Progressive Collapse Of Structure Research Articles

Risk-based life cycle cost–benefit analysis for progressive collapse design of RC frame structures

Progressive structural collapse is a typical low-probability high-consequence event. Progressive collapse design can effectively improve the robustness of structures against accidental local damage and reduce the probability of collapse. However, progressive collapse design also increases the construction cost of buildings. Hence, it is necessary to conduct cost-benefit analyses for the progressive collapse design of building structures. This study first designs a reinforced concrete (RC) frame based on a progressive collapse design program that simultaneously optimizes material consumption and structural resistance. Then, the structural failure probability is quantified using an alternative path (AP) method-based fragility analysis that considers the structural uncertainties. Based on this, the life cycle costs and benefits of the structure designed with different design load factors are investigated. A four-story RC frame is used as an example. By considering the time value of money and threat probability, the break-even points and optimized design load factors for the progressive collapse design of the RC frame are analyzed. These research outcomes can help promote progressive collapse design in engineering practice and provide references for proposing scientific and reasonable design load factors.

A comprehensive review of ultra-high performance concrete (UHPC) behaviour under blast loads

Blasts resulted from industrial/residential accidents and deliberate attacks can impose extremely hazardous loading conditions upon nearby structures. The repercussions of these blasts encompass not only direct effects such as blast overpressure and fragments but also indirect outcomes like progressive collapse of structures. In the pursuit of enhanced protection for concrete structures, substantial endeavors have been directed towards developing innovative construction materials with outstanding properties, among which the ultra-high performance concrete (UHPC) has emerged as a notable representative. Drawing from existing experimental, numerical and theoretical studies, this paper presents an inclusive overview of recent progress in UHPC structural members (slabs, beams and columns) and UHPC-based composite structures (mesh reinforced UHPC, UHPC-filled steel tube and UHPC strengthening of normal reinforced concrete (NRC) structures) in their ability to withstand blast loads. While discussing the exceptional material and structural dynamic performance of UHPC, recommendations are offered for the further research directions in utilising UHPC structures to resist blast loads, which include exploring eco-friendly UHPC, integrating 3D printing technology and employing machine learning analytical methods.

Multi‐indicator evaluation method of important members of truss string structures

SummaryDuring the past decade, the progressive collapse of structures has received growing attention, and the study of member importance is a key step for investigating the progressive collapse resistance. However, traditional methods for evaluating the member importance usually employ a single indicator, and when multiple indicators are involved, different indicators may generate different member rankings. Moreover, the truss string structure is a multiple super‐stationary structure with many members, and the current studies mainly focus on cable failure, which does not mean that other members are not important. In this study, the initial selection of important members is first performed based on concept evaluation, and then, the alternate path method is used to analyze the progressive collapse resistance of truss string structures; the slope degradation coefficient γ of incremental dynamic analysis curve, load capacity degradation coefficient β, and nested load capacity degradation coefficient β′ are introduced; and the sensitivity coefficient SIj and fragility coefficient VIi are defined with axial force as the structural response. Based on the above five indicators, two cases are conducted to evaluate the member importance. The analysis results show that the cable and the bottom chord member at the support are evaluated as the first‐level important members. Through the analysis of different indicators, it is found that the regularity of the coefficient of each member is inconsistent for different indicators. The results could be one‐sided if the important members were evaluated by a single indicator only. In addition, the second‐level important members of truss string structures are evaluated by multi‐indicator analysis. Finally, the nominal progressive collapse resistance of truss string structures is given based on the importance coefficient of the first‐ and second‐level important members.

Damage and failure of semi-rigid steel joints during progressive collapse

Ductile metal materials during a ductile failure will suffer from micro-void damage, simulation of which can contribute to the prediction of the macro fracture of steel structure. In this paper, the Gurson-Tvergaard-Needleman (GTN) constitutive model which describes the aggregate failure of metal voids is selected as the constitutive relation to investigating the damage evolution and fracture of semi-rigid joints in steel structures during a progressive collapse. During the process, specific parameters of the GTN model of steel are confirmed based on the combined results of the test and numerical simulation. The progressive collapse of two kinds of semi-rigid joints of steel pipe-to-H shaped steel were simulated by a nonlinear finite element method. A comparison between the simulation and test results verified that the GTN constitutive model can accurately simulate the fracture failure of the steel semi-rigid joints. Besides, a simplified joint failure model based on concentrated plastic hinge theory is proposed. Considering the damage and fracture of semi-rigid joints and the collision contact among different components, the progressive collapse of the semi-rigid steel frame structure is simulated by explicit dynamic analysis based on a finite particle method. Afterwards, the dynamic response of the structural progressive collapse can be predicted more accurately.

