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目的:研究P波斜入射下的地基动应力路径,探讨其影响因素和可能变化范围,为进一步研究斜入射地震波作用下场地动力响应奠定理论基础。创新点:1.从数学上证明斜入射P波在任一深度的地基中形成的应力路径在剪应力分量(偏差正应力-水平剪应力)组成的平面中为一个斜椭圆;2.分析了P波入射角、土体泊松比和单位波长深度对斜椭圆应力路径形状与大小的影响。方法:1.基于半无限弹性空间的地震波传播理论,考虑地震波在自由界面的反射,推导土体中任一深度处由P波斜入射产生的动应力,并表示成由剪应力分量组成的平面下的应力路径(公式(9))及该应力路径的特征参数表达式(公式(A12)~(A14));2.通过控制变量法,分析参数敏感性(图7、9、10和12)。结论:1.虽然证实P波斜入射引起的应力路径为斜椭圆形式,但在地基深度、入射波频率和波速的特定组合下,斜椭圆仍可从斜线一直变化到圆形,形式较为多样化;2.P波斜入射角度在30?~60?时引起的动偏应力幅最大,最大可达同等条件下其它入射角产生的动应力幅的2倍以上;3.斜入射角大于45?后,斜椭圆路径形状几乎不随入射角改变,在研究范围内以竖直扁椭圆形为主;4.土体饱和度大于70%时,泊松比的变化对土体斜椭圆路径形状影响不大,但动应力幅随泊松比增大而显著降低。
OBJECTIVE: To study the dynamic stress path of ground under P-wave oblique incidence, discuss its influencing factors and possible variation range, and lay a theoretical foundation for further study of dynamic response of site under oblique incident seismic wave. Innovative points: 1. It is mathematically proved that the stress path formed by inclined incident P waves in the ground at any depth is an oblique ellipse in the plane composed of shear stress components (normalized stress-horizontal shear stress); 2. The P Influence of wave incident angle, Poisson’s ratio of soil and unit wave length on shape and size of oblique elliptical stress path. Based on the theory of seismic wave propagation in semi-infinite elastic space, considering the reflection of seismic wave in the free interface, the dynamic stress generated by oblique incidence of P wave at any depth in soil is deduced and expressed as a plane composed of shear stress components (Eq. (9)) and the characteristic parameters of the stress path (Eqs. (A12) ~ (A14)); 2. Analyze the sensitivity of the parameters through the control variable method ). Although it is confirmed that the stress path caused by the oblique incidence of P wave is oblique ellipse, under the specific combination of ground depth, incident wave frequency and wave velocity, the oblique ellipse can change from the oblique line to the circle all the time in various forms 2. The maximum value of dynamic stress amplitude caused by oblique incident angle of P wave from 30 ° to 60 ° is more than twice of the dynamic stress amplitude caused by other incident angles under the same conditions.后, the shape of oblique elliptical path almost does not change with the incident angle, which is dominated by vertical oblate ellipsoid in the study area; 4. The influence of Poisson’s ratio on the shape of oblique elliptical path of soil when soil saturation is more than 70% It is not significant, but the dynamic stress amplitude decreases with the increase of Poisson’s ratio.