## 1 Introduction
The \(k_{v}\) under single loading was significantly lower than that under step-by-step loading. [PERSON] [15] and [PERSON] [16] found, through tests, that with an increase in the \(\sigma_{r}\), the stress shared by the solid skeleton of the sample is obviously greater than that borne by the pore water, leading to compaction of the sample pores and a decrease in the \(k_{v}\). [PERSON] [17] and [PERSON] [18] studied the permeability of bentonite under different pressures and found that the coefficient of permeability also decreases with an increasing \(\sigma_{r}\). [PERSON] [19] found through permeability tests of compacted clay under different axial strains that the relative magnitude of the current confining pressure and preconsolidation pressure of the sample determined the deformation patterns as well as the permeability change. Different pore structures and particle gradations have a great influence on the \(k_{v}\)[20; 21; 22]. [PERSON] [23] investigated the relationship between the type of pore distribution and the \(k_{v}\) under different consolidation stresses by means of mercury injection testing. The study of [PERSON] [24] also found that the \(k_{v}\) does not change much when the content of fine particles in the sandy soil is less than 5%. When the fine particle content is between 5% and 10%, the \(k_{v}\) sharply decreases with an increasing fine particle content. In contrast, the coefficient of permeability of sandy soils tends to be relatively stable when the fine particle content is greater than 25%. [PERSON] [25] proposed an empirical formula for the coefficient of permeability of soils: \(k=Cd_{10}^{2}\). In regard to the deep soil mechanics test, domestic scholars such as [PERSON] [26; 27], [PERSON] [1], [PERSON] [28] and [PERSON] [29] have carried out quite effective research on the mechanical characteristics of the consolidation of deep clay under high stress, but research on the nonlinear permeability characteristics of soil under high stress is still in its initial stage [30]. There are few reports on deep soil mechanics in foreign countries because of the energy policy and natural endowment of coal seam. Because of the characteristics of high total stress and high water pressure, the bottom aquifers of thick alluviums with a permeable path have been subjected to long geological sedimentation during their formation. A high \(\sigma_{r}\) causes soil particles to break, thus changing the gradation of soil and changing its \(k_{v}\). To sum up, studying the nonlinear permeability characteristics of bottom aquifers of thick alluviums under high stress provide an indispensable theoretical basis for revealing the deformation mechanism of hydrophobic settlement in deep alluviums and the mechanism and prevention of indirect shaft mining fractures after mines are put into production. In view of the above, in this paper, against the background of shaft damage caused by the hydrophobic consolidation and settlement of high-confined aquifers at the bottom of thick alluviums, a joint HPLTC-HPPNP experimental study was carried out using an environmental triaxial automated system (hereafter referred to as \"ETAS\"). After high-pressure consolidation, the \(k_{v}\) under a constant \(\sigma_{r}\) was directly measured, and the nonlinear permeability characteristics of deep clayy sand were analyzed by determining the relationships amongst the consolidation pressure, hydraulic gradient, loading-unloading methods and permeability coefficient. Additionally, the pore structure characteristics of clayy sand were explored by low-field NMR technology, and the nonlinear permeability mechanism of deep clayy sand is discussed. The research results are expected to be beneficial for the study of the hydrophobic consolidation characteristics of confined aquifers and to make up for the shortcomings of deep soil mechanics in the study of permeability characteristics.