear responses of shear walls.

For slender walls under specific load conditions, Cheng and Zhang [55] developed a finite element model on the VecTor2 platform. Results showed that the model accurately predicted the peak strength and ultimate deformation capacity of slender walls under axial tension and cyclic loads, providing robust tools for design. Kolozvari et al. [56] further integrated 2D and 3D shear-flexural interaction models, significantly enhancing computational efficiency and prediction accuracy, as shown in Figure 6.

Fig. 6 Prediction of different finite element models [56].

4.3 Modeling complex behaviors and failure modes

Under extreme loads, shear walls exhibit diverse failure modes, including flexural, shear, and mixed failure. Lu et al. [48] simulated the seismic collapse processes of 10-story, 18-story, and 20-story buildings, identifying potential structural weaknesses. Ji et al. [57] found through experimental studies on T-shaped walls that the ALR significantly influences failure modes, and displacement-based design methods effectively enhance wall deformation capacity.

Under complex boundary conditions, Wang et al. [50] investigated shear walls with openings, finding that the role of braces and rod nodes significantly affects wall performance. Cheng et al. [58] further studied the impact of variable axial tension-compression loads on shear wall shear behavior, revealing that loading history significantly influences hysteretic responses. These studies highlight the importance of accurately modeling local and overall wall behavior under extreme environments and complex conditions to improve design precision.

5 Discussion

The study of squat shear walls, perforated shear walls, and their numerical simulations yields the following conclusions:

Squat shear walls, characterized by a low aspect ratio and high load-bearing capacity, are widely applied in seismic and impact-resistant structures. However, their complex stress characteristics make them prone to shear failure. Research highlights that ALR, reinforcement ratio, and loading conditions significantly influence ductility and energy dissipation. Effective design must optimize these factors to balance strength and ductility, thereby enhancing overall seismic performance.

Perforated shear walls are extensively used to meet functional requirements, yet the shape, location, and number of openings substantially affect their mechanical performance. Openings near the wall’s centre markedly reduce shear strength, while edge openings have a lesser impact. Different layouts yield varied shear failure modes and ductility, with vertical openings better-preserving stiffness and horizontal openings offering inferior ductility. Optimized designs should balance functional demands with proper reinforcement to improve performance.

Numerical simulation serves as a vital tool for studying shear wall behavior under complex loading conditions. From material constitutive models to layered shell element methods, simulations demonstrate high accuracy in predicting nonlinear behavior and failure modes. These techniques significantly enhance computational efficiency, providing robust support for seismic design in high-rise buildings and complex scenarios.

To further advance the understanding and application of squat shear walls in seismic-resistant structures, several key research directions are proposed. First, the performance of squat shear walls under multi-hazard scenarios, such as combined seismic, blast, and fire loads, should be investigated to enhance their resilience in critical infrastructure. Second, the use of advanced materials, including UHPC and fiber-reinforced polymers, could be explored to improve the strength, ductility, and durability of squat shear walls. Third, innovative design methodologies, such as performance-based approaches that account for the unique nonlinear behavior of squat shear walls under extreme loading conditions, need to be developed and validated. Fourth, the long-term durability of squat shear walls under environmental effects, such as corrosion and fatigue, should be assessed to ensure their sustainability over the lifecycle of structures. Finally, large-scale experimental tests and high-fidelity numerical simulations are essential to validate and refine existing design models. Addressing these research gaps will not only improve the current understanding of squat shear walls but also promote their wider application in seismic-resistant design.

Funding

Research supported by the Technologies R&D Project of China State Construction Engrg. Corp. LTD (No. CSCEC-2023-Z-8), Technologies R&D Project of China Construction First Group Corporation Limited (No. PT-2022-09), National Natural Science Foundation of China (Grant No. 52378150).

Conflicts of interest

The authors have nothing to disclose.

Data availability statement

This article has no associated data generated.

Author contribution statement

Lichang Zheng: Writing – Original Draft Preparation, Investigation, Formal analysis; Dongmei Wang: Writing – Review & Editing, Resources; Guoshan Xu: Methodology, Funding acquisition; Wei Zhou: Conceptualization, Funding acquisition; Changhai Zhai: Conceptualization, Resources. All authors contributed to the study’s conception and design. All authors read and approved the final manuscript.

References

All Figures

	Fig. 1 Failure mode of shear wall specimen with different SSR: (a) Shear failure, (b) Shear-flexural failure, and (c) flexural failure [20].
In the text

	Fig. 2 Failure modes of squat walls: (a) Diagonal tension, (b) Diagonal compression, and (c) Sliding shear [21].
In the text

	Fig. 3 Scheme of crack propagation [29].
In the text

	Fig. 4 Wall panels and failure mode [27].
In the text

	Fig. 5 (a) Multi-layer shell element and (b) Distribution of the rebar layer [48].
In the text

	Fig. 6 Prediction of different finite element models [56].
In the text