The compressible inclusion function of EPS geofoam

An alternative to the Mononobe–Okabe equations for seismic earth pressures

Underground structures, tunnels, subways, metro stations and parking lots, are crucial components of the build environment and transportation networks. Considering their importance for life save and economy, appropriate seismic design is of prior significance. Their seismic performance during past earthquakes is generally better than aboveground structures. However several cases of severe damage to total collapse have been reported in the literature, with that of the Daikai metro station in Kobe during the Hyogoken-Nambu earthquake (1995) being one of the most characteristic. These recent damages revealed some important weaknesses in the current seismic design practices. The aim of this chapter is not to make another general presentation of the methods used for the seismic design of underground structures, but rather to discuss and highlight the most important needs for an improved seismic performance and design. In that respect it is important to consider that the specific geometric and conceptual features of underground structures make their seismic behavior and performance very distinct from the behavior of aboveground structures, as they are subjected to strong seismic ground deformations and distortions, rather than inertial loads. Several methods are available, from simplified analytical elastic solutions, to sophisticated and in principal more accurate, full dynamic numerical models. Most of them have noticeable weaknesses on the description of the physical phenomenon, the design assumptions and principles and the evaluation of the parameters they need. The chapter presents a short but comprehensive review of the available design methods, denoting the crucial issues and the problems that an engineer could face during the seismic analysis. The main issues discussed herein cover the following topics: (i) force based design against displacement based design, (ii) deformation modes of rectangular underground structures under seismic excitation, (iii) seismic earth pressures on underground structures, (iv) seismic shear stresses distribution on the perimeter of the structure, (v) appropriateness of the presently used impedance functions to model the inertial and the kinematic soil-structure interaction effects, (vi) design seismic input motion, accounting of the incoherence effects and the spatial variation of the motion and (vii) effect of the build environment (i.e. city-effects) on the seismic response of underground structures. The discussion is based on detailed numerical analysis of specific cases and recent experimental results in centrifuge tests. Other important issues like the design of submerged tunnels to liquefaction risk, or the complexity to evaluate the response of the joints of submerged tunnels are also shortly addressed. Finally we present the most recent developments on the evaluation of adequate fragility curves for shallow tunnels.

Performance and Seismic Design of Underground Structures

http://ssi.civil.ntua.gr/downloads/journals/2005-SDEE_Seismic%20earth%20pressures%20on%20rigid%20and%20flexible%20walls.pdf

Seismic earth pressures on rigid and flexible retaining walls

A critical evaluation is made of the response to horizontal ground shaking of flexible cantilever retaining walls that are elastically constrained against rotation at their base. The retained medium is idealized as a uniform, linear, viscoelastic stratum of constant thickness and semi-infinite extent in the horizontal direction. The parameters varied include the flexibilities of the wall and its base, the properties of the retained medium, and the characteristics of the ground motion. In addition to long-period, effectively static excitations, both harmonic base motions and an actual earthquake record are considered. The response quantities examined include the displacements of the wall relative to the moving base, the wall pressures, and the associated shears and bending moments. The method of analysis used is described only briefly, emphasis being placed on the presentation and interpretation of the comprehensive numerical solutions. It is shown that, for realistic wall flexibilities, the maximum wall f...

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Dynamic response of cantilever retaining walls

A critical evaluation is made of the dynamic pressures and the associated forces induced by ground shaking on a rigid, straight, vertical wall retaining a semi-infinite, uniform viscoelastic layer of constant thickness. The effects of both harmonic and earthquake-induced excitations are examined. Simple approximate expressions for the responses of the system are developed, and comprehensive numerical data are presented which elucidate the effects and relative importance of the various parameters involved. These solutions are then compared with those obtained by use of a simple model proposed previously by Scott, and the accuracy of this model is assessed. Finally, two versions of an alternative model are proposed which better approximate the action of the system. In the first, the properties of the model are defined by frequency-dependent parameters, whereas in the second, which is particularly helpful in analyses of transient response, they are represented by frequency-independent, constant parameters.

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Dynamic soil pressures on rigid vertical walls

Following a brief review of the inaccuracies that may result from the use of a popular model for evaluating the dynamic soil pressures and associated forces induced by ground shaking in a rigid wall retaining an elastic stratum, the sources of the inaccuracies are identified and a modification is proposed which, while retaining the attractiveness of the original model, defines correctly the action of the system. In the proposed modification, the soil stratum is modeled by a series of elastically supported, semiinfinite horizontal bars with distributed mass rather than by massless springs. The concepts involved are introduced by reference to a fixed-based wall retaining a homogeneous elastic stratum, and are then applied to the analysis of more complex soil-wall systems. Both harmonic and transient excitations are considered, and comprehensive numerical solutions are presented that elucidate the actions of the systems examined, and the effects and relative importance of the numerous parameters involved.

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Dynamic modeling and response of soil-wall systems

Making use of an extension of a recently proposed, relatively simple, approximate method of analysis, a critical evaluation is made of the response to horizontal ground shaking of flexible walls retaining a uniform, linear, viscoelastic stratum of constant thickness and semi-infinite extent in the horizontal direction. Both cantilever and top-supported walls are examined. Following a detailed description of the method and of its rate of convergence, comprehensive numerical solutions are presented that elucidate the action of the system and the effects of the various parameters involved. The parameters varied include the flexibility of the wall, the condition of top support, and the characteristics of the ground motion. The effects of both harmonic base motions and an actual earthquake record are examined. Special attention is paid to the effects of long-period, effectively static excitations. A maximum dynamic response is then expressed as the product of the corresponding static response and an appropriate amplification or deamplification factor. The response quantities examined include the displacements of the wall relative to its moving base, the dynamic wall pressures, and the total wall force, base shear and base moment. Copyright © 2000 John Wiley & Sons, Ltd.

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Dynamic response of flexible retaining walls

The analysis of the response to horizontal base shaking for solid-containing rigid tanks, described in a companion paper, is extended to flexible tanks. Simple, approximate expressions for the critical responses are formulated, and comprehensive numerical data are presented that elucidate the effects of wall flexibility over wide ranges of the parameters involved. The response quantities examined include the stresses induced on the wall, the maximum wall forces, and the forces transmitted to the foundation. in addition to long-period, effectively static excitations, harmonic motions of arbitrary frequency and an actual earthquake ground motion are considered. A brief account is also given of the interrelationship of the critical responses of solid-containing tanks and those induced in tanks storing a liquid of the same mass density.

A. H. Younan

Papers

Dynamic soil pressures on rigid vertical walls

Dynamic response of cantilever retaining walls

Dynamic modeling and response of soil-wall systems

Dynamic response of flexible retaining walls

Dynamics of Solid-Containing Tanks. II: Flexible Tanks