Resistance functions for blast fragility quantification of reinforced concrete block masonry shear walls

Highlights

• Numerical OpenSees model to simulate the out-of-plane resistance of masonry shear walls.

• Investigate the influence of blast variability/uncertainty on the performance of masonry shear walls.

• Blast fragility curves and surfaces are generated for masonry shear walls.

Abstract

Reinforced masonry shear wall (RMSW) systems constructed using concrete blocks are widely used within the current North American construction practices. The limited research carried out on the performance of RMSWs under blast loading has reviled their high vulnerability. This study evaluates the blast performance of such loadbearing and non-loadbearing RMSWs considering the variability associated with different blast wavefront parameters, specifically the positive specific impulse and the peak reflected pressure. In this respect, a concentrated plasticity model is created using OpenSees that simulates the out-of-plane behavior of RMSWs. The model is first validated both statically and dynamically using different experimental datasets. Afterward, the model is utilized within an iterative framework to track the strain rates of different RMSW constituent materials, thus extracting the corresponding dynamic increase factors. Finally, the developed model is used to generate fragility curves and surfaces considering the expected variability/uncertainty in blast wavefront parameters on the response of RMSWs with different axial stress levels and reinforcement ratios. The proposed fragility quantification approach paves the way to develop new blast risk assessment tools for the next generation of blast-resistant construction standards.

Introduction

The interest in quantifying and improving blast-resistant construction performance has been escalating in the last two decades given the increased frequency of terrorist attack events [63], [81]. Generally, an attack using an improvised explosive device can be categorized as either suicidal, vehicle-born, or military [58]. According to the Global Terrorism Database [99], both suicidal and vehicle-borne attacks have exhibited an increasing trend in terms of frequency and impact (i.e., fatalities). Subsequently, several studies have been conducted to develop mitigation measures through either minimizing the structural vulnerability and/or reducing the hazard intensity [4], [24], [39]. However, such measures impose economic constraints as their direct (e.g., strengthening) and indirect (e.g., perimeter security) costs may add up to 30% to the facility construction cost [18].

Although terrorism risks are considered among the most difficult anthropogenic risks to predict [35], blast design provisions (e.g., [4], [24]) are still based on deterministic design-basis threats (DBTs) with only a few recommendations pertaining to the uncertain nature of the blast hazard, structural response and performance, as well as the resulting loss cost and risk [89]. Terrorist attacks utilizing improvised explosive devices are typically characterized by their highly uncertain DBT (i.e., charge weight and standoff distance) and subsequently their induced shock wave parameters. As such, blast hazard reliability analyses have been recommended [68], where the consideration of blast uncertainty even within a deterministic DBT can yield a reliable tool to assess the effectiveness of different blast protective measures [104]. To address this need, different researchers have attempted to include blast hazard uncertainty in the context of a probabilistic-risk-assessment (PRA). For example, Stewart [102] proposed a risk-informed framework to, economically, probabilistically evaluate different blast risk mitigation measures. This framework was utilized later to quantify the risk in terms of annual casualties per building [43], [44]. Other PRA frameworks were presented to probabilistically optimize the application of the blast mitigation measures [107], [104], [32]. These frameworks are capable of considering different sources of blast uncertainties, namely epistemic and aleatory uncertainties [104]. The epistemic uncertainty includes the loading (i.e., detonation charge) and the model (i.e., accuracy of prediction models) uncertainties, while aleatory uncertainty accounts for the inherent variability (i.e., blast environment, etc.) [107].

Several researchers have accounted for different blast uncertainty sources through the assessment of structural and non-structural components [3], [14], [32], [55], [75], [76], [90], [101]. Most of the available literature, accounting for uncertainties, has presented the analysis results through fragility curves. These curves represent the probability of reaching a pre-defined performance state at a specific hazard intensity measure. Within the context of blast design, several intensity measures can be used to characterize the positive/negative phases of the blast wavefront. Although some measures (e.g., negative phase duration) might influence the dynamic response of blast-resistance components, the positive reflected peak pressure (P_r) and the positive reflected specific impulse (I_s) are the most commonly used, as presented in Fig. 1 [109]. In addition, most available blast fragility curves are based on a single intensity measure, specifically I_s at constant P_r [15], [17], [76], [80]. Although this might be valid for components responding within the impulsive regime (i.e., when the blast pressure magnitude does not significantly affect the component response) [76], such an approach might not be applicable to components responding within the dynamic- or the quasi-static regimes (i.e., when the component response is highly influenced by the blast load pulse shape and its pressure magnitude) [45], [76]. As such, a fragility surface approach has been recently introduced to simultaneously account for reflected peak pressure and impulse [76]. Nevertheless, limited number of studies have adopted this approach within the blast performance prediction of different structural- [80] and non-structural [9], [97] components.

Masonry façade/walls are typically selected by designers due to their aesthetic appearance and ease of construction [91]. These walls might be subjected to out-of-plane blast-induced loading scenarios, as observed through far-field explosive testing [11], [14], [46], [64], [74], [98] and simulated blast waves using shock tube tests [113], [77], [78], [23], [60]. However, available studies were limited to only non-loadbearing (i.e., not subjected to axial loads) masonry walls with different boundary conditions that do not well represent the typical RMSWs used in actual construction practices [30]. Subsequently, a reliable computational tool remains needed to assess the blast performance of loadbearing RMSWs. Furthermore, such a tool should account for the multiple sources of blast-related uncertainty as it may result in significant variability of the structural response [16]. Several investigations addressed different sources of masonry-related uncertainties either aleatory or epistemic [55], [61], [70], [75].

The current study first develops a numerical model to simulate resistance functions of fully grouted loadbearing and non-loadbearing RMSWs. The study then utilizes the developed model to investigate the influence of the variability/uncertainty associated with different blast wavefront parameters (i.e., P_r and I_s) on the response of RMSWs. These two wavefront parameters were selected in the current study as they are typically used to estimate the blast performance [96] and are also considered one of the largest sources of blast response uncertainty [70], [103]. In this respect, the study first develops an OpenSees (i.e., [65]) numerical model to simulate the out-of-plane behavior of RMSWs. The developed model is validated against static results based on previous test programs. Following the static model validation, the model is used for blast response predictions utilizing the dynamic increase factors (DIFs) recommended by the USACE [110], and USDOD [111]. The results of the model are also compared to those of a simple (and widely accepted by relevant blast standards) single-degree-of-freedom (SDOF) model such as [4], [24].

The results of the model are also compared to those of a simple (and widely accepted by relevant blast standards) single-degree-of-freedom (SDOF) model [4], [24]. An iterative model is subsequently proposed and validated to assess the impact of using several DIF models on the blast response of RMSWs. The developed model is subsequently utilized to probabilistically evaluate the effect of the blast wavefront variability/uncertainty through generating relevant fragility surfaces. Finally, the model is utilized to quantify the probabilistic effect of different axial stress levels on RMSWs fragility.