Behavior of Gravity Type Retaining Wall under Earthquake Load with Generalized Backfill

Dynamic response of gravity type retaining wall under seismic load is a topic of considerable research for the last 90 years or more. The concept of deriving dynamic pressure based on rigid body mechanics as proposed by Mononobe and Okabe (M-O method) in 1929 continues to dominate the majority of the codes around the world, although it is reported in a number of cases that the M-O method underestimates the response in many cases. Although the M-O method was originally derived for cohesion less soil yet it is used frequently in deriving pressure for other general soil conditions also, like c-φ soil, c-φ soil with surcharge, etc.

This article is an attempt to predict the response of a gravity wall having a generalized backfill (i.e., c-φ soil with surcharge q and that could also be partially saturated) considering its structural deformation as well as the effect of dynamic soil structure interaction (DSSI), a phenomenon which is often ignored in practice. The results are finally compared with a 2-D finite element analysis carried out in ANSYS to check its validity.     

SEISMIC AMPLIFICATION AT A SOFT SOIL SITE WITH LIQUEFIABLE LAYER

It is well known that local soil conditions play a key role in the amplification of earthquake waves. In particular, a liquefiable shallow soil layer may produce a significant influence on ground motion during strong earthquakes. In this paper, the response of a liquefiable site during the 1995 Kobe earthquake is studied using vertical array records, with particular attention on the effects of nonlinear soil behaviour and liquefaction on the ground motion. Variations of the characteristics of the recorded ground motions are analysed using the spectral ratio technique, and the nonlinearity occurring in the shallow liquefied layer during earthquake is identified. A fully coupled, inelastic finite element analysis of the response of the array site is performed. The calculated stress-strain histories of soils and excess pore water pressures at different depths are presented, and their relations to the characteristics of the ground motions are addressed.     

Dynamic Response of Saturated Soil - Foundation System Acted upon by Vibration

In this study, the response and behavior of machine foundations resting on dry and saturated sand was investigated experimentally. In order to investigate the response of soil and footing to steady state dynamic loading, a physical model was manufactured to simulate steady state harmonic load at different operating frequencies. Total of 84 physical models were performed. The footing parameters are related to the size of the rectangular footing and depth of embedment. Two sizes of rectangular steel model footing were tested at the surface and at 50 mm depth below model surface. Meanwhile the investigated parameters of the soil condition include dry and saturated sand for two relative densities 30% and 80%. The response of the footing was elaborated by measuring the amplitude of displacement by the vibration meter. The response of the soil to dynamic loading includes measuring the stresses inside the soil using piezoelectric sensors as well as measuring the excess pore water pressure using pore water pressure transducers. It was concluded that the maximum displacement amplitude response of the foundation resting on dry sand models is more than that on the saturated sand by about 5.0–10%. The maximum displacement amplitude of footing is reduced to half when the size of footing is doubled for dry and saturated sand. The final settlement (St) of the foundation increases with increasing the amplitude of dynamic force, operating frequency and degree of saturation. Meanwhile, it is reduced with increasing the relative density of sand, modulus of elasticity, and embedding inside soils. The excess pore water pressure increases with increasing the relative density of the sand, the amplitude of dynamic loading and the operating frequency. In contrast, the rate of dissipation of the excess pore water pressure during dynamic loading is more in the case of loose sand.     

Interaction Curves for In-Plane and Out-of-Plane Behaviors of Unreinforced Masonry Walls

Different types of macro-elements have been proposed to simulate the behavior of unreinforced masonry (URM) structures under seismic loads. In many of these, macro-elements URM walls are replaced with beam elements with different hysteretic behaviors. The effect of out-of-plane loading or change of gravity load due to the overturning moment is usually not considered in the behavior of these macro-elements. This article presents interaction curves for bidirectional loadings of unreinforced masonry walls to investigate the importance of these factors. Two parameters are systematically changed to derive the interaction curves for a wall with specific dimensions, including compressive traction atop the wall to represent gravity loading, and loading angle that represents a combination of in-plane and out-of-plane earthquake loadings. Interaction curves are developed considering various possible failure modes for bricks and mortar, including tension, crushing and a combination of shear and compression/tension failures. The proposed interaction curves show the initiation of failure of URM walls as a function of compressive traction and loading angle. Several examples are presented for URM walls with different aspect ratios to aid in understanding the effects of various parameters on the derived interaction curves. Finally, for a specific case, the derived interaction curve is compared with nonlinear finite element results and ASCE41. The results show that, as a simplified method, the derived interaction curves can be used for the preliminary evaluation of URM walls under bidirectional loadings.     

