Pseudo-static Approach Research Articles

Pseudo-static approach for damage identification of bridges based on coupling vibration with a moving vehicle

This paper presents a methodology for damage identification based on a time domain approach, considering the coupling vibration between a bridge and a moving vehicle, including the effect of roadway surface roughness. The fundamental idea of the proposed method is to identify damage directly from changes in the element stiffness using a pseudo-static formulation derived from the equations of motion for coupling vibration. The element stiffness index (ESI), which indicates the ratio of a damaged flexural rigidity of the finite element of bridges to an undamaged one, is adopted as the indicator of bridge damage. A numerical example reveals that the concept and procedure suggested in this paper can provide a method for extending engineering choices in damage identification of bridge structures.

Equivalent seismic coefficient in geocell retention systems

Ideal design of an earthquake resistant earth structure would consider the time records of future seismic events. Objectively, such time records are difficult to predict especially when compared with prediction of the design peak ground acceleration (PGA), a single-value parameter. Furthermore, relevant soil properties are not easily obtainable in the field. Consequently, in routine stability designs, the state of practice utilizing a pseudostatic analysis has not changed for many years. To reduce the inherent conservatism of the pseudostatic approach, it is common to use a fraction of PGA in the stability analysis. For earth structures such as slopes, existing standards suggest a value of this fraction, typically varying between 0.3 and 0.5 times PGA. While one hopes that such values are calibrated against case histories, it is doubtful if there is sufficient field data for a value corresponding to geocell gravity walls and geocell reinforced slopes. Reported here are relevant results of shake table tests on five different geocell structures, each 2.8 m high, subjected to an excitation simulating the Kobe earthquake. Exhumation enabled the tracing of slip surfaces that developed during the shaking. Back-analysis resulted in the fraction of the applied PGA needed to establish a slip surface. The formation of slip surfaces in the context of this work should not be interpreted as collapse or catastrophic failure; rather it signifies the development of an active wedge. Hence, the equivalent coefficients in this work are an upper bound value for the magnitude and intensity of the ground motion applied in the analysis. It was found that for geocell gravity walls, essentially flexible structures, the upper bound seismic coefficient for the applied motion is about 0.4 times PGA. For reinforced geocell walls the upper bound coefficient would be 0.3 times PGA.

Seismic active thrust on cantilever walls with short heel

This note presents an analytical solution of the thrust on retaining walls with short heel, where the seismic action is simulated through the pseudo-static approach. The critical shape of the thrust wedge is assumed to be that minimizing the safety factor against wall sliding. This procedure is also congruent with the original method of Coulomb. The problem is mathematically expressed by a system of two equations, the first cubic and the second quadratic, whose solution converges quickly.

STABILITY OF WATERFRONT RETAINING WALL SUBJECTED TO PSEUDO-DYNAMIC EARTHQUAKE FORCES AND TSUNAMI

The paper pertains to a study in which the waterfront retaining wall has been analyzed for its stability when it is exposed to the forces jointly coming from an earthquake and tsunami. Closed form solutions following the simple limit equilibrium principles have been proposed. For the calculation of the seismic passive earth pressure and the wall inertia force, pseudo-dynamic approach has been considered, while the hydrodynamic and the tsunami wave pressures have been calculated using different approximating solutions available in literature. The results presented in the sliding and overturning modes of failure of the wall show that the stability of the wall gets seriously challenged when it gets jointly exposed to the effects of the tsunami and earthquake. About 92% decrease is observed in the value of the factor of safety in sliding mode of failure of the wall as the ratio of tsunami wave height to the upstream still water height increases from 0 to 1.5. Also, the critical mode of failure of the wall has been found to be that of the overturning. Effect of different parameters involved in the analysis has also been studied and it has been observed that quite a few of them like kh, kv, ϕ, δ, ru have a significant effect on the stability of the wall. Comparison with a previously existing methodology using pseudo-static approach suggests that the present pseudo-dynamic approach is more realistic and comparatively less conservative and hence can be used as a handy simple economic method for the design of the waterfront retaining walls exposed to the combined effects of earthquake and tsunami.