Collapse-resisting mechanism and damage propagation pattern of suspended-domes following sudden cable loss

This paper aimed to reveal two important mechanisms that determine the survival of suspended-domes subjected to a sudden cable rupture scenario: the mechanism for the initial local damage to be arrested by the remaining structure, and, the mechanism for the local damage to propagate throughout the remaining structure in case it is not fully arrested. A test was performed on a scale-down suspended-dome model respecting all structural details. After one of the outer-ring hoop cables was suddenly ruptured by an innovative remotely-controlled cable-breaking device, the remaining structure established an alternative path at the outer ring, tying the remaining hoop cables, and thereby regained balance. Complementary finite-element analysis was performed and validated. Other cable rupture scenarios were investigated, for which the alternative path for hoop cables was also confirmed. The cable rupture-induced damage, characterised primarily by the relaxation of hoop cables, was able to transmit outwards and inwards to the other rings of the suspended-dome, during which the relaxation of diagonal cables was a critical step. The hoop cable relaxation propagated easier inwards than outwards, and the rupture of outer-ring hoop cable caused the most severe damage. The failure of a hoop cable and resultant relaxation of neighbouring cables would effectively turn the suspended-dome into a single-layer latticed dome within the local range of failure, and point buckling of the latticed dome may occur and even cause structural progressive collapse. The failure of one diagonal cable would hardly cause the hoop cable to relax and thus normally caused no further damage.

Design Optimisation for Cable Dome Structures Based on Progressive Collapse Resistance

This study proposed a framework of optimal design for flexible cable dome structures based on progressive collapse resistance. First, a quantitative evaluation method for nonlinear robustness based on robustness control theory to reflect the structural progressive collapse resistance was proposed. Second, an actual engineering structure was used as a case study to evaluate the effects of design parameters on structural robustness. Finally, a genetic algorithm was used as an optimisation algorithm to further optimise the element cross-section and the structural shape and obtain a combined optimisation rate. The results indicated that increasing the element cross-sectional area, decreasing the structural span, and increasing the rise-to-span ratio effectively improved the structural robustness. The structural robustness was also effectively improved through the optimal design of element cross-sections by increasing element cross-sections sensitive to structural robustness and decreasing those insensitive to structural robustness. In this study, the combined optimisation rate was 38.27%, which was not only greater than the individual optimisation rates of 11.2% for element cross-sectional area optimisation and 22.5% for structural shape optimisation but also the sum of these two rates.

Dynamic Increase Factors for progressive collapse anaylsis of steel structures accounting for column buckling

AbstractMan‐made hazards, such as fire, explosions, or impacts, may induce the progressive collapse of structures, in which the localised failure spreads from the single affected structural component to other parts of the structure. A typical approach to model progressive collapse consists in performing static column removal analyses considering a Dynamic Increase Factor (DIF), whose determination becomes paramount to account for the dynamic effects related to a sudden column loss scenario. Current recommendations on the definition of such factor mainly consider a beam‐type collapse in non‐linear analyses, though different mechanisms, e.g., column buckling, may govern progressive collapse events. This paper presents the determination of the DIFs through a numerical procedure for five steel structures with an increasing number of storeys. Both global and local imperfections are modeled to account for the geometric non‐linearities of the structure and column buckling. DIF values are obtained considering two different Engineering Demand Parameters (EDPs), suited for describing beam‐type and column‐type mechanisms respectively. The evaluated DIFs are compared with the values recommended in the current UFC design prescriptions for progressive collapse, and considerations on the choice of the appropriate DIF values are provided.