Optimum Design of Bridge Abutments Under High Seismic Loading Using Modified Pseudo-Static Method

This article focuses on the optimum design of bridge abutments when subjected to earthquake loading. Planar failure surface has been used in conjunction with modified pseudo-static approach to compute the seismic active earth pressures on an abutment. The proposed modified Mononobe-Okabe method considers the effects of strain localization in the backfill soil and associated post-peak reduction in the shear resistance from peak to residual values along a previously formed failure plane, phase difference in shear waves, and soil amplification along with the horizontal seismic accelerations. Four modes of stability viz. sliding, overturning, eccentricity, and bearing capacity of the foundation soil are considered in the analysis. The influence of various design parameters on the seismic stability of abutments is presented. The optimum values of base width of the abutment needed to maintain the stability are obtained against four modes of failure, based on the suggestions of Japan Road Association, Caltrans Bridge Design Specifications, and U.S Department of the Army.     

EVALUATION OF ACCIDENTAL ECCENTRICITY IN BUILDINGS DUE TO ROTATIONAL COMPONENT OF EARTHQUAKE

This study adopts a random procedure in the evaluation of the effect of the rotational component of earthquake on the accidental eccentricity of symmetric and asymmetric buildings. The spectral density function of the rotational component of earthquake acceleration (about the vertical axis) is obtained on the basis of the spectral density function of the horizontal component of earthquake acceleration. The rotational component of an earthquake can increase the response of the structure. The degree of the increase is highly dependent upon the dynamic characteristics of the system and the rotational component of the earthquake. To bring this increase under consideration, seismic codes represent a parameter referred to as accidental eccentricity, as a part of the design eccentricity. The purpose of the present study is to estimate the value of this increase and to make appropriate suggestions based on frequency domain analysis.     

Seismic Load Capacity of Historical Masonry Mosques by Rigid Body Kinetics

ABSTRACT

Kinetic analysis methods based on linear and nonlinear rigid body dynamics are used to evaluate earthquake safety of masonry structures. In this study, the formulas used to calculate the in-plane and out-of-plane load capacities of masonry load-bearing walls were evaluated and a procedure based on rigid body mechanism was proposed to calculate the out-of-plane load capacities of the walls of Ottoman period masonry mosques. New aspects of the method with respect to existing formulations is the inclusion of dynamic axial load and definition of the collapse limit spectral acceleration on the overturning wall. The calculated capacities of the mosque and individual walls were compared with the results of nonlinear pushover analysis and time history analyses performed under 1.0 and 0.5 scaled forms of nine different 3-component ground motion records. It was displayed that the seismic load capacity estimated by the proposed method is very close to the values calculated by pushover and time history analyses. The method was developed on Lala Pasha Mosque, and the reliability and applicability of the proposed methodology is verified on a different historical masonry mosque in comparison to finite element analyses results.     

A Simple Model for Estimating Shocks in Unrestrained Building Contents in an Earthquake

Building contents that include cabinets housing electronic equipment are typically not rigidly secured to the floor, nor to the adjacent wall except in regions of high seismic activities. The behavior of unrestrained building contents in an earthquake is a cause of concern because of the consequence of damage to certain equipment or other forms of fragile items. Much of the research reported in the literature has been devoted to studying the rocking and sliding motion behavior of base-excited rigid objects and their risks of overturning. In contrast, this paper is concerned with estimating the impact acceleration that can be generated by the pounding of the rocking object onto the floor. Algebraic expressions for predicting the acceleration level, which can be translated into dynamic force values, are derived and illustrated by case studies. Importantly, the proposed expressions have been verified by comparisons with results from both simulated and physical experiments. In illustrating the use of the proposed analytical procedure, a parametric experimental study has been undertaken on a cushion material to study the sensitivity of its static and dynamic stiffness to changes in the boundary conditions of the cushion. The proposed calculation procedure, while simple to apply, can be used as a means of predicting shock and the dynamic forces that can be generated in an object in the course of the response to an earthquake.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (I): Displacement-based Approach Using Simple Failure Mechanisms

ABSTRACT

A displacement-based (DB) assessment procedure was used to predict the results of shake table testing of two unreinforced masonry buildings, one made of clay bricks and the other of stone masonry. The simple buildings were subject to an acceleration history, with the maximum acceleration incrementally increased until a collapse mechanism formed. Using the test data, the accuracy and limitations of a displacement-based procedure to predict the maximum building displacements are studied. In particular, the displacement demand was calculated using the displacement response spectrum corresponding to the actual shake table earthquake motion that caused wall collapse (or near collapse). This approach was found to give displacements in reasonable agreement with the wall’s displacement capacity.     

