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248   Analysis and Design of Energy Geostructures


                Tabucanon et al. (1995), Porcino et al. (2003), Hu and Pu (2004), Tan et al. (2008)
                and Di Donna et al. (2015). The higher the interface roughness, the higher the inter-
                face angle of shear strength and the closer this angle to the one of the soil. These data
                agree with the relationships proposed by Kulhawy et al. (1983) for interfaces with
                sands, as well as with those proposed by Burland (1973) and Randolph and Wroth
                (1981) for interfaces with clay.
                   Besides the structure roughness, the main factors that affect the behaviour of soil
                structure interfaces are (1) the normal stress acting on the structure, (2) the soil density,
                (3) particle angularity and (4) the soil grain size distribution (Uesugi and Kishida,
                1986).

                5.7.3 Normal stress and soil density

                                                                                          0
                Similar to soils, when interfaces are subjected to a greater effective normal stress, σ ,
                                                                                          n
                they have greater interface shear strengths, τ. Soil density influences behaviour
                of the interface because it is responsible, together with the stress state, for the
                dilative contractive behaviour of the soil.
                   Dense soil structure interfaces show dilatancy while loose soil structure interfaces
                show a contractive behaviour (Fioravante et al., 1999). The behaviour of structural
                interfaces with clay is generally contractive, but might be dilative if the soil is subjected
                to highly OC conditions (Shakir and Zhu, 2009). These aspects are particularly impor-
                tant for the understanding of the response of interface of geostructures because the
                volumetric behaviour of the soil at the interface cannot freely develop as it is partially
                prevented by the presence of the surrounding ground (Di Donna et al., 2015).

                5.7.4 Constant normal stiffness conditions
                The far-field ground acts as a spring at soil structure interface and reacts to the
                dilative contractive behaviour of the interface according to Hooke’s law. Such condi-
                tions are known as constant normal stiffness (CNS) conditions, in which the stiffness is
                equal to the stiffness of the equivalent far-field soil spring (Lehane et al., 1993). The
                considered conditions differ from the so-called constant normal load (CNL) conditions,
                wherein the stress (not the stiffness) remains constant upon loading and unloading.
                   Under CNS conditions, the normal effective stress applied to the interface varies as
                (Ooi and Carter, 1987; Tabucanon et al., 1995; Porcino et al., 2003; Mortara et al.,
                2007)
                                        0    0      0    0                             ð5:7Þ
                                             n0          n0
                                       σ 5 σ 1 Δσ 5 σ 2 K int Δδ n
                                        n           n
                where σ  0  and Δσ are the initial and increment of the normal effective stress, respec-
                                0
                       n0       n
                tively; K int is the far-field normal stiffness; and Δδ n is the variation of displacement
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