Analysis and Evaluation of the Progressive Collapse of Cable Dome Structures Induced by Joint Damage

The current literature lacks an effective progressive collapse analysis of a cable dome structure induced by joint damage. In this study, a dynamic analysis was performed using actual construction cases, an ANSYS LS-DYNA analysis platform, and a fully dynamic equivalent load instantaneous removal method. First, the structure’s dynamic responses and collapse modes induced by different joints with different types of damage were explored. Subsequently, joint importance coefficients were proposed depending on the structure’s displacement before and after joint removal, and the relationships between the joint importance coefficients and the joint properties and collapse modes, respectively, were then identified. Finally, the relationship between the joint damage and the connected component damage was explored. The results revealed that different joints and identical joints with different types induced a variety of dynamic responses. However, the dynamic response induced by the discontinuous joint damage was more apparent than that induced by the continuous joint damage. When a continuous joint model was used, the damage on all joints did not result in the progressive or local progressive collapse of the structure. Thus, all these joints were considered as common joints. However, when a discontinuous joint model was used, the failure of the joints resulted in three distinct collapse modes, namely a progressive collapse, a local progressive collapse, and a nonprogressive collapse, corresponding to the key joints, the important joints, and the common joints, respectively. These three types of joints corresponded to different importance coefficients. When damage occurred in the discontinuous joints separately linked to the key components, the important components, and the common components, the joints resulted in the progressive collapse, local progressive collapse, and nonprogressive collapse, respectively, of the structure.

PDEM-based reliability assessment of RC frames against progressive collapse considering initial local failure

With the increased frequency of progressive collapse events, an accurate and efficient reliability-based method for preventing potential structural collapse has become a research focus. Several methods for structural reliability against progressive collapse have recently been proposed; however, they ignore the effect of initial local failure, which may have a significant influence on risk management in protecting structures against progressive collapse. Therefore, this study developed a computation framework for assessing the overall reliability of reinforced concrete (RC) frames against progressive collapse that considers the impact of the initial local failure. The proposed framework quantifies the overall reliability of the structure using the full probability method, which comprises three levels of determination of the initial local failure location, initial local failure assessment, and structural progressive collapse analysis. The efficient probability density evolution method (PDEM) was then employed to calculate the initial local failure probability and structural progressive collapse probability, which are required for achieving a trade-off between computational efficiency and accuracy. Thereafter, the developed framework was applied to a prototype RC frame, in which the structural resistance was captured using 3-D macro-based numerical modeling, which was initially validated by experimental data. Finally, the overall reliability of the RC frame was evaluated according to three different failure criteria, and based on reliability results, various structural strengthening strategies were discussed. Results show that the developed framework can effectively quantify the impact of initial local failure on the reliability of RC frames against progressive collapse. The overall reliability of the structure increases as the input energy decreases. When the input energy greater than or equal to 132 kJ, the overall reliability of the structure investigated is 0.933 for the ultimate damage criterion.

Nonlinear Dynamic Assessment of a Steel Frame Structure Subjected to Truck Collision

The progressive collapse of structures subjected to a truck collision with ground floor columns is numerically investigated in this paper. For this purpose, a four-story steel building with a dual system (including an intermediate steel moment frame, with a special concentric steel bracing system in the longitudinal (x) direction, and an intermediate steel moment frame in the transversal (y) direction) is considered. The structure, which was designed according to AISC, ASCE7 and 2800 Iranian seismic standard guidelines, is located in seismic-prone area and subjected to eight different truck collision scenarios. The nonlinear dynamic analyses carried out in ABAQUS on a three-dimensional finite element (FE) numerical model include variations in collision features (i.e., mass and speed of the truck, the height of collision point), and are used to support the analysis of expected damage. The presented results confirm that increasing the truck mass and speed increases damage entity for the column and structure. Several influencing parameters are involved in damage location and progressive evolution. The height of the collision point from the ground also significantly affects the magnitude of structural damage, especially in terms of stress peaks in the panel zones for the target column. Finally, the perimeter columns are more vulnerable to impact than corner columns, in structures with dual system as with the examined four-story building. The presence of a bracing system parallel to the impacting vehicle can in fact reduce the deformation—and thus the expected damage—of the adjacent target column. Most importantly, it is shown that the numerically reproduced collision scenarios (and the associated damage configurations) based on truck impact are significantly more severe than those artificially created based on the conventional column removal method (i.e., alternate path (AP) analysis approach), which confirms the importance of more sophisticated numerical calculation procedures to investigate and assess the progressive collapse of structures.

A Review Paper on Progressive Collapse Analysis of Different Shell Structure: A Critical Review

Abstract: Progressive collapse occurs when one of the structural members fails, causing other structural members to fail. This leads to the collapse of all or part of the structure. Failure of a vertical structural member is the most common cause of progressive structural collapse Explosive charges, accidents or deliberate destruction can cause the column to fail and collapse. The analysis is performed by removing the columns at different locations one by one according to General Service Administration (GSA) guidelines, and then evaluating the radius and column DCR values. The results concluded that the column removed from the center is more vulnerable to progressive collapse.

