# The effect of overlapping passive zones in sand investigated by a geotechnical centrifuge model

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## Abstract

This thesis presents an investigation on the effect of overlapping passive zones in sand. The hypothesis of larger stresses in the soil and a larger ultimate resistance capacity in case of overlapping passive zones was firstly investigated in the numerical study by Joosse (2015). He introduced an intensification factor as a design optimization tool for economic design and optimization of retaining walls in narrow trenches. The intensification factor is defined as the ratio between the ultimate passive capacity in a restrained situation (overlapping passive zones) and in an unrestrained situation (no overlapping effects). To verify the numerical design approach, a physical model was developed and used for centrifuge testing by Hopman (2016). The developed actuator is used again in this thesis to do extensive centrifuge tests to model the effect of overlapping passive zones in sand. Together with the newly developed sand model preparation method, as introduced in this thesis, it is possible to produce accurate and repeatable sand samples. The main objectives of this thesis are to investigate the effects of a variation in density and the effect of a layered sand sample on the intensification factor. The intensification factors in this thesis are determined at wall displacements corresponding to 0.01, 0.02 and 0.04 times the embedded depth (D) as well as at the wall displacement corresponding to the ultimate passive load. The ultimate passive load is found by the plateau state in the Load-displacement curve and by the development of the full shear plane as visualized by image analysis. It turns out that the ultimate passive load and the formation of the associated shear band have a significant dependency on the relative density. Although the ultimate passive loads differ significantly, the intensification factors at the plateau states are similar with 1.33 and 1.34 for the loose and dense sand respectively. The shapes of the shear planes as visualized by image analysis are in accordance to theory and numerical calculations. Grain size seems to be of less importance on the ultimate passive load. Also the intensification factor at plateau state for coarse sand is similar to that of fine sand. Investigation on the friction between the plexiglass and sand showed that by applying membranes to the plexiglass with silicon grease, frictionless boundaries could be created. It turns out that the friction has a significant impact on the width of the shear planes in the physical model. The observed shear planes are smaller than in a frictionless environment. The shear planes develop up to 29% further in the frictionless unrestrained situation. The reduction in friction also means a reduction in measured loads by the actuator which must be taken into account when using the results from the load vs. displacement data. The intensification for a trench with varying embedded depth but constant trench width (W) over embedded depth ratio is investigated with centrifuge tests. When comparing an embedded depth of 3 m and 5 m with a constant W/D ratio of 2.0, the intensification factor turns out to be identical. The shape of the shear plane is proportional to the embedded depth. The intensification in layered sand consisting of loose sand on top of dense sand in an equal division is investigated. The load curves for the layered sand are bounded by the load curves of homogenous loose and dense sands at the bottom and top respectively. Because the loads in unrestrained situation are higher in proportion to the restrained loads, the intensification turns out to be significantly less than for homogenous sands.