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The Shrinkage Geometry Factor of a Soil Layer

Agricultural Engineering Division, Faculty of Civil and Environmental Engineering, Technion, Haifa 32000, Israel

View larger version (15K): [in a new window]   Fig. 1. Scheme of correspondence between a real layer and a model from Bronswijk (1988)(1989, 1990, 1991a, 1991b) (vertical cross-sections). (a) The real connected layer of thickness z with distributed cracks. Initial saturated state at the gravimetric water content w = wo. (b) Model layer of disconnected cubes of size z without cracks at w = wo. (c) Real subsidence z of the layer and the same cracks after drying to w < wo and opening (openings are symbolized by thicker lines; additional developing cracks are not shown). (d) Model layer after drying to w < wo. All cracks are concentrated as gaps (shaded strips) between shrinking parallelepipeds of horizontal size x' without cracks. Subsidence of the disconnected parallelepipeds, z' < z.

View larger version (24K): [in a new window]   Fig. 2. Scheme of the different shrinkage curves of an aggregated clay soil based on Hallaire's (1984) Fig. 2. 1—initial specific volume of a shrinking and cracking soil layer. 2—shrinkage curve 'l(w) of a shrinking soil layer with cracks in Bronswijk's approximation (see Fig. 1b and d, disconnected layer). 3—shrinkage curve l(w) of a shrinking soil layer with cracks in approximation of the present work (connected layer). 4—shrinkage curve s(w) of a shrinking soil sample with cracks. 5—shrinkage curve (w) of a soil matrix without cracks. 6—1:1 theoretical line. 'lz, lz, sz, and z designate values of corresponding specific volumes after oven drying. In general z < sz, that is, the oven-dried sample contains cracks. AB—the specific volume of the layer subsidence in Bronswijk's approximation at a given w; AC—the true specific volume of the layer subsidence at a given w; BE—the specific volume of cracks in the soil layer in Bronswijk's approximation at a given w; CE—the true specific volume of cracks in the soil layer at a given w; DE—the specific volume of cracks in the sample with free boundaries at a given w.

View larger version (13K): [in a new window]   Fig. 3. Scheme of horizontal shrinkage deformation (horizontal cross-sections) at the drying of an isolated cube (Bronswijk's approximation) and a cube that is part of a real connected layer and only mentally outlined in it. In Fig. 3b, c, and d the shrinkage of a soil matrix in the horizontal plane is considered to be isotropic. a. The horizontal basis at w = wo. b. The basis of the isolated cube without cracks and with free boundaries after shrinkage at w < wo. c. The basis of the mentally separated cube with fixed boundaries after shrinkage at w < wo. Internal tensile stresses developing at layer shrinkage lead to cracking (black strips). d. The area of the stretched soil matrix in Fig. 3c after the mental extraction of a crack area (area of black strips). The size of the stretched-matrix area, x > x'.

View larger version (16K): [in a new window]   Fig. 4. Subsidence and horizontal deformation of the matrix of a shrinking soil layer with cracks compared with those of the matrix of an isolated shrinking soil cube without cracks (vertical cross-section).

View larger version (26K): [in a new window]   Fig. 5. The experimental specific volumes, 'l (asterisks) and l (squares), of an unlimited clay layer including cracks in Bronswijk's approximation and corrected accounting for violation of Assumption 1, respectively; the experimental specific volume, s (circles) of clay samples including cracks, and the specific volume (solid line) of a clay matrix without cracks, predicted from Chertkov (2000b)(2003) for the clay of the 0- to 30-cm depths of Sarid soil, Israel. The specific volumes 'l, s, and are from Chertkov et al. (2004). The maximum standard deviations of all the experimental points are less than 0.01 to 0.02 cm3 g–1. The inclined straight line is 1:1 theoretical one. Figures near the experimental points correspond to the measurement numbers in Table 1.

View larger version (26K): [in a new window]   Fig. 6. Data on the shrinkage curves of an aggregated clay soil from Hallaire (1984). The el' values (asterisks) give the layer void ratio in Bronswijk's approximation. The es values (circles) give the sample void ratio. The e values (dots) give the aggregate void ratio. The e1 values (squares) give the true layer void ratio. The el values (solid line) give the least squares approximation (and extrapolation) of the square points that were used in the present work. Goodness of fit of the approximation is r2 = 0.975.

View larger version (23K): [in a new window]   Fig. 7. The experimental (squares) values in clay paste samples for the drying clay of a 0- to 30-cm layer of Sarid soil. The maximum standard deviations of all the experimental points are less than 0.01. Figures near experimental points correspond to the measurement numbers in Table 1.

View larger version (24K): [in a new window]   Fig. 8. Three different approximations of the rs factor for Hallaire's (1984) aggregated clay soil as functions of water content. The rs' values (diamonds) of the rs factor for the soil sample or layer in Bronswijk's approximation; the rsM values (squares) of the rs factor corrected in part for the soil layer; and the totally corrected rs factor values (circles) for the soil layer.

View larger version (24K): [in a new window]   Fig. 9. Three correcting factors, M, L, and ML for Hallaire's (1984) aggregated clay soil as functions of water content.

View larger version (22K): [in a new window]   Fig. 10. Poisson's ratio of Hallaire's (1984) aggregated clay soil as a function of water content.

View larger version (17K): [in a new window]   Fig. A2.1. Two-dimensional illustration of the analogy between the three-dimensional shrinkage of a layer and a sample of an arbitrary shape. (a) The current specific volume of a layer with dotted initial upper surface (corresponding to l = = o) is equal to the current specific volume () of a soil matrix (shaded area) plus the current specific crack volume (cr.l) (black strips; vertical cracks are only shown for simplicity). , o, and l are connected by Eq. [A2.1]. (b) The current specific volume (s) of a sample of an arbitrary shape with dotted initial surface (corresponding to s = = o) is equal to the current specific volume () of a soil matrix (shaded area) plus the current specific crack volume (cr.s) (black strips). , o, and s are connected by Eq.[A2.2], which is similar to Eq.[A2.1]. The M factor is the generalization of the rs factor for a sample of an arbitrary shape.

View larger version (16K): [in a new window]   Fig. A5.1. Qualitative view of the dependence of the parameter on water content. 1. The average dependence, (w); 2. The minimal dependence, min(w) = x'(w)/z (min(0) > 0.5).