Progressive collapse design optimization of RC frame structures using high-performance computing

Structural progressive collapse design is essential for improving the robustness of structures against accidental local loads. In this study, a design framework was developed for optimizing the nonlinear dynamic progressive collapse design of reinforced concrete (RC) frame structures. An objective function featuring both structural response and material consumption was combined with a cluster computing technology and the global optimization algorithm to optimize a structure for resisting progressive collapse. A four-story RC frame was taken as an example. The design framework was adopted to achieve precise control of its structural progressive collapse response with optimization of the material consumption to the maximum extent. The design outcomes of global and sequential design schemes, including structural resistance and material consumption, were compared to devise the best optimized progressive collapse design strategy. This research can serve as a reference for the development of efficient and accurate structural progressive collapse design methods.

Shaking table test study on dynamic performance of a base-isolated frame structure under an isolation bearing removal scenario

Studies on the progressive collapse of structures have been at the forefront in structural engineering domain recently. The progressive collapse of isolated structures is quite different from that of conventional fixed-base structures. Once an initial failure occurs in the isolation layer which is the most vulnerable to accidental events due to the low horizontal stiffness, progressive failures at other locations may lead to a large-scale collapse of isolated structures. This paper presents a 1:4 scale model shaking table test of a three-story irregular plane reinforced concrete (RC) frame isolated structure to investigate the progressive collapse resistance of isolated structures. An edge bearing was removed quickly by an electromagnetic failure excitation device during the first seismic input case. The dynamic responses such as the macroscopic crack distribution, acceleration responses, displacement responses, internal forces of the isolation bearings, and concrete and reinforcement strains of the failure span beams were evaluated. The results show that the significant vertical deformation with dynamic impact response was produced at the failure point under multi-directional dynamic coupling excitation, i.e., the combined effect of the vertical unbalanced load caused by sudden failure of a bearing and horizontal earthquakes. This sudden failure of the isolation bearing not only had an impact on the internal forces of bearings adjacent to the failure bearing, but also on other non-adjacent bearings. As the tensile and compressive stress of adjacent bearings were more likely to exceed design limits under earthquakes, the risk of overturning collapse for isolated structures markedly increased following the failure of a few bearings. In addition, vertical and low-frequency components of earthquakes could have a significant influence on dynamic responses and damages of isolated structures, especially in the area of bearing failure. The experimental results obtained in this study act as important references for the progressive collapse design of isolated structures.

Probabilistic progressive collapse assessment for RC framed-wall structure

Since the progressive collapse of structures could cause disastrous consequences for humans and society, therefore assessing and improving the vulnerability of our buildings against progressive collapse is urgently needed. The current research presents a high-fidelity simulation procedure for an existing RC framed-wall structure and aims to investigate the structure’s resistance to progressive collapse under column/shear wall removal scenarios at different levels through deterministic analysis. Based on the considered removal scenarios, the dynamic effect of the sudden column/shear wall removal is studied, and a simple procedure to predict the vertical reaction of the neighboring columns/shear walls to the removed one is proposed with a dynamic amplification factor (DAF) 1.80 and 2.40 for the column and shear wall removal, respectively. The results revealed that the sudden column/shear wall removal at the higher floor is more critical than the lower one; since more floors participate in absorbing the released energy in the latter. Moreover, in some cases, the horizontal displacement resulting from the sudden shear wall removal is found to be more critical than the vertical displacement. Since there are several sources of uncertainties that significantly affect the building resistance to progressive collapse and the deterministic analysis neglects these uncertainties; therefore, it cannot quantify the failure probability of the structures. Consequently, based on the deterministic analysis results, the critical removal scenario is selected to perform the stochastic analysis via the probability density evolution method (PDEM), where both the stochastic response and the instantaneous probability density function (PDF) can be obtained. Finally, the failure probability of the studied structure is assessed using the PDEM combined with the absorbing boundary condition. The stochastic analysis revealed that the maximum vertical displacement increased to roughly 1.6 times its value compared with the deterministic analysis. Simultaneously, a failure probability of approximately 40% is recorded through the stochastic analysis, while no global or even local collapse is observed in the deterministic analysis.

