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The Reference Shrinkage Curve at Higher than Critical Soil Clay Content

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

View larger version (20K): [in this window] [in a new window]   Fig. 1. The qualitative look of (a) the clay and (b) soil shrinkage curves. The points Wz, Wn, and Wh are the shrinkage limit, air-entry point, and maximum swelling point, respectively, which differ for (a) and (b) cases; Ws is the final point of the structural shrinkage area; Wm* is the soil water content not reached if the maximum volume, Yh, is reached at Wh on the pseudo-saturation (dash-dot) line. If Wh = Wm*, the volume Yh is reached at the true saturation (dashed) line. Curves 1 and 2 are the observed variants of the shrinkage curve. The curve slope in the basic shrinkage area for clay is always unity and for soil can be less than unity.

View larger version (43K): [in this window] [in a new window]   Fig. 2. The illustrative scheme of the internal structure of aggregates at a clay content (a) c > c* and (b) c < c*, where c is the weight fraction of clay solids and c* is the critical soil clay content.

View larger version (40K): [in this window] [in a new window]   Fig. 3. Qualitative view of the reference shrinkage curve, Y(W) (specific volume of soil vs. total gravimetric water content) and that of aggregates, Ua(W) (for two options 1 and 2) where the clay content c > the critical value c* as well as a number of auxiliary curves: the specific volme of soil vs. intraaggregate contribution to total water content,Y(w'); specific volume of aggregates vs. intraaggregate contribution to total water content, Ua(w'); specific volume of intraaggregate matrix vs. its gravimetric water content, U(w); and intraaggregate contribution to the specific volume of aggregates vs. intraaggregate contribution to total water content, U'(w'). The water contents Wz, Wn, Ws, and Wh and water contents wz', wn', ws', and wh' are the values that correspond to the shrinkage limit, endpoint of basic shrinkage, endpoint of structural shrinkage, and maximum swelling of the soil, respectively; Wm is the maximum soil water content; water contents wz, wn, and wh are the values that correspond to the shrinkage limit, endpoint of basic shrinkage, and maximum swelling of the intraaggregate matrix, respectively; is the interface contribution to the total water content; K is the ratio of the aggregate solid mass to the solid mass of intraaggregate matrix; and Ui and Us are the specific volumes of an interface layer and structural pores, respectively. The 1:1 line denotes the saturation line for both the w and W axes.

View larger version (26K): [in this window] [in a new window]   Fig. 4. The general form of the shrinkage curve of a clay matrix (modified from Chertkov, 2000a, Fig. 2). Subscripts z, n, and h indicate values at the shrinkage limit, endpoint of basic shrinkage, and maximum swelling of the clay, respectively; s and vs are the density and relative volume, respectively, of clay solids.

View larger version (11K): [in this window] [in a new window]   Fig. 5. The two-dimensional scheme of a clay particle network (a) before disconnections at relative water content maximum swelling point h and (b) after disconnections at liquid limit M = 1 (r is a clay particle size; a clay particle surface is r2; r is the distance between the edges of the disconnected clay particles; is the mean thickness of clay particles).

View larger version (13K): [in this window] [in a new window]   Fig. 6. A qualitative view of the maximum internal size of intraaggregate pores, rm, vs. water content, w'. Subscripts n, s, and h indicate the w' and rm values at the endpoint of the basic shrinkage, endpoint of the structural shrinkage, and maximum swelling of the soil, respectively; Rmin is the minimum size of interface pores; and Rm2 is the larger value of two possible maximum sizes of interface pores.

View larger version (29K): [in this window] [in a new window]   Fig. 7. Shrinkage curve data (white triangles) and prediction (solid line) for the soil of Braudeau et al. (2005) using the specific volume of the aggregates (Ua), the intraaggregate matrix (U), and the intraaggregate contribution to the specific volume of aggregates (U') vs. total water content (W), water content of the intraaggregate matrix (w), and the intraaggregate contributions to W (w') for the case Us 0, Ua(W) Y(W), and Wh = Wm. The water contents Wz, Wn, Ws, and Wh and water contents wz', wn', ws', and wh' are the values that correspond to the shrinkage limit, endpoint of basic shrinkage, endpoint of structural shrinkage, and maximum swelling of the soil, respectively; water contents wz, wn, and wh are the values that correspond to the shrinkage limit, endpoint of basic shrinkage, and maximum swelling of the intraaggregate matrix, respectively; and Ui is the specific volume of an interface layer.

View larger version (30K): [in this window] [in a new window]   Fig. 8. Shrinkage curve data (white squares) and prediction (solid line) for the soil of Baer and Anderson (1997) using the specific volume of the aggregates (Ua), the intraaggregate matrix (U), and the intraaggregate contribution to the specific volume of aggregates (U') vs. total water content (W), water content of the intraaggregate matrix (w), and the intraaggregate contributions to W (w') for the case Us 0, Ua(W) Y(W), and Wh = Wm. The water contents Wz, Wn, Ws, and Wh and water contents wz', wn', ws', and wh' are the values that correspond to the shrinkage limit, endpoint of basic shrinkage, endpoint of structural shrinkage, and maximum swelling of the soil, respectively; water contents wz, wn, and wh are the values that correspond to the shrinkage limit, endpoint of basic shrinkage, and maximum swelling of the intraaggregate matrix, respectively; and Ui is the specific volume of an interface layer.

View larger version (24K): [in this window] [in a new window]   Fig. 9. Shrinkage curve data (white squares) and prediction (solid line) for the Wyre Bw soil of Reeve and Hall (1978) as void ratio, e, vs. total moisture ratio, . Subscripts z, n, s, and h indicate values at the shrinkage limit, endpoint of basic shrinkage, endpoint of structural shrinkage, and maximum swelling of the soil, respectively; ' is the intraaggregate contribution to ; and e() (1) and e() (2) are the two possible options of the shrinkage curve in the structural shrinkage area.