南京长江大桥桥头堡抗震加固受力性能研究

为研究南京长江大桥桥头堡填充墙加固对结构抗震性能的影响,提出考虑较高填充墙开裂的双斜撑模型,用于罕遇地震工况下桥头堡的抗震性能计算,同时提出考虑填充墙加固后刚度增强效应的建模方法。利用SAP2000建立了加固前后用于多遇地震工况、设防地震工况及罕遇地震工况的分析模型,并选取了桥头堡在1974年经历的实际地震激励时程及El-Centro地震激励时程作为激励进行了加固前后结构的抗震性能分析比较。研究发现,填充墙加固后桥头堡的抗震性能有了明显提升,其位移响应峰值约下降8%~23%,层间位移角响应峰值约下降12%~22%,而且桥头堡结构在设防地震情况下2个方向的层间位移角均满足了规范要求。另外,在罕遇地震工况下,未加固的填充墙开裂会使结构的扭转刚度下降,而填充墙加固可有效提升结构的扭转刚度,降低桥头堡在地震时发生扭转振动的概率。这2种地震荷载激励的分析结果差异约在3%~21%不等,且响应峰值出现的位置也有一些不同,故对桥头堡进行抗震时程分析时建议选取多条地震波输入综合分析。研究成果可为同类型的钢筋混凝土建筑遗产的抗震加固提供借鉴和参考。     

Aseismic Assessment of the Qiantang River Levee

Liquefaction potential is evaluated using both in-situ and laboratory testing methods. Liquefaction and dynamic stability for the levee are determined using Biot’s dynamic consolidation equation which is used to analyze the increase and dissipation of pore water pressure as well as liquefaction and dynamic stability in the levee during a magnitude 7 earthquake. By inverse analysis, the acceleration at the bedrock is obtained from the acceleration data monitored previously at free surface and is inputted as the seismic loading. Results presented in this paper can provide improved stability assessment for levees experiencing seismic events of this magnitude.     

ANALYSIS OF PORE PRESSURE GENERATION AND DISSIPATION IN COHESIONLESS MATERIALS DURING SEISMIC LOADING

The earthquake loading of a shallow foundation resting on top of a cohesionless layer creates cyclic variations in the shear force and overturning moment acting on the supporting soil. These loads induce a tendency for volume change which, in turn, depending on the drainage conditions and material permeability, may cause in addition to a cyclic pore pressure variation a progressive pore pressure buildup. The paper develops an efficient and elegant way, based on a multiple time scale analysis, of solving this fully coupled problem. The theoretical solution is implemented in a finite element code and is applied to predict the pore pressure development and dissipation under a bridge pier foundation for which it was essential to limit the pore pressure increase.     

Optimal Control of Structures under Earthquakes Including Soil-Structure Interaction

It is well known that the soil-structure interaction (SSI) changes the dynamic response of a structure supported on flexible soil. The analysis of optimally controlled SSI systems has certain difficulties due to the nature of the SSI and the optimal control problem. In this paper, a two-step iteration-based numerical algorithm is proposed to handle optimally controlled SSI systems under earthquakes. First, the optimal control forces are obtained by using a fixed-base system. Then, the optimal control forces are converted to the frequency domain by the Fourier transform technique to be used in the equations of the SSI system. The lateral displacement and the rocking of the foundation are obtained from the equations of the SSI system containing the optimal control forces in the frequency domain. The lateral displacement and rocking of the foundation are then converted to the time domain by the inverse Fourier transform technique, and the lateral accelerations and the rocking accelerations of the foundation are obtained by the forward finite difference method. During the second step, the optimal control forces are calculated again by using the lateral acceleration and the rocking acceleration of the foundation along with the earthquake ground motion. Using the method explained above, the optimal control forces obtained in the time domain are used in the equations of the soil-structure system from which the behavior of foundation and structure is obtained. In the final section of the paper, a numerical study is conducted for a controlled structure supported on flexible soil.     

Seismic Behavior Prediction of Flanged Unreinforced Masonry (FURM) Walls

In most available studies, unreinforced masonry (URM) walls are idealized as rectangular sections, while in reality walls have effective sectional shapes such as C, I, T, and L. In this article, the results of experimental and analytical assessment of flange effects on the behavior of I- and C-shaped URM walls are reported. Four clay brick walls at half scale were tested. Two specimens were designed with I- and C-shaped sections, and for comparison, two additional specimens were designed without flanges. The tests showed that under constant axial load the strength of the I-shaped wall increases, but that of the C-shaped wall decreases, because of out-of-plane distortion effects. Despite the loss of strength, both flanged walls indicated almost similar initial stiffness, deformation capacity, and mode of failure in comparison with walls without flanges. A mixed-mode analytical model is proposed to predict the lateral force displacement curve of flanged URM (FURM) walls. The proposed analytical model is based on section analysis of the walls and shows good agreement with previous experimental results.     