Study on mechanism and influential factors of progressive collapse resistance of base-isolated structure

The progressive collapse of the structure caused by the partial failure of the structure will cause severe consequences and massive losses, and structural progressive collapse resistance has always been a hot topic of current research. In order to study the progressive collapse mechanism of base-isolated structures, the test study and numerical simulation of the base-isolated structures were carried out based on the vertical Pushover method and analysis of the variation rule of the capacity of the remaining structure and influence mechanism. The isolation bearing failure position, the size of the beam of the seismic isolation layer, the type of the isolation bearing, and the horizontal stiffness of the seismic isolation layer on the capacity of the remaining structure were compared and analyzed. The results show that the non-uniformity of the beams and the concentrated loading at the nodes were easy to form a linear catenary mechanism, resulting in more severe beam end damage than mid-span damage. In the case of side isolation bearing failure, due to the lack of sufficient lateral restraint, the capacity was significantly lower than other conditions, which were more likely to cause partly collapse. Therefore, setting more transfer paths to improve the structure’s resistance to progressive collapses was necessary. Increasing the size of the beam of the seismic isolation layer could improve the capacity of the remaining structure of the alternate load path in the base-isolated structure. The changes in the horizontal stiffness of the seismic isolation layer and the type of the isolation bearing have little effect on the progressive collapse resistance capacity of the remaining structure.

Theoretical study on progressive collapse of truss string structures under cable rupture

Cables are critical components of truss string structures and cable failure can cause serious damage to the structure or even progressive collapse. However, little theoretical research work deals with this phenomenon. In this study, a rapid analysis method for the progressive collapse of truss string structures based on the nonlinear buckling material model was proposed. The results showed that the rapid analysis method could reduce the computational time by at least 30% and effectively improve computational efficiency. Based on the validated rapid analysis method, the progressive collapse failure mechanism of truss string structures under cable rupture was analyzed. The results showed that progressive collapse failure mechanisms could be divided into two categories. In one category, compression buckling of the upper chord member leads to a loss of load capacity and a rapid increase in deflection without convergence, resulting in progressive collapse of the structure. In the other category, tensile yielding of the lower chord member results in a gradual loss of stiffness and a slow increase in deflection without convergence, leading to progressive collapse of the structure. Moreover, a series of assumptions and simplifications were made, followed by the establishment of calculation equations for the progressive collapse load capacity and deflection of truss string structures under cable rupture. By comparing the theoretical values with the finite element values as well as test values, the accuracy of the equations proposed in this study for calculating the progressive collapse load capacity and deflection of truss string structures was verified.

Creep behavior of Grade 10.9 high-strength bolts under and after fire

• Experiments were conducted on creep behaviour of Grade 10.9 high-strength bolts under and after fire. • The Field & Field model is calibrated for simulating creep behavior of high-strength bolts at elevated temperatures. • The temperature, load ratio and loading duration are key factors affecting the creep behavior of T -stub connections. • High-strength bolts have more obvious creep deformation at high temperatures than high-strength steels. • A reduction factor is recommended to consider the creep effect on determining strength of T -stub connections in Eurocode 3. High-strength bolts are widely used in beam-column connections of high-rise steel framed buildings. At the event of a fire, high-strength bolts may experience significant creep in a state of both high stress and high temperature, leading to fracture of connections and even progressive collapse of structures . This paper experimentally and numerically investigates the creep behavior of Grade 10.9 high-strength bolts under and after fire. The creep strain–time curves at different temperatures and stress ratios are obtained using DIC systems. The micromorphology and failure mechanism of high-strength bolts is examined by SEM. The Field & Field creep model is calibrated against test results, and parametric studies are conducted on creep behavior of T -stub connections. The experimental results show that the creep deformation of high-strength bolts is significant at high temperatures, and the creep strain is positively correlated with temperatures and stress ratios. While the creep effect of high-strength bolts after fire can be ignored. The creep-induced fracture of high-strength bolts under fire is in a ductile manner, and that after fire is in a brittle manner. High-strength bolts have more obvious creep phenomenon at high temperatures than high-strength steels, and it is unsafe to directly apply creep data of high-strength steels to high-strength bolts. The numerical results show that the Field & Field model is suitable for characterizing the creep behavior of high-strength bolts under fire with an applicable temperature range of 20–600 °C and stress ratio range of 0.4–0.8. The temperature, load ratio and loading duration significantly affect the creep behavior of T -stub connections under fire conditions. A reduction factor of 0.8 for 500 °C and 0.6 for 600 °C is recommended to consider the effect of creep on the strength of bolts in determining bearing capacity of T -stub connections in Eurocode 3. It is necessary to consider the effect of creep for predicting the fire behavior of high-strength bolts and steel connections, ensuring a safe design.