Upper bound solutions of bearing capacity of strip footing by pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis of seismic bearing capacity of a strip footing using upper bound limit analysis. However, in the literature, the pseudo-static approach was frequently used by several researchers to compute the seismic bearing capacity factor theoretically, where the real dynamic nature of the earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of bearing capacity factor NγE are determined for different magnitudes of soil friction angle, soil amplification and seismic acceleration coefficients both in the horizontal and vertical directions. The results obtained from the present study are shown both graphically as well as in the tabular form. It is observed that the bearing capacity factor NγE decreases significantly with the increase in seismic accelerations and amplification. The results are thoroughly compared with the existing values in the literature and the significance of the present methodology for designing the shallow footing is discussed.

Seismic vertical uplift capacity of horizontal strip anchors using pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis to determine the seismic vertical uplift capacity of a horizontal strip anchor using upper bound limit analysis. However, in the literature, the pseudo-static approach was used by few researchers to compute the seismic vertical pullout resistance, where the real dynamic nature of earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of uplift factor f γE are determined for different magnitudes of soil friction angle, soil amplification, embedment ratio and seismic acceleration coefficients both in the horizontal and vertical directions. It is observed that the uplift factor f γE decreases significantly with the increase in seismic accelerations and amplification but increases with the increase in embedment ratio. The results are compared with the existing values in the literature and the significance of the present methodology for designing the horizontal strip anchor is discussed. In presence of vertical earthquake acceleration and amplification of vibration, the present values of f γE compare reasonably well with the existing pseudo-static values obtained by modifying the horizontal acceleration coefficient.

EFFECTS OF BODY WAVES AND SOIL AMPLIFICATION ON SEISMIC EARTH PRESSURES

To design a retaining wall, conventional Mononobe–Okabe method, which is based on the pseudo-static approach and gives the linear distribution of seismic earth pressures in an approximate way, is used to compute the seismic earth pressures. In this paper, pseudo-dynamic approach is used to compute the seismic earth pressures on a rigid retaining wall by considering the effects of time, phase difference in shear and primary waves and soil amplification along with the horizontal and vertical seismic accelerations and other soil properties. Design value of the seismic active earth pressure coefficient is found to increase with increase in the seismic accelerations, phase difference in body waves and soil amplification, whereas the reverse trend is observed for the passive case. Influence of various soil parameters on seismic passive earth pressure is more significant than that for the active case under harmonic seismic loading. Results are provided in the combined tabular and graphical non-dimensional form for both the seismic active and passive earth pressures. Present results are compared with the available results in literature to validate the proposed non-linearity of seismic earth pressure distribution.

Analysis of stability of earthen dams in kachchh region, Gujarat, India

The Kachchh region of Gujarat, India bore the brunt of a disastrous earthquake of magnitude M w = 7.6 that occurred on January 26, 2001. The major cause of failure of various structures including earthen dams was noted to be the presence of liquefiable alluvium in the foundation soil. Results of back-analysis of failures of Chang, Tappar, Kaswati and Rudramata earth dams using pseudo-static limit equilibrium approach presented in this paper confirm that the presence of liquefiable layer contributed to lesser factors of safety leading to a base type of failure that was also observed in the field. Following the earthquake, earth dams have been rehabilitated by the concerned authority and it is imperative that the reconstructed sections of earth dams be reanalyzed. It is also increasingly realized that risk assessment of dams in view of the large-scale investment made and probabilistic analysis is necessary. In this study, it is demonstrated that the probabilistic approach when used in conjunction with deterministic approach helps in providing a rational solution for quantification of safety of the dam and in the estimation of risk associated with the dam construction.

