From force-based to displacement-based seismic design. What comes next?

Publicado: 09 Nov 2017Vistas 30 días: 29Vistas totales: [totalcount]

Extended summary

To the present day, the seismic design of structures is force-based: like wind, earthquakes are considered to impose lateral (i.e., horizontal) forces. A linear-elastic analysis of the structure gives the seismic internal force/moment demands in order to verify/adjust the capacities (i.e., the resistances in terms of internal forces/ moments) against them. This time-honored practice survives thanks to its solid foundation, namely equilibrium, and to its convenience: internal forces/moments from the linear analysis for the earthquake are easily combined with those due to gravity, which is a force-based loading.
Contrary to the presumption that an earthquake exerts specified forces on a structure, in reality it imparts to it (through the foundation) seismic energy. From another viewpoint, it produces displacements relative to the ground. The forces are a by-product of the displacements, not the other way around. The magnitude of the internal forces is controlled by the members' resistance at a number of locations sufficient to turn the structure into a mechanism, swaying back and forth up to the peak lateral displacement produced by the earthquake. Fortunately, this displacement may be estimated through an empirical observation: the "equal displacement" approximation (often called "rule") holds that the peak seismic displacement is about equal to that of the elastic structure, for any value of the ratio, R, between the resultant of the lateral forces produced by the earthquake on the elastic structure to the global lateral force resistance equilibrated by member resistances. If the global lateral force-displacement relationship is elastic-perfectly plastic, the ratio, μ, of the peak seismic displacement to the displacement at the instant the structure turns from elastic to a plastic mechanism (called ductility factor) is about equal to the force reduction factor R.
In force-based design member deformation capacities are indirectly addressed at the end of the design process through the ductility factor μ: members which are part of the plastic mechanism and have their resistance checked against the internal force/moment demands obtained from the elastic seismic analysis divided by R, should have deformation capacity not less than μ times the deformation at yielding. By contrast, in displacement-based design seismic deformation demands are meant to be directly checked against the deformation capacities.
Displacement-based design saw independent versions being conceived by two major figures of Earthquake Engineering and soon developing into two competing schools of thought and practice, attracting, therefore, the full attention of influential academics, practitioners and code-drafters. As a matter of fact, design of members to match seismic displacement or deformation demands with their own capacities is not central to either of these versions of displacement-based design. One version converts top displacement demands to internal forces and moments for which members are designed (as in force-based design); in the other version, members provisionally designed for other types of loadings (gravity, wind, etc.) have their design updated to match seismic deformation demands with their capacities.
In displacement-based design simple means are needed to estimate the member deformation capacities and seismic deformation demands. Deformation measures to be used in member checks should be easy to extract from analysis results, and at the same time constitute meaningful indicators of failure or not of the member. Strains are almost meaningless as indicators of loss of member resistance; moreover, their prediction by analysis is model-dependent. In contrast, chord rotations of member ends correlate well in capacity terms with local damage and loss of resistance. In terms of inelastic demands, robust estimates of chord rotations may be obtained rather easily, even by linear elastic analysis. However, the value of the elastic stiffness to be used for members holds the key to a relatively accurate estimation of member chord rotation demands. A strong (hence rare) earthquake will find the members cracked due to gravity loads or the restraint of thermal and drying shrinkage and will drive them past yielding. Therefore, a seismic response analysis should use as elastic stiffness the secant value to the apparent yield point in a bilinear approximation of the envelope to the moment-chord rotation response in cyclic loading.
Practical models for the secant-to-yield point stiffness of concrete members and for their deformations at flexure-controlled RC members at ultimate conditions have been developed t the University of Patras, after assembling a database of about four-and-a-half-thousands of tests - by far the largest and most diverse database of its kind in the world. The models apply to cyclic lateral loading and cover seamlessly beams, rectangular columns or walls, members with circular, T-, H-, U- or box section, conforming or not to seismic design codes, with continuous or lap-spliced deformed or plain (smooth) bars, with wrapping of the plastic hinge region with Fiber-Reinforced-Plastic (FRP) or without. The portfolio of models succeeds an earlier one of more narrow scope which had been adopted in the 2005 European structural design standard (the "Eurocode") on seismic assessment and retrofitting, or in the Model Code 2010 of the International Federation for Structural Concrete (fib). The latest more complete and reliable version has been tentatively adopted in the second generation of the same Eurocode.
Despite the rationality of the new paradigm, displacement-based design has not made a serious dent yet in seismic design codes or practice: it is used only for seismic assessment and retrofitting of older structures. The new generation of Eurocodes tentatively considers it as an alternative to force-based design for new structures.
Shortly before the emergence of displacement-based design, a few seminal publications co-authored by important personalities of the international community of Earthquake Engineering drew its attention to the seismic energy imparted to the structure through the foundation.
Energy provides much better ground for seismic design than forces or displacements: 
  • Energy conservation, the basis of the energy approach, is a law of nature, as solid, familiar to engineers and easy to apply as the foundation of the force-based approach, i.e., equilibrium.
  • The total energy per unit mass due to an earthquake depends on the pre-yielding fundamental period of a structure but is (almost) independent of its strength, viscous damping ratio, etc. This is the equivalent of the "equal displacement rule" and matches the prime advantage of displacements over forces.
  • Forces and displacements are vectors; their components in two (often arbitrarily chosen) orthogonal horizontal directions are normally considered separately in design, despite the fact that the most critical response to concurrent shaking in both horizontal directions and the associated damage occur in an intermediate direction. The true response is better described by a scalar measure, such as energy. 
  • Energy embodies more damage-related information than displacements, e.g., the number of equivalent cycles.
  • Numerical instabilities or lack of convergence during a nonlinear response-history analysis clearly show up in the evolution of the components of energy; so, a positive side-effect of tracing the energy components is the awareness of any numerical problems. 
Initial enthusiasm for seismic energy was great, as evidenced by the dozens of papers that followed in the short- to medium-term. Today the State-of-the-art may be considered as satisfactory only as far as the total energy demand is concerned. Its flow and distribution within the structure during the inelastic response is an open issue, to be answered on a case-by-case basis through nonlinear response-history analysis. The recently acknowledged, yet unresolved, problems attributed to the viscous damping model are an important hurdle to the distribution of the energy demand within the structure.
With time, research interest shifted to seismic design with energy dissipation devices or other supplemental protection techniques, where energy concepts is the natural approach to follow. By contrast, research output concerning energy-based seismic design or evaluation and retrofitting of conventional structures without seismic protection devices reduced to a trickle, both in terms of volume and/or substance.
To date, the promising energy approach to seismic design has fallen short of its true potential. Perhaps it fell victim to circumstances, as it was pre-maturely surpassed and overshadowed by displacement-based design. Instead of developing all the way, to bear fruits for Engineering practice and improve the seismic resistance of structures, it remained an academic exercise, and indeed a quite imbalanced one, as it has focused on the facet of the problem that is easier to tackle, i.e., the energy demand, ignoring the energy capacity, which is more challenging and requires much more R&D work. Indeed, the largest gap of knowledge concerns the energy capacity of structural elements, where nothing has been done. Moreover, despite the huge leaps it has made in recent years, the S/T community of Geotechnical Earthquake Engineering has completely overlooked the concept of seismic energy and the opportunities it opens for whatever concerns the behavior of the foundation soil in earthquakes and its interaction with the seismic response of the structure.

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