Nozomu Yoshida

Equivalent linear method considering frequency dependent characteristics of stiffness and damping

Abstract Equivalent linear dynamic response analysis of ground is based on complex moduli and Fourier series expansion; therefore, it is not an equivalent method but an approximate method. Two deficiencies in the conventional equivalent linear method represented by SHAKE are described first. The maximum shear strength is overestimated, resulting in overestimation of the peak acceleration under a strong ground motion, and the amplification is underestimated at high frequency. The latter sometimes results in underestimation of the peak acceleration under weak ground shaking, and gives an incident wave with unrealistic large accelerations or a divergence of analysis in deconvolution analysis under strong ground motion. Both deficiencies are shown to come from the same cause, i.e. computing the effective strain as a constant fraction of the maximum strain. Since this is a key concept of the equivalent linear analysis, one cannot overcome both deficiencies at the same time in the conventional method. An apparent frequency dependence in stiffness and damping is shown to appear in the dynamic response, although soil itself does not show frequency dependent characteristics. Following this observation, the effective strain is expressed in terms of frequency from the similarity concept of the strain–frequency relationship between time domain and frequency domain. This enables the reduction of both deficiencies at the same time, resulting in a marked improvement in the equivalent linear analysis. The accuracy of the proposed method is examined by the simulations of three vertical array records during large earthquakes. The proposed method always gives much better prediction than conventional equivalent linear methods for both convolution and deconvolution analyses, and it is confirmed to be applicable at more than 1% shear strain.

In Situ Soil Testing

Mechanical properties of the geomaterial frequently change during the sampling and the traveling as will be described in Sect. 6.5. Therefore, it is recommended to obtain the mechanical properties in situ as possible. As shown in Fig. 4.4, however, an in situ test is difficult to obtain the behavior at large strain. The elastic modulus is to be measured in situ at minimum.

SIMPLIFIED METHOD FOR ESTIMATING MAXIMUM SHEAR STRESS IN THE GROUND DURING EARTHQUAKES

地表面の最大加速度及び Spectrum Intensity (SI) を用いて液状化判定に用いる地震時の地盤のせん断応力を精度良く求めるための推定式を提案している. ここで提案した方法は, 従来の簡易判定法における推定式と同じ情報にSIを加味するだけで地震時の地盤のせん断応力比を推定でき, 地盤剛性や基盤深さ等の地盤の詳細データは不要であるという特徴がある. SIは最大加速度と同じく地表面加速度波形から得られる情報であるので, この方法は簡便的な方法といえる. この方法を用いて, 兵庫県南部地震におけるポートアイランド及び第二鹿児島県北西部地震における阿久根市と川内市の地震時最大せん断応力分布の推定を行い, 従来法による結果と比較して, 提案した手法の有効性について検討している.

Equation of Motion

Governing differential equation to control the vibration of the ground is called a wave equation, an equation of vibration, or an equation of motion. They are essentially equivalent but appearance may be different depending on the way to derive it.

Propagation of Earthquake Waves in the Ground and Fundamentals of Earthquake Motion

Fundamental knowledge on the amplification and the attenuation of the earthquake waves, which is necessary to understand the wave propagation in the ground, is introduced in this chapter.

Engineering Seismic Base Layer for Defining Design Earthquake Motion

Engineers common sense that incident wave is common in a widespread area at the engineering seismic base layer is shown not to be correct. An exhibiting example is first shown, which indicates that earthquake motion at the ground surface evaluated by the analysis considering the ground from a seismic bedrock to a ground surface simultaneously (continuous analysis) is different from the one by the analysis in which the ground is separated at the engineering seismic base layer and analyzed separately (separate analysis). The reason is investigated by several approaches. Investigation based on eigen value problem indicates that the first predominant period in the continuous analysis cannot be found in the separate analysis, and predominant period at higher order does not match in the upper and lower ground in the separate analysis. The earthquake response analysis indicates that reflected wave at the engineering seismic base layer is not zero, which indicates that conventional engineering seismic base layer...

Evaluation of Damping

The equation of motion is introduced in Chap. 9 as

Estimation of Mechanical Soil Properties

m\ddot{u}+c\dot{u}+ ku=-m{\ddot{u}}_g,