Design implications of the vertical pseudo-static coefficient in slope analysis

Most design manuals and codes recommend a simple pseudo-static (PS) approach for analysis of slope stability under seismic conditions. Exceptions to this recommendation include problems involving liquefaction, and exceptionally large earthquakes. These extreme situations are not considered in the present work. Most codes neglect the vertical component of the PS force. The rational basis for this practice has not been properly established in the professional literature, and the main purpose of the present work is to check the validity of this assumption. The analysis is based on the realization that the direction (up or down), of the vertical PS force of a future earthquake cannot be predicted, so the designer must consider the direction leading to a minimum safety factor. It is shown that under most conditions the vertical PS force has significant effect on slope stability, and neglecting this force leads to over estimation of safety factors. An analytical solution of the PS stability problem in cohesionless material shows that in this case the critical conditions are realized when the vertical PS force acts opposite to the direction of gravity. In such materials the errors introduced by neglecting the vertical pseudo-static forces may be considered acceptable. A strength reduction numerical procedure was used to solve PS stability problems in a frictional-cohesive material. These solutions show that for steep slopes the critical vertical PS force acts in the direction of gravity, but for small slope inclinations the critical direction of this force is upwards. The errors in safety factors introduced by the common practice of neglecting vertical PS forces are proportional to the absolute value of the ratio between vertical and horizontal pseudo-static coefficients. These errors are relatively small for intermediate slope inclinations, but they become unacceptable for very steep and very gentle slopes.

Design of waterfront retaining wall for the passive case under earthquake and tsunami

The paper pertains to a study of analysing a waterfront retaining wall under the combined action of tsunami and earthquake forces. The stability of the waterfront retaining wall is assessed in terms of its sliding and overturning modes of failure. Pseudo-static approach has been used for the calculation of the passive seismic earth pressure. Hydrodynamic pressure generated behind the backfill due to shaking of the wet backfill soil is considered in the analysis. Tsunami force is considered to be an additional force acting on the upstream face of the wall and is calculated using a simple formula. It is observed that the factor of safety in sliding mode of failure decreases by about 70% when the ratio of tsunami water height to initial water height is changed from 0.375 to 1.125. Variations of different parameters involved in the analysis suggest sensitiveness of the factor of safety against both the sliding and overturning modes of failure of the wall and provides a better guideline for design.

Analytical earth thrust on walls with bilinear backface

This paper gives the analytical solution of the active thrust on retaining walls with bilinear backface. The solution is obtained using the limit equilibrium method, following the approach of Coulomb. The topographic profile of the backfill behind the soil is considered to be linear or bilinear. The solution proposed here can also be used to calculate thrust in seismic conditions with the pseudo-static approach. The position of the application point of the active thrust is also given in a simple analytical form.

Dynamic active earth pressure on retaining structures

Earth-retaining structures constitute an important topic of research in civil engineering, more so under earthquake conditions. For the analysis and design of retaining walls in earthquake-prone zones, accurate estimation of dynamic earth pressures is very important. Conventional methods either use pseudo-static approaches of analysis even for dynamic cases or a simple single-degree of freedom model for the retaining wall-soil system. In this paper, a simplified two-degree of freedom mass-spring-dashpot (2-DOF) dynamic model has been proposed to estimate the active earth pressure at the back of the retaining walls for translation modes of wall movement under seismic conditions. The horizontal zone of influence on dynamic earth force on the wall is estimated. Results in terms of displacement, velocity and acceleration-time history are presented for some typical cases, which show the final movement of the wall in terms of wall height, which is required for the design. The non-dimensional design chart proposed in the present study can be used to compute the total dynamic earth force on the wall under different input ground motion and backfill conditions. Finally, the results obtained have been compared with those of the available Scott model and the merits of the present results have been discussed.

Pseudo-dynamic approach of seismic active earth pressure behind retaining wall

Knowledge of seismic active earth pressure behind rigid retaining wall is very important in the design of retaining wall in earthquake prone region. Commonly used Mononobe-Okabe method considers pseudo-static approach, which gives the linear distribution of seismic earth pressure in an approximate way. In this paper, the pseudo-dynamic method is used to compute the distribution of seismic active earth pressure on a rigid retaining wall supporting cohesionless backfill in more realistic manner by considering time and phase difference within the backfill. Planar rupture surface is considered in the analysis. Effects of a wide range of parameters like wall friction angle, soil friction angle, shear wave velocity, primary wave velocity and horizontal and vertical seismic accelerations on seismic active earth pressure have been studied. Results are provided in tabular and graphical non-dimensional form with a comparison to pseudo-static method to highlight the realistic non-linearity of seismic active earth pressures distribution.

Stability charts for pseudo-static slope stability analysis

Most design manuals and codes recommend a simple pseudo-static approach for analysis of slope stability under seismic conditions. Exceptions to this recommendation include problems involving liquefaction, soils exhibiting significant strength loss under cyclic loading, and exceptionally large earthquakes. These unusual situations are not considered in the present work. Conventional applications of the pseudo-static approach are based on slice methods which involve various kinematic and static assumptions. The present work is based on a variational formulation of limiting equilibrium and a strength reduction procedure. The advantage of these formulations is that they do not involve kinematic and/or static assumptions. The main purpose of the present work is to present a design chart for pseudo-static analysis of homogeneous slopes applicable over a wide range of input parameters. Such charts are useful for preliminary design, and allow the designer to assess the effects of various parameters on stability “at a glance”.

Pseudostatic Approach for Seismic Analysis of Piles in Liquefying Soil

The performance of pile foundations during an earthquake significantly influences the integrity of structures supported by them. Therefore, in the overall seismic design process of the structures, modeling of the soil–pile-superstructure interaction is an essential part. Although finite element based coupled analysis of the soil–pile-superstructure interaction models have the potential to provide accurate results, they are computationally expensive and often complex to utilize. In practice, many geotechnical engineers tend to use simple methods for obtaining the internal response of piles subjected to earthquake loading. Therefore this paper presents a simple pseudostatic approach where a single pile is considered, including the contribution of the superstructure to the pile and the interaction between the pile and the soil. The method involves two main steps. First a nonlinear free-field site response analysis is carried out to obtain the maximum ground displacements along the pile and the degraded soil ...

Shaking table tests and stability analysis of steep nailed slopes

Shaking table tests were performed on five model slopes to examine the effects of the angle and length of the nails and the frequency of excitation on the seismic resistance and failure mechanism of the slopes. Seismic excitation was also applied to slopes at various angles. Experimental results showed that nails markedly improved the seismic resistance of all model steep slopes. Additionally, nailed slopes exhibit characteristics of ductility under strong excitation. The angle of the nails influences the deformation of the slope but only slightly affects seismic resistance. An increase in the length of the nails increased the seismic resistance of the slope and reduced the displacement of the facing only when subjected to strong excitation. The slope at an angle of 90° to the horizontal has a markedly lower seismic resistance than that at 80°. The rocking of the model slope was strong for the slope with inclined nails and the slope at 90° to the horizontal. The failure surface of the soil mass is approximately a bilinear surface; the pullout of nails from the lower rows of nails caused total slope failure. The seismic resistance of a nailed slope is categorized viz. response of the models by three stages: stable, seismic resistance, and incipient collapse phases. Critical seismic acceleration coefficients of all models are evaluated and compared with values predicted by a developed pseudo-static, limit-equilibrium-based slope stability approach, which postulates a two-wedge failure mechanism.Key words: shaking table test, steep nailed slope, seismic resistance, pseudo-static approach.

Seismic Passive Earth Pressures in Soils

Seismic passive earth pressure coefficients were computed by the method of limit equilibrium using a pseudostatic approach for seismic forces. Composite curved rupture surfaces were considered in the analysis. While earlier studies using this type of analysis were mainly for sands, seismic passive earth pressure coefficients were obtained in the present study considering the effects of cohesion, surcharge, and own weight. The minimum seismic passive force was obtained by adding the individual minimum values of these components and the validity of the principle of superposition was examined. Other parameters considered in the analysis were wall batter angle, ground surface slope, soil friction angle, wall friction angle, wall adhesion to soil cohesion ratio, and horizontal and vertical seismic accelerations. The seismic earth pressure coefficients were found to be highly sensitive to the seismic acceleration coefficients both in the horizontal and vertical directions. Results of the study are presented in the form of figures and tables. Comparisons of the proposed method with available theories in the seismic case are also presented.

Seismic design and analysis of underground structures

Underground facilities are an integral part of the infrastructure of modern society and are used for a wide range of applications, including subways and railways, highways, material storage, and sewage and water transport. Underground facilities built in areas subject to earthquake activity must withstand both seismic and static loading. Historically, underground facilities have experienced a lower rate of damage than surface structures. Nevertheless, some underground structures have experienced significant damage in recent large earthquakes, including the 1995 Kobe, Japan earthquake, the 1999 Chi-Chi, Taiwan earthquake and the 1999 Kocaeli, Turkey earthquake. This report presents a summary of the current state of seismic analysis and design for underground structures. This report describes approaches used by engineers in quantifying the seismic effect on an underground structure. Deterministic and probabilistic seismic hazard analysis approaches are reviewed. The development of appropriate ground motion parameters, including peak accelerations and velocities, target response spectra, and ground motion time histories, is briefly described. In general, seismic design loads for underground structures are characterized in terms of the deformations and strains imposed on the structure by the surrounding ground, often due to the interaction between the two. In contrast, surface structures are designed for the inertial forces caused by ground accelerations. The simplest approach is to ignore the interaction of the underground structure with the surrounding ground. The free-field ground deformations due to a seismic event are estimated, and the underground structure is designed to accommodate these deformations. This approach is satisfactory when low levels of shaking are anticipated or the underground facility is in a stiff medium such as rock. Other approaches that account for the interaction between the structural supports and the surrounding ground are then described. In the pseudo-static analysis approach, the ground deformations are imposed as a static load and the soil-structure interaction does not include dynamic or wave propagation effects. In the dynamic analysis approach, a dynamic soil structure interaction is conducted using numerical analysis tools such as finite element or finite difference methods. The report discusses special design issues, including the design of tunnel segment joints and joints between tunnels and portal structures. Examples of seismic design used for underground structures are included in an appendix at the end of the report.

Pseudostatic Approach for Seismic Analysis of Single Piles

This paper evaluates a simple approximate methodology for estimating the maximum internal forces of piles subjected to lateral seismic excitation. The method involves two main steps: computation of the free-field soil movements caused by the earthquake and the analysis of the response of the pile to the maximum free-field soil movements (considered as static movements) plus a static loading at the pile head, which depends on the computed spectral acceleration of the structure being supported. The applicability of this approach has been verified by an independent benchmark analysis developed by the writers. It is demonstrated that the proposed method yields reasonable estimates of the pile maximum moment and shear. The methodology is then used to obtain the response of the Ohba-Ohashi bridge in Japan to one of the earthquakes that occurred in the 1980s. Good agreement is found between the computed and measured pile moments.

Numerical Analysis Of Non-linear Soil-structure Interaction

The present paper deals with a parametric study of soil-foundation-frame interaction in pseudo-static conditions by means of a new finite element code, named SOFIA. The analysis is performed considering strip foundations resting on linear and non-linear soil elements. The seismic actions are simulated by means of a pseudo-static approach. Even if the code is used for soil-foundationframe systems in plane-strain conditions, the 3-D effect is taken into account through an approximate procedure. In particular, in this paper the effects due to the soil-structure relative stiffness and the number of storeys in the superstructure are taken into account. The results, reported in a-dimensional form to be as general as possible. show some interesting differences between the static and pseudo-static behaviour of the soil-structure system and the importance of considering the soil nonlinearity.