عنوان مقاله [English]
Considering countless repetitions of Gaussian-shape bending moment-depth curves, M(z)-z, in the results of several experimental/numerical and static-seismic physical modeling, suggestion of a new relationship for using this opportunity appears to be suitable. This relationship is created a connection between high-used p-y curves and the structural internal efforts of piles in the form of bending moment along the piles lengths. In this study, the bending moment equation along the depth for the issue of floating pile row under near-fault earthquake lateral loading in the dry sandy slope is obtained by using the results of the three-dimensional numerical models and physical models. Therefore, in the next step, the values of bending moment by the suggested new relationships transform to the proportional p-y curves. The main abilities and advantages of the new suggested relationships include generation of relationships compatible for different soil types such as clayey soils (i.e., cohesive soils), mixed cohesive-granular soils, sandy soil and some weak rocks. Furthermore, other advantages of new relationships include (1) the
compatibility of relationships with the experimental tests and the static field tests, cyclic, and seismic modeling, (2) have no need to calculate slip depth in the sliding sand mass in the sandy slope failure problem and the fully analytical form of the relationships. In addition, all the conducted mathematical calculations are done in the parametric form; therefore, all other kinds of similar problems can be totally computed by the suggested new analytical relationships. In this study, the mathematical-analytical relationships among monotonic static p-y curves, tangent hyperbolic cyclic p-y curves, and Gaussian bending moment curves were presented. The Gaussian-shape bending-moment curves have been calculated for dynamic loading of floating pile row in the dry sandy slope under different combinations of near-fault earthquakes. According to the findings of the present paper, the values of Gaussian bending moment curves can be simply transformed to the soil pressure, p, and relative pile-soil deflection, y. Essentially, by using this strategy, the quantity of generated stresses within the soil due to pile lateral loading and soil yielding or soil plasticity can be controlled. On the other hand, by understanding the deflection of pile, y, the values of pile lateral deflection can be compared with allowable deflections in each project; the surviving of the superstructure can be judged based on the pile in the safe zone. In each arbitrary depth, the values of two parameters pu and Ki are different, and the values of these two parameters generally depend on the depth change; in addition, these differences there are between p-y curves in the different depths. The slope of the initial portion of both static and cyclic p-y curves at points p=0 (equivalent to the earth surface i.e., z=0 in the sandy soils) and y=0, according to the present article calculations is always Ki, which is a stress-kind parameter and has a stress unit. The findings of the paper show that the shape of the bending moment curves obtained from the double integration of static and cyclic p-y curves, p(z) component, similar to the shape of numerical bending moment curves, is Gaussian. Moreover, the sign and depth-pattern of the obtained bending moment curves are completely similar to the considered predictions. The depth location of the maximum bending moment from double integration of static monotonic p-y curves is in a depth that is close to the depth of the maximum bending moment of numerical results, while the maximum bending moment from double integration of cyclic p-y curves occurs in the shallow depth (i.e., at the zone of failure surface of the slope).