Vulnerability and risks of collapse of structural concrete walls in regions of low to moderate seismicity

© 2016 Dr. Abdulrahman Sulaiman AlbidahReinforced concrete shear walls are prevalent lateral load-resisting systems in buildings. Elaborate design and detailing provisions are required to ensure ductile behaviour, and to avoid premature shear failure. In regions of low to moderate seismicity like Australia, a significant number of existing (particularly old) reinforced concrete buildings have only been designed to withstand wind and gravitational loads, and have not been checked for seismic resistance. Consequently, lateral load-resisting systems in such buildings, including shear walls, are of non-ductile construction featuring low longitudinal reinforcement content and poor confinement. Research described in this thesis was mainly concerned with the seismic performance behaviour of slender lightly reinforced concrete shear walls employing the displacement-based assessment procedure (which involves making realistic estimates of the imposed seismic demand for comparison with the wall resistant capacity). Buildings that are supported by lateral-load resisting elements of non-ductile detailing could still perform satisfactorily in a low, or moderate, intensity earthquake typifying design scenarios in regions of low to moderate seismicity. Satisfactory performance of low ductility shear walls in certain earthquake scenarios is considered possible in view of findings from experimental studies of pre-cast, and cast in-situ, reinforced concrete columns (Kafle 2011; Rodsin 2007) and from field observations in earthquake events. A survey conducted by Wood, Wight and Moehle (1987) following the 3 March 1985 earthquake (M=7.8) in Chile revealed that the majority of buildings sustained only minor, to moderate, damage. Out of a total of 415 buildings surveyed, only 6 buildings experienced catastrophic damage. Shear walls performed reasonably well, in spite of the fact that detailing provisions for walls in Chile are less strict than those in the high seismic regions of the United States (Oh, Han & Lee 2002). A field reconnaissance survey on shear wall characteristics was conducted on eight buildings: four in Saudi Arabia, three in Australia and one in Malaysia. Observations from the survey were employed to make recommendations over design parameter values for the planning of the experimental investigation and the probabilistic assessment. Because of lack of research on lightly reinforced walls typifying regions of low to moderate seismicity, experimental testing of three large-scale slender walls was undertaken. The walls were tested simultaneously under quasi-static cyclic lateral loading, with a constant axial load ratio of 5%, up to the limit of axial collapse. Output from the test results in addition to extra data obtained from walls tested elsewhere, were utilised to calibrate the non-linear force-deformation behaviour of the walls. Various models that were proposed to estimate the effective stiffness and plastic hinge length of shear walls were evaluated, to determine their applicability to lightly reinforced walls with deficient detailing. The findings of the evaluation, together with a well-validated moment-curvature relationship, were employed, to propose a representative backbone curve to characterise the behaviour of shear wall. Other components of the walls’ non-linear behaviour included modelling of the hysteretic (i.e., strength and stiffness degradation) behaviour. To investigate the dynamic properties of the building structures in response to ground excitations, a numerical multi-degree-of-freedom, non-linear time history model was developed using the RUAUMOKO software. The structural model was established in support of the proposed non-linear force-deformation relationship (i.e., backbone curve in addition to the hysteretic characteristics). Probabilistic assessment tools in the form of fragility curves were constructed to assess the seismic performance of lightly reinforced walls under two performance levels: Immediate Occupancy and Life Safety. This included an extensive set of 54 wall cases, which were selected for different combinations of wall heights (5, 10, 15 and 20 storeys), wall lengths (3, 4, 5, 6, 7 and 8 m) and longitudinal reinforcement content (0.25%, 0.5% and 1%). Ground motions employed for this purpose were simulated for the city of Melbourne, as an example of a region of low to moderate seismicity, and included comprehensive combinations of earthquake scenarios with magnitudes of 5.5, 6, 6.5 and 7, that are generated in the near-field or in the far-field. Results from the fragility curves were used to evaluate the seismic vulnerability of lightly reinforced walls in conditions of low seismic hazards (e.g., the case of Melbourne), and to observe the effects of various design parameters on the seismic fragility behaviour of the walls. Two conservative simplified expressions were recommended for estimating the level of earthquake intensity corresponding to a 5% probability of exceedance as per the Immediate Occupancy and Life Safety performance criteria. The seismic assessment of lightly reinforced walls was extended to quantify the extent of soil-structure interaction (SSI) effect on inelastic displacement demand behaviour of isolated and coupled shear walls. Parametric studies involving non-linear time history analyses were performed when considering three variables: geometry, base flexibility and ground motion excitations with special emphasis on uncertainties associated with ground motion excitations. Observations of the displacement demand amplification behaviour were made with particular reference to SSI and its correlation with wall height, slenderness of the coupling beam, base flexibility and exciting ground motions. Results of the investigation were then used to produce simple conservative expressions, for predicting the displacement demand behaviour taking into account the base flexibility. References were made to the RSDmax value (the maximum value of the elastic displacement response spectrum in the 0 – 5 s range) as read off from the response spectrum. The RSDmax parameter has been effectively implemented for estimating the inelastic displacement demand of buildings in regions of low to moderate seismicity benefiting from the displacement-controlled behaviour, which is a common feature of ground motions in such regions