SIMPLIFIED MODELLING STRATEGIES TO SIMULATE THE DYNAMIC BEHAVIOUR OF R/C WALLS

A continuous damage model and different simplified numerical strategies are proposed to simulate the behaviour of reinforced concrete (R/C) walls subjected to earthquake ground motions. For 2D modelling of R/C walls controlled primarily by bending, an Euler multilayered beam element is adopted. For 3D problems, a multifibre Timoshenko beam element having higher order interpolation functions has been developed. Finally, for walls with a small slenderness ratio we use the Equivalent Reinforced Concrete model. For each case, comparison with experimental results of R/C walls tested on shaking table or reaction wall shows the advantages but also the limitations of the approach.     

Experimental Study on Self-Centering Concrete Wall with Distributed Friction Devices

A self-centering concrete wall with distributed friction devices is proposed to achieve seismic resilient building structures. Unbonded post-tensioned tendons, running vertically through wall panels, provide a restoring force that pulls the structure back toward its undeformed plumb position after earthquake. Two steel jackets are installed at wall toes to prevent concrete spalling and crushing. Friction devices are distributed between the wall and its adjacent gravity columns to achieve controllable energy dissipation, and these devices are readily replaceable. Desirable self-centering and energy dissipation capacities were observed in low-cyclic loading tests, and influences of various parameters on the hysteretic behavior were investigated.     

ELASTIC EARTH PRESSURES ON RIGID WALLS UNDER EARTHQUAKE LOADING

Elastic dynamic earth pressures induced by earthquakes are computed by analyzing a wall-foundation-backfill system. Both foundation and backfill are considered viscoelastic; the foundation is a semi-infinite space and the backfill, a uniform layer of constant thickness. A simple analytical solution is developed by assuming an approximate backfill-foundation interface condition and adopting the least squares method. The response functions computed indicate the large influence of the various system parameters on earth pressure, including the foundation characteristics,as well as wall geometry and mass. The transient response of the system is also studied by obtaining spectra for base shear. A large number of seismic records are analyzed to obtain average spectra and a total of three correction functions are used to take into account the foundation stiffness and density as well as wall inertia. A simple design method is proposed to estimate the maximum base shear.     

Maximum Possible Ground Motion for Linear Structures

This article develops a method to generate ground motion time histories that maximize the response of a given linearly elastic structure. The root mean square (RMS) level of the input power spectral density (PSD) is used as a strong motion parameter. It is related to seismological data that is readily available. An empirical relation to estimate RMS value of the PSD from peak ground acceleration, magnitude, rupture distance, and shear wave velocity is derived from world-wide strong motion data. The ground motion is obtained by solving the inverse problem such that the structural response is maximized under the constraint of fixed value of RMS level of the input PSD enforced using a Lagrange multiplier. The proposed methodology is illustrated for a single-degree of freedom system, a six storey building and an earthen dam. It is shown that the critical PSD obtained in all the cases is a narrow band process resulting in stochastic resonance and not a Dirac-delta function with the entire energy of the system concentrated at its natural frequency. Moreover, the critical excitation samples generated using this critical PSD resembles actual earthquake acceleration time histories.     

Real-time Seismic Damage Detection of Concrete Shear Walls Using Artificial Neural Networks

Concrete shear walls are widely employed in buildings as a main resistance system against lateral loads. Early identification of seismic damage to concrete shear walls is vital for deciding post-earthquake occupancy in these structures. In this article, a method based on artificial neural networks for real-time identification of seismic damage to concrete shear walls was proposed. Inter-story drifts and plastic hinge rotation of concrete walls were used as the inputs and outputs of a MLP neural network. Modal Pushover Analysis was employed to prepare well-distributed data sets for training the neural network. The proposed method was applied to a five-story concrete shear wall building. The results from the network were compared with those obtained from Nonlinear Time History Analysis. It was observed that the trained neural network successfully detected damage to concrete shear walls and accurately estimated the severity of seismic-induced damage.     

Estimation of Strong Ground Motions in Southwest Western Australia with a Combined Green's Function and Stochastic Approach

As only a very limited number of earthquake strong ground motion records are available in southwest Western Australia (SWWA), it is difficult to derive a reliable and unbiased strong ground motion attenuation model based on these data. To overcome this, in this study a combined approach is used to simulate ground motions. First, the stochastic approach is used to simulate ground motion time histories at various epicentral distances from small earthquake events. Then, the Green's function method, with the stochastically simulated time histories as input, is used to generate large event ground motion time histories. Comparing the Fourier spectra of the simulated motions with the recorded motions of a ML6.2 event in Cadoux in June 1979 and a ML5.5 event in Meckering in January 1990, provides good evidence in support of this method. This approach is then used to simulate a series of ground motion time histories from earthquakes of varying magnitudes and distances. From the regression analyses of these simulated data, the attenuation relations of peak ground acceleration (PGA), peak ground velocity (PGV), and response spectrum of ground motions on rock site in SWWA are derived.