## 1 Introduction  
As the product of the weathering of parent rocks, granite residual soils are widely distributed in the tropics and subtropics, including some developed regions such as Singapore, Hong Kong, and the southeast coastal areas of China [1, 2, 3]. In the past few decades, with the rapid development of the economy and the continuous advancement of urbanization in these regions, granite residual soils have been encountered more and more frequently in geotechnical engineering projects such as the excavation of foundation pits and subway tunnels [4, 5, 6, 7]. Moreover, granite residual soils are also frequently-used building materials, utilized for the filling of embankments and dams [3, 8]. As a result, granite residual soils have attracted considerable attention from many scholars. Many aspects of granite residual soils have been studied, including the engineering geological characteristics [2, 9], index properties [10, 11], mechanical properties [8, 12, 13, 14], heterogeneity [15, 16, 17, 18] (soil properties vary vertically and horizontally due to the variable degree of weathering), small strain stiffness [19, 20], unsaturated soil behavior [21, 22, 23, 24, 25], and the in situ measurement of soil properties [26; 27; 28; 29]. It is generally recognized that granite residual soils have unusual grain size distributions from gravel to clay [2; 30]. Another two typical features of granite residual soils are the degradation of soil properties when soaked [31] and the heterogeneous nature [17], both making it hard to predict engineering behavior of the soils. Due to the special microstructures developed in the process of weathering, granite residual soils exhibit quite different engineering properties from those of sedimentary soils [32], and are generally considered as problem soils [33; 34]. In geotechnical engineering, the stress paths experienced by soil elements are diverse and can be very complicated [35], causing various possible patterns of variation of mean effective stress (\(p\)'), which can be roughly classified into three categories: increasing-\(p\)', constant-\(p\)', and decreasing-\(p\)'. It is widely known that during excavation of a foundation pit, stress paths experienced by soil elements in different positions of the foundation pit are quite different [36], as shown in Figure 1. Different from the stress path of conventional triaxial tests (constant \(\sigma_{3}\) and increasing \(\sigma_{1}\)), soil elements in the side of pits experience stress paths with decreasing \(\sigma_{3}\) and constant \(\sigma_{1}\), while \(\sigma_{3}\) remains constant and \(\sigma_{1}\) decreases for soil elements in the bottom. It is obvious that both soil elements in the bottom and the side of the pit experience decreasing-\(p\)' stress paths. Therefore, prior to the design of retaining structures and the prediction of deformation for a foundation pit, the mechanical behavior of soil under decreasing-\(p\)' stress paths must be sufficiently studied [37]. However, to the best of the authors' knowledge, in most of reported experimental studies concerning granite residual soils [3; 14; 38; 39], soil specimens were sheared using the conventional stress path with constant \(\sigma_{3}\) and increasing \(\sigma_{1}\) in triaxial tests, in which case soil elements experience an increasing-\(p\)' stress path. Although some scholars investigated the mechanical behaviors of decomposed granite under the stress paths of rainfall-induced slope failures [8; 13], which are characterized by constant \(q\) and decreasing \(p\)', soil behaviors under decreasing-\(p\)' stress paths have not been systematically compared with those under increasing-\(p\)' stress paths. Moreover, the effects of patterns of variation of mean effective stress on shearing strength and the stiffness of granite residual soils have not been evaluated quantitatively; it is hard to make practical suggestions for excavation engineering.