The estimation of moisture flow through unsaturated soil for geotechnical engineering applications is a multifaceted problem involving a combination of empiricism and unsaturated soil mechanics theory. Due to the complexity of the problem and difficulties associated with the implementation, the industry has adopted a semi-empirical approach to the design and mitigation of foundations on expansive soils for residential dwellings. Many of these methodologies have been developed based on regional environmental conditions and therefore are applicable only to those specific regions of the world. Difficulties frequently arise when local experience is applied to different environmental conditions and soil properties. The literature review presented summarizes empirical findings relative to the moisture flow through unsaturated soil and the observed impact on lightly loaded structures.
Two types of slab systems are commonly used in residential construction, conventional stem-and-footer (with un-reinforced or lightly reinforced slab) and post-tensioned slabs. The design methodologies, in large part, are based on the anticipated post-construction change in the depth of wetting and degree of saturation. It is assumed that the soil suction of the undeveloped site comes to equilibrium with the existing environmental conditions at depth unaffected by seasonal climate variation. Thus the soil suction is referred to as the equilibrium. Based on literature findings, the active zone depth was estimated to vary between 1.2 m to 12 m
(4 feet to 39 feet), depending on the definition of the term and environmental conditions of test region (McKeen, 1980, 1981, 1985; O’Neill and Poormoayed, 1980; Thompson, 1992; Thompson and McKeen, 1995; Wray, 1989, 1997; Durkee, 2000, Chao et al., 2006).
An introduction of an impermeable cover at the soil surface, such as a slab-on-grade or a pavement, results in elimination of precipitation and reduction in potential evaporation (Day, 1994). Also, it is common for conditions in landscaped areas to change relative to pre-developed conditions. With time the suction within the soil profile comes to an equilibrium with the new environmental conditions. It is sometimes postulated that the suction below the slab is constant with depth and equal to the initial equilibrium suction (Nelson et al., 2001). Based on empirical evidence, the process of monotonic moisture migration due to capillary forces, moisture condensation below the slab and temperature gradients (Chen, 1988) occurs up to six years (Donaldson, 1965). Furthermore, it was observed that the 6-10 year long equilibration process is followed by a uniform relative reduction in heave (Donaldson, 1965), which might be related to fatigue of swelling. Fatigue of swelling refers to a decrease in a soil’s swelling potential as the drying-wetting cycles repeat. Chen (1988) illustrated that swell levels off at the fifth cycle when “relative equilibrium” is reached.
A long-term study of slab-on-grade behavior by Wray (1992) illustrated that short-term post-construction slab movement in arid regions is attributed to seasonal climate variation resulting in edge lift slab distortion. Continued monitoring revealed slow but increasing mound in the center of the slab, indicating that subsequently center lift distortion might occur if soils are not placed at the appropriate moisture content. On the other hand in humid regions, the short-term edge lift slab distress is quickly replaced with a center lift scenario, which is likely to occur due to edge drop (Wray, 1992).
An important parameter for slab design is the suction variation below the edges of the slab due to environmental or human imposed conditions. It has been postulated that the suction may vary 1) between liquid limit and shrinkage limit (conclusion based on measured gravimetric water content data of SM and CL soils below 10 000 slab-on-grades in Houston and San
Antonio, Texas, (Stryron et al., 2001)), 2) between 98 kPa and 9 800 kPa (McKeen, 2001), and 3) between 33 kPa to 3 300kPa in terms of total suction (PTI, 2004).
The edge moisture variation distance, em, defined as the distance over “which moisture will change due to wetting or drying influences around the perimeter of the foundation” (PTI, 2004), is difficult to measure experimentally. Few case studies include measured em values in arid regions. The existing data shows that em varies between 1.75 m (study of bike trail by Nevels, 2001) and more than 4.5 m (study of slab-on-grade where em exceeded half of the slab width Durkee, 2000). The em might approach the active zone depth (McKeen et al., 1990), although the PTI (2004) procedure limits the magnitude of em to 3 m (9 ft).
The slab-soil system performance is frequently evaluated in terms of slab relative deflection, angular distortion, or overall magnitude and extent of superstructure distress. Based on forensic engineering studies, cