Formulation Of Earthquake Input Energy Research Articles

Analysis of Earthquake Energy Input in Soil-Pile-Structure System with Uncertain Soil Parameter

The energy flow in a soil-pile-structure (SPS) system during an earthquake is an important consideration in seismic-resistant design. The energy input to the structure is formulated here in the frequency domain. The frequency-domain approach enables the exact and complete treatment of frequency-dependent stiffness and damping properties. It is shown that the input energy can be derived in a compact form through the frequency integration of the product of the ground-motion input component and the structural model component. By taking full advantage of this compact form, it is demonstrated that the formulation of earthquake input energy in the frequency domain is essentially appropriate for deriving the exact first and second-order sensitivities of the input energy with respect to an uncertain soil stiffness parameter. The sensitivity expressions derived for swaying-rocking models with independent uncertain parameters are used here for the efficient formulation in a new model. The exact second-order sensitivities facilitate the expression of input energy variation due to uncertainty in ground stiffness, which is useful seismic design data.

Closed-Form Sensitivity of Earthquake Input Energy to Soil-Structure Interaction System

The input energy to a soil-structure interaction (SSI) system during earthquake shaking is taken as a structural performance measure and is formulated in the frequency domain. The purpose of this paper is to derive the closed-form expression of the sensitivity of the input energy to the SSI system with respect to uncertain parameters representing soil stiffness and damping. It is demonstrated first that the input energy expression can be of a compact form consisting of the product between the input motion component (Fourier amplitude spectrum of acceleration) and the structural model component (so-called energy transfer function). With the help of this compact form, it is shown that the formulation of earthquake input energy in the frequency domain is essential for deriving the closed-form expressions of the sensitivity of the input energy to the SSI system with respect to uncertain parameters in contrast to the time-domain formulation including inevitable numerical error and instability. This formulation is then extended to a multidegree-of-freedom superstructure model. Numerical examples support the fact that the closed-form expressions enable one to find in a reliable and efficient way the most critical combination of the uncertain parameters that leads to the maximum energy input.

Exact Higher-Order Sensitivity and Variation of Earthquake Energy Input in Soil-Structure Interaction System

The energy input to a soil-structure interaction (SSI) system during an earthquake is an important measure of seismic demand. It is formulated here in the frequency domain. Exact higher-order sensitivities of the input energy to the SSI system are derived with respect to uncertain soil stiffness and damping parameters. It is shown that the input energy can be derived in a compact form through the frequency integration of the product between the ground-motion input component and the structural model component. By taking full advantage of this compact form, it is demonstrated that the formulation of earthquake input energy in the frequency domain is essentially appropriate for deriving the exact higher-order sensitivities of the input energy to the SSI system with respect to the uncertain parameters. The exact higher-order sensitivities facilitate to express the input energy variation due to uncertainty of ground stiffness and damping, and to find the most unfavorable combination of the uncertain parameters leading to the maximum energy input.

Uncertain-parameter sensitivity of earthquake input energy to base-isolated structure

The input energy to a base-isolated (BI) building during an earthquake is considered and formulated in the frequency domain. The frequency-domain approach for input energy computation has some notable advantages over the conventional time-domain approach. Sensitivities of the input energy to the BI building are derived with respect to uncertain parameters in the base-isolation system. It is demonstrated that the input energy can be of a compact form via the frequency integration of the product between the input component (Fourier amplitude spectrum of acceleration) and the structural model component (so-called energy transfer function). With the help of this compact form, it is shown that the formulation of earthquake input energy in the frequency domain is essential for deriving the sensitivities of the input energy to the BI building with respect to uncertain parameters. The sensitivity expressions provide us with information on the most unfavorable combination of the uncertain parameters which leads to the maximum energy input.

Bound of earthquake input energy to soil–structure interaction systems

A new critical excitation method is developed for soil–structure interaction systems. In contrast to previous studies considering amplitude nonstationarity only, no special constraint of input motions is needed on nonstationarity. The input energy to the soil–structure interaction system during an earthquake is introduced as a new measure of criticality. It is demonstrated that the input energy expression can be of a compact form via the frequency integration of the product between the input component (Fourier amplitude spectrum) and the structural model component (so-called energy transfer function). With the help of this compact form, it is shown that the formulation of earthquake input energy in the frequency domain is essential for solving the critical excitation problem and deriving a bound on the earthquake input energy for a class of ground motions. The extension of the concept to MDOF systems is also presented.

Bound of Earthquake Input Energy

A new general critical excitation method is developed for a damped linear elastic single-degree-of-freedom structure. In contrast to previous studies considering amplitude nonstationarity only, no special constraint of input motions is needed on nonstationarity. The input energy to the structure during an earthquake is introduced as a new measure of criticality. It is shown that the formulation of earthquake input energy in the frequency domain is essential for solving the critical excitation problem and deriving a bound on the earthquake input energy for a class of ground motions. It is remarkable that no mathematical programming technique is required in the solution procedure. This enables structural engineers to use the method in their structural design practice without difficulty. The constancy of earthquake input energy for various natural periods and damping ratios is discussed based on an original sophisticated mathematical treatment. Through numerical examinations for four classes of recorded ground motions, the bounds under acceleration and velocity constraints (time integral of the squared base acceleration and time integral of the squared base velocity) are clarified to be meaningful in the short and intermediate/long natural period ranges, respectively.