Performance of the CFST column to composite beam connection under static and impact loads

A progressive collapse of structures is usually triggered by extreme incidents, especially explosions and impacts, resulting in a dynamic response that differs from the conventional column removal scenario. However, the design solutions in the criteria may not be applicable for evaluating the progressive collapse resistance of structures under the impact load. To ascertain the influence of the high strain rate effect, a finite element (FE) study is conducted on the CFST column to composite beam connection under impact and static loads. The failure modes and resistance mechanisms for two types of composite connections under the two loads are compared. Moreover, the effects of different impact energies on the impact load, vertical deflection, vertical force, and energy dissipation are discussed by varying the impact mass and velocity. Finally, the dynamic increase factors (DIFs) based on force, deflection, and energy with various impact energies are investigated. It is found that the impact load is chiefly contributed by the inertia effect (IE) at initial loading stage and by the flexural action (FA) at large deformation stage. Interestingly, the vertical force for the connection under an impact loading is negative before the approximate plastic chord rotation (θy). Although the peak impact force, maximum vertical deflection, and energy absorption ratio all increase with the impact energy raised, the former is more sensitive to impact velocity, and the latter two are more sensitive to impact mass. Moreover, a series of findings from the study demonstrate that the DIFs based on force, deflection, and energy under the impact load are significantly different from the conventional dynamic load.

Investigation on the progressive collapse resistance of three-dimensional concrete frame structures reinforced by steel-FRP composite bar

Compared with conventional steel bars, steel-FRP (fiber reinforced polymer) composite bars (SFCBs) have distinctive post-yield stiffness, and the high efficiency of SFCBs in enhancing the progressive collapse resistance of concrete frames has been confirmed by recent quasi-static experimental studies on SFCB beam–column subassemblages. However, the realistic progressive collapse of structures is a dynamic process, and the three-dimensional (3D) effects are essentially important for determining the collapse response. In this study, numerical models are built to explore the progressive collapse behavior of 3D frame structures reinforced by SFCBs. The static and dynamic capacities of five SFCB frames and one reinforced concrete (RC) frame are compared under different column–removal cases. Results show that by virtue of the post-yield stiffness, the static load factors of SFCB frames are much larger than those of RC frames at the same deformation, proving that SFCB frames have better robustness against collapse failure than RC frames. After the dynamic removal of columns, all RC frames are subjected to progressive collapse failure, while SFCB frames can successfully complete the dynamic load redistributions and quickly reach a steady state. Further, the dynamic increase factor (DIF) of SFCB frames is proposed based on the ratio of maximum dynamic flexural responses to static flexural responses of beam joint sections under the same gravity loads (1.2 times dead load plus 0.5 times live load), and the conservative DIFs of 1.55 and 1.3 are recommended for a corner column–removal case and the other single column–removal cases, respectively. Finally, parametric analyses are conducted to reveal the effect of beam longitudinal reinforcement ratio, beam span-to-depth ratio, and dynamic duration for the column removal on the progressive collapse resistance of SFCB frames. The results lay a foundation for the progressive collapse design of 3D SFCB frame structures.

Evaluation on the progressive collapse resistance of infilled reinforced concrete frames based on numerical and semi-analytical methods

The effect of infill walls on the progressive collapse behaviour of reinforced concrete (RC) frames should be fully considered due to the formation of alternative load paths. To explore the configuration that could affect the progressive collapse resistance of infilled RC frames, parametric analyses are performed based on the validated simulation method. In the study, the impact introduced by the extra tie and integrity rebars in walls is emphasised. It is indicated that the variation in the reinforcement ratio of tie rebars leads to a limited change in structural progressive collapse resistance. In contrast, with the arrangement of the integrity reinforcement, the progressive collapse resistance of the infilled frames is enhanced and the propagation of the diagonal cracks in partial infill walls is suppressed. The notable re-ascending trend in the resistance curve for models with integrity rebars reveals the significant development of the catenary action in the integrity reinforcement. Then, with the help of linear regression and gene expression programming (GEP) techniques, a semi-analytical model is proposed for the prediction of the load-bearing capacity of infilled frames after column loss. In the prediction model, the linear effect of geometrical parameters and the non-linear effect of openings on the progressive collapse resistance are included by introducing three modification coefficients. Based on the statistical assessment, the capability of this explainable model is verified, and the appropriate amount of integrity reinforcement to mitigate the progressive collapse is discussed.