Halo Orbits under Some Perturbations in cr3bp

The general idea of this paper is to study the effect of mass variation of a test particle on periodic orbits in the restricted three-body model. In the circular restricted three-body problem (cr3bp), two bigger bodies (known as primary and secondary or sometime only primaries) are placed at either side of the origin on abscissa while moving in circular orbits around their common center of mass (here origin), while the third body (known as smallest body or infinitesimal body or test particle) is moving in space and varies its mass according to Jeans law. Using the Lindstedt–Poincaré method, we determine equations of motion and their solutions under various perturbations. The time-series and halo orbits around one of the collinear critical points of this model are drawn under the effects of the solar radiation pressure of the primary and the oblateness of the secondary. In general, these two dynamical properties are symmetrical

A Proposed Analytical and Numerical Treatment for the Nonlinear SIR Model via a Hybrid Approach

This paper re-analyzes the nonlinear Susceptible–Infected–Recovered (SIR) model using a hybrid approach based on the Laplace–Padé technique. The proposed approach is successfully applied to extract several analytic approximations for the infected and recovered individuals. The domains of applicability of such analytic approximations are addressed. In addition, the present results are validated through various comparisons with the Runge–Kutta numerical method. The obtained analytical results agree with the numerical ones for a wide range of numbers of contacts featured in the studied model. The efficiency of the present analysis reveals that it can be implemented to deal with other systems describing real-life phenomena

Influence of aggregate source and size on the shear behavior of high strength reinforced concrete deep beams

This paper aims to examine the influence of coarse aggregate characteristics, including toughness and nominal maximum size of aggregate on the RC deep beams’ shear behavior made with and without shear reinforcement. Nine deep beams were prepared with three coarse aggregate types (i.e., limestone, steel slag, and quartzite) having different toughness properties and two nominal maximum aggregate (10 mm and 20 mm) sizes, which were examined under four-point bending. The experimental findings showed that the deep beams exhibited shear failure caused by diagonal shear cracks initiated between the supports and the loading point. Utilizing bigger coarse aggregate size has led to reducing the number of shear cracks. The deep beam stiffness was not impacted by the change in coarse aggregate toughness, aggregate size, or the use of shear reinforcement. For the beams without shear reinforcement, increasing the nominal maximum coarse aggregate size improved the deep beams normalized shear strength. This improvement depended on the coarse aggregate’s toughness with the toughest aggregate (steel slag) showing the greatest improvement. Moreover, using shear reinforcement has contributed to improving the deep beams’ normalized shear strength. The normalized shear strength increased from 6% to 16% compared to deep beams without shear reinforcement

Exact and Numerical Analysis of the Pantograph Delay Differential Equation via the Homotopy Perturbation Method

The delay differential equations are of great importance in real-life phenomena. A special type of these equations is the Pantograph delay differential equation. Generally, solving a delay differential equation is a challenge, especially when the complexity of the delay terms increases. In this paper, the homotopy perturbation method is proposed to solve the Pantograph delay differential equation via two different canonical forms; thus, two types of closed-form solutions are determined. The first gives the standard power series solution while the second introduces the exponential function solution. It is declared that the current solution agrees with the corresponding ones in the literature in special cases. In addition, the properties of the solution are provided. Furthermore, the results are numerically validated through performing several comparisons with the available exact solutions. Moreover, the calculated residuals tend to zero, even in a huge domain, which reflects the high accuracy of the current analysis. The obtained results reveal the effectiveness and efficiency of the current analysis which can be further extended to other types of delay equations

