## 4 Conclusions  
In this study, using a large-scale high-pressure triaxial shear apparatus and a self-designed microfriction load-transfer plate for triaxial compression tests in geotechnical engineering, large-scale triaxial shear tests of coarse-grained soil samples with end-restraint and end-free (microfriction) characteristics were conducted. Under typical end-restraint and end-free (microfriction) conditions, the strength and deformation characteristics of the coarse-grained soil were investigated. The effect of the end restraint on the stress and strain properties of the coarse-grained soil was analyzed. The following conclusions can be drawn:  
1. The stress-strain relationship curves of the coarse-grained soil had similar properties under the end-restraint and end-free (microfriction) conditions. With regards to the dense coarse-grained soil, the deviator stress-strain curve of the specimen with the end restraint showed strain-softening behavior under a smaller confining pressure but strain-hardening behavior under a larger confining pressure. When it was subjected to a modest confining pressure, the behavior of the end-free specimen showed a more pronounced propensity to soften than the specimen with the end restraint. 2. The volumetric strain behavior of the coarse-grained soil was consistent both under the end-restraint and end-free (microfriction) conditions. Under a low confining pressure, the coarse-grained soil first exhibited volumetric contraction, followed by volumetric dilation, and only exhibited volumetric contraction under a higher confining pressure. The tendency of the coarse-grained soil to show volumetric shrinkage under a low confining pressure was more pronounced in the initial stages of shearing. With the emergence of shearing, the volumetric dilation tendency of the coarse-grained soil under the end-free (microfriction) condition became more pronounced. When the confining pressure was higher, the volumetric strain of the specimen with the end restraint was consistently greater than the end-free specimen, which displayed a marked tendency for volumetric contraction throughout the whole shearing process. 3. The end restraint had little effect on the strength parameters of the coarse-grained soil, but it had a greater impact on its deformation parameters. When the Duncan-Chang E-B and E-\(\mu\) models were used for fitting, compared with the end-free (microfriction) model, the linear strength indices \(c\) and \(\varphi\) and the nonlinear strength indices \(\varphi_{0}\) and \(\Delta\varphi\) of the end-restraint model were slightly increased. Further, the deformation parameter indicators \(K\) and \(K_{b}\) increased significantly, indicating that the end restraint condition had a higher effect than the end-free condition on the deformation properties of the coarse-grained soil. Figure 11: Comparison of deformation of coarse-grained soil specimens under different end-restraint conditions after testing (0.4 MPa): (**a**) End restraint; (**b**) End free (microfriction). * For the end-restraint specimen, it can be seen that the end-restraint restricted the radial deformation at the specimen's end, but the radial deformation of the specimen's middle portion was significantly larger than that of the end-free specimen, indicating bulging. The microfriction-affected specimens had a substantially more consistent deformation distribution. Methodology and writing, Y.W. ; conceptualization, J.P.; resources, H.Z. ; investigation, S.Z. ; test, H.X. All authors have read and agreed to the published version of the manuscript. This research was supported by the National Natural Science Foundation of China (Grants No. 51,779,017 and U21A20158), and the Foundation of Yangtze River Scientific Research Institute in China (Grants No. CKSF2021484/YT), to whom we are all grateful. * _[PERSON] and [PERSON] (1994)_ _[PERSON]; [PERSON] The influence of geometry and end restraint on the strength in triaxial compression in numerical simulation.