Anisotropic elasticity of a natural clay

Abstract

Lightly overconsolidated natural clays are commonly anisotropic because of their mode of deposition. They exhibit substantial ranges of approximately linear, reversible (elastic) behaviour at stress levels which do not produce yielding of the particle structure of the clay. The Paper examines the five elastic parameters needed to describe transverse isotropy, sometimes called crossanisotropy. Only three parameters can be measured in triaxial tests, and reasonable assumptions, with easily identifiable physical significance, are proposed which permit extrapolation from triaxial to more general stress conditions. Convenient parameters are identified such as the bulk modulus K, shear modulus G, and a cross modulus J which expresses the relationships in a transversely isotropic soil between mean stress and shear strain and between shear stress and volumetric strain. A least squares solution is used to evaluate these parameters from 76mm diameter triaxial tests on Lake Agassiz clay from Winnipeg, Canada. The solution suggests that the clay is approximately 1.8 times stiffer in the horizontal than the vertical direction. This is shown to be consistent with measured relationships between Au and Ap in undrained shear tests, and between Au and BE, in isotropic consolidation tests. Les argiles naturelles légément surconsolidées sont généralement anisotropes à cause de leur mode de dépôt. Elles montrent des variations considéables de comportement reversible (ćlastique) sensiblement linéaire à des niveaux de contrainte qui ne font pas fluer la structure particulaire de l'argile. Cet article examine les cinq paramétres élastiques nécessaires pour décrire l'isotropie transversale. Seulement trois paramétres peuvent se mesurer dans des essais triaxiaux, et l'article propose trois hypothèses raisonnables de caractéristique physique facilement reconnaissable qui permettent l'extrapolation des conditions triaxiales á des conditions de contrainte plus générales. Des paramètres convenables sont définis, tel que le module de masse K, le module de cisaillement G, et un module transversal J qui exprime les rapports dans un sol transversalement isotrope entre la contrainte moyenne et la déformation de cisaillement d'une part et entre la contrainte de cisaillement et la déformation volumétrique de l'autre. La méthode des moindres carrés est employée pour évaluer ces paramètres à partir d'essais triaxiaux (diamère 76mm) sur de l'argile du Lac Agassiz (Winnipeg, Canada). Le résulat donne l'impression que l'argile est approximativement 1.8 fois plus raide dans la direction horizontale que dans la direction verticale. L'article démontre que ce résultat est compatible avec des rapports mesurks entre &atal;u et &atal;p dans des essais de cisaillement sans drainage et aussi entre &atal;D et &atal;C, dans des essais de consolidation isotrope.

A laboratory study of the development of earth pressure behind integral bridge abutments

“…The rate of stiffness reduction with increasing axial strain is similar for the two types of loading. As shown in the inset to the figure, the initial portions of the stress paths are not vertical in q/p9 stress space, suggesting anisotropy of stiffness (Graham & Houlsby, 1983).…”

“…Analysis of strains during isotropic consolidation and effective stress paths during monotonic shearing suggested (Graham & Houlsby, 1983) that the stiffness of the Atherfield I Clay was strongly anisotropic, with an effective Young's modulus in the horizontal direction of between 1 . 6 and 2 .…”

Behavior of a Stiff Clay behind Embedded Integral Abutments

“…The effective stress paths for specimens AC2 and AC3 did not follow a constant mean effective stress (p' ) line, which indicates a strong anisotropy in stiffness (Graham and Houlsby 1983) and will be discussed further later.…”

“…The normalised horizontal stiffness is seen to be higher than the normalised vertical stiffness. Further evidence of this stiffness anisotropy comes from the pore water pressure change against mean total stress change for specimens AC1 and AC3 during undrained shearing under constant cell pressure, and the volumetric strain against axial strain for AC3 during isotropic consolidation, which are shown in Figures 10 and 11 respectively, together with an idealized response of isotropic material superimposed (Graham and Houlsby 1983). These data suggest a strong anisotropy in stiffness, which is an inherent consequence of the microstructure of this stiff clay (Figure 2).…”

Effect of anisotropy in ground movements caused by tunnelling

“…The Authors modified the constitutive model to include non-linear crossanisotropic stiffness properties (using a simplified 3 parameter formulation proposed by Graham and Houlsby, 1983). They were only able to achieve good agreement with the measured settlement trough in the 2D analyses using an unrealistically high elastic Young's modulus ratio, n = E h /E v = 6.5 (i.e., outside the theoretical elastic range of n, 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 …”