Lightweight SCC Development in a Low-Carbon Cementitious System for Structural Applications

The utilization of manufactured lightweight aggregates adds another dimension to the cost of the preparation of self-compacting concrete (SCC). The common practice of adding absorption water to the lightweight aggregates before concreting leads to inaccurate calculations of the water-to-cement ratio. Moreover, the absorption of water weakens this interfacial bond between aggregates and the cementitious matrix. A particular type of black volcanic rock with a vesicular texture known as scoria rocks (SR) is utilized. With an adapted sequence of additions, the occurrence of water absorption can be minimized to overcome the issue of calculating the true water content. In this study, the approach of preparing the cementitious paste first with adjusted rheology followed by the addition of fine and coarse SR aggregates enabled us to circumvent the need for adding absorption water to the aggregates. This step has improved the overall strength due to the enhanced bond between the aggregate and the cementitious matrix, rendering a lightweight SCC mix with a target compressive strength of 40 MPa at 28 days, which makes it appropriate for structural applications. Different mixes were prepared and optimized for the best cementitious system that achieved the goal of this study. The optimized quaternary cementitious system included silica fume, class F fly ash, and limestone dust as essential ingredients for low-carbon footprint concrete. The rheological properties and parameters of the optimized mix were tested, evaluated, and compared to a control mix prepared using normal-weight aggregates. The results showed that the optimized quaternary mix satisfied both fresh and hardened properties. Slump flow, T50, J-ring flow, and average V-funnel flow time were in the ranges of 790–800 mm, 3.78–5.67 s, 750–780 mm, and 9.17 s, respectively. Moreover, the equilibrium density was in the range of 1770–1800 kg/m3. After 28 days an average compressive strength of 42.7 MPa, a corresponding flexural load of over 2000 N, and a modulus of rupture of 6.2 MPa were obtained. The conclusion is then drawn that altering the sequence of mixing ingredients becomes a mandatory process with scoria aggregates to obtain high-quality lightweight concrete for structural applications. This process leads to a significant improvement in the precise control of the fresh and hardened properties, which was unachievable with the normal practice used with lightweight concrete

Concrete Performance Produced Using Recycled Construction and By-Product Industrial Waste Coarse Aggregates

Concrete is classified as a multi-composite material comprising three phases: coarse aggregate, mortar, and interfacial transition zone (ITZ). Fine and coarse aggregates occupy approximately 70–85% by volume, of which coarse aggregate typically constitutes more than two-thirds of the total quantity of aggregate by volume. The current study investigates the concrete performance produced using various recycled construction and by-product industrial waste coarse aggregates. Six types of coarse aggregates: manufactured limestone, quartzite, natural scoria, by-product industrial waste aggregate, and two sources of recycled concrete aggregates with densities ranging from 860 to 2300 kg/m3 and with different strength properties were studied. To determine the coarse aggregate contribution to the overall concrete performance, lean and rich concrete mixtures (Mix 1 and Mix 2) were used. Mix 1 (lean mixture) consisted of a ratio of water to cement (w/c) of 0.5 and cement content of 300 kg/m3, whereas a higher quantity of cement of 500 kg/m3 and a lower w/c ratio of 0.3 were used for Mix 2 (rich mixture). The results showed that while the compressive strength for different aggregate types in Mix 1 was comparable, the contribution of aggregate to concrete performance was very significant for Mix 2. Heavyweight aggregate produced the highest strength, while the lightweight and recycled aggregates resulted in lower mechanical properties compared to normal weight aggregates. The modulus of elasticity was also substantially affected by the coarse aggregate characteristics and even for Mix 1. The ACI 363R-92 and CSA A23.3-04 appeared to have the best model for predicting the modulus of elasticity, followed by the ACI-318-19 (density-based formula) and AS-3600-09. The density of coarse aggregate, and hence concrete, greatly influenced the mechanical properties of concrete. The water absorption percentage for the concrete produced from various types of aggregates was found to be higher for the aggregates of higher absorption capacity