Progressive failure of buildings under landslide impact

Abstract

Buildings are the most concerned element in landslide risk assessment. A weak link in landslide risk analysis is the evaluation of building response and vulnerability when impacted by a landslide. In this paper, failure mechanisms and processes of typical reinforced concrete buildings upon landslide impacts are discovered through an explicit time integration analysis in LS-DYNA. The Arbitrary Lagrangian–Eulerian formulation, which allows automatic rezoning, is applied to simulate the landslide flow dynamics and the impact into the building. Three landslide intensity levels are considered. Progressive collapse of the building is observed in the high-impact intensity case. The frontal walls are firstly destroyed due to its low out-of-plane flexural capacity, followed by the progressive failure of columns at the ground floor. The collapse of building occurs when the remaining load-bearing components cannot resist the superstructure loadings. Two plastic hinge failure mechanisms are observed on the damaged columns when the ultimate bending moments of the columns are exceeded at both ends. Finally, a five-class classification system is proposed to evaluate building damage states based on field observations and the numerical simulation results. The analysis helps robust building design and assessment of building vulnerability to landslides.

Appendix-model verification: beam analysis

In order to validate the applied numerical model, a typical RC beam, which is commonly used in China, is selected to conduct the three-point bending test simulation (Zeng et al. 2015). Two rigid cylindrical supports are set to support the beam. A concentrated load is imposed on the middle span of the beam in a ramp function and monotonically increased until failure. The failure process is analyzed, and the simulated cracking moment of concrete, ultimate bending moment of the beam, and time history of axial stress in the rebar are compared with the analytical results calculated based on the limit state theory for reinforced concrete structure design. The material parameters for the beam model are identical to those for the building model in Table 1. The cracking moment can be calculated based on the specification for the design of concrete structure (MOHURD 2010): M_Cr = f_tkW₀ = 7 MPa, where f_tk is the concrete tensile characteristic strength and W₀ is the resistance moment of the equivalent cross-section. For the cross-section at the middle span, the stress in the rebar before cracking is calculated as σ_cr-b = E_s∙f_tk/E_c = 14 MPa, where E_s and E_c are the Young’s modulus of rebar and concrete, respectively. After cracking, the stress in the rebar is expressed as σ_cr-a = E_s∙f_tk/E_c + f_tk∙A_c/A_s = 154 MPa, where A_c and A_s are the areas of tensile concrete and tensile rebar, respectively. Besides, as shown in Fig. 12, the ultimate bending moment of the beam can be calculated based on force equilibrium (Eq. (11)) and moment equilibrium (Eq. (12)):

$$ {f}_y{A}_s={\alpha}_1{f}_{ck} bx+{f}_y^{\hbox{'}}{A}_s^{\hbox{'}} $$

(11)

$$ {M}_u={\alpha}_1{f}_{ck} bx\times \left({h}_0-\frac{x}{2}\right)+{f}_y^{\hbox{'}}{A}_s^{\hbox{'}}\left({h}_0-{a}_s^{\hbox{'}}\right) $$

(12)

where f_y and f_y^’ are the tensile and compressive stresses of the longitudinal reinforcement, respectively; A_s and A_s^’ are the areas of tensile and compressive longitudinal reinforcement, respectively; α₁ is a coefficient of concrete grade; f_ck is the concrete compressive characteristic strength; b is the width of column section; x is the compression height; and h₀ is the effective height of the cross-section. If x < a_s^’, the compressive stress of the rebar does not reach f_y^’; so, the ultimate bending moment can be calculated by assuming x = a_s^’ and taking a moment to the centroid of compressive rebar; M_u = f_yA_s(h₀ − a^’_s) = 40 kNm.

Fig. 12

(a) Cross-section and (b) diagrams for calculating bearing capacity of beam

Snapshots of typical beam failure process from the numerical analysis are shown in Fig. 13. The development and distribution of cracks are described by the contours of the plastic strain. At 0.10 s, the cracking moment is reached, and, then, cracks occur in the tensile zone. Besides, the stress of the tensile rebar experiences a rapid increase at the crack point, from 16 to 157 MPa (Fig. 14). After cracking, the stresses of the tensile reinforcement and compressive concrete increase with the applied pressure, and, finally, the beam reaches the ultimate bending moment state. The numerical model reflects well the typical beam failure process, and the simulated results are very close to those from the static analysis.

Fig. 13

Snapshots of beam failure process: contours of plastic strain

Fig. 14

Time histories of bending moment and axial stress of the reinforcement at the middle span

To consider the mesh size effect, the same three-point bending tests are simulated using different element sizes of the concrete beam. The time histories of bending moment at the middle section are compared in Fig. 15. The different element sizes almost produce the same results. Considering that the stability of the explicit integration scheme is determined by the time step, a smaller element size allows smaller time step to ensure a stable analysis and, thus, requires significantly longer computing time. So, a mesh size of 0.075 m is applied in the impact analysis.

Fig. 15

Time histories of bending moment at the middle span for different concrete element sizes