# Role of Bimodal Water Retention Curve on the Unsaturated Shear Strength
## 1 Introduction  
Many regions in the world have a geological profile that is characterized by a deep groundwater table. Since the location of the groundwater table varies from 5 to 20 m underneath ground surface, the vadose zone or the unsaturated soil zone cannot be neglected for geotechnical-related issues in many parts of the world [1; 2; 3; 4; 5; 6]. One such issue is slope instability due to rainfall. Prolonged rainfall would result in an increased occurrence of rainfall-induced slope failures and prolonged drought would adversely affect the water content in soil and plant health [7; 8; 9; 10]. The changes in rainfall intensity would affect the groundwater fluctuations, which may significantly impact the quality of surface water [11]. These adverse effects of climate change could be mitigated by having a comprehensive knowledge about hydraulic properties of unsaturated soils--bimodal water retention curve (WRC) and permeability functions. Past studies [12; 13; 14] indicated that compacted soils with bimodal pore size distribution (PSD) are less susceptible to changes in the external environment (prolonged drying and intense rainfall). As a result, bimodal soils would be beneficial for plant health, as they would be able to retain more water during prolonged drying and for slope stability because they would be able to drain out water faster during intense rainfall [15; 16]. Soils with a bimodal grain-size distribution can exhibit bimodal characteristics in their WRC, however, a bimodal grain-size distribution does not guarantee the bimodality of the WRC [17; 18; 19; 20; 21]. Bimodality can be exhibited in the WRC and, consequently, in the permeability function since the permeability function takes up the shape of the WRC [22; 23; 24]. A bimodal PSD is highly associated with a bimodal WRC [25; 26; 27]. A bimodal PSD consists of two pore series, the larger of the two corresponds to the macropores, while the smaller one corresponds to the micropores [27]. [PERSON] et al. [28] investigated the pore-size distribution of compacted kaolinite soil, a type of fine-grained soil, which was compacted at three distinct water contents across the compaction curve: dry of optimum, optimum moisture content, and wet of optimum. Only the specimen compacted in the dry of optimum exhibits a bimodal PSD. Based on the relations of the pores to the PSD, the inter-aggregate pores and intra-aggregate pores can be seen as equivalent to the macropores and micropores mentioned by [PERSON] et al. [17], respectively. The inter-aggregate pores referred to by [PERSON] et al. [12] correspond to the first sub-curve of the bimodal WRC, whereas the intra-aggregate pores correspond to the second sub-curve, very similar to the macropores referred to by [PERSON] et al. [17], which correspond to the first sub-curve and the micropores that correspond to the second sub-curve. The terms micropores and macropores will be used in this paper for consistency. Shear strength of unsaturated soil is required for addressing numerous geotechnical problems such as slope stability [29; 30]. An increase in shear strength is closely related to an increase in matric suction as governed by unsaturated shear strength angle (\(\phi^{\text{b}}\)). \(\phi^{\text{b}}\) is equal to effective friction angle \(\phi^{\prime}\) for matric suction up to the air-entry value (\(AEV\)) of soil [29]. Therefore, a linear relationship between shear strength and matric suction is normally obtained experimentally at matric suctions up to \(AEV\). Beyond \(AEV\), the soil starts to become unsaturated and the shear strength envelope become non-linear and \(\phi^{\text{b}}\) is not equal to \(\phi^{\prime}\) anymore but \(\phi^{\text{b}}\) decreases with increasing matric suctions [31]. Beyond residual matric suction, the shear strength of an unsaturated soil may increase, decrease or remain constant when the matric suction increases [32]. Laboratory measurement of unsaturated shear strength is costly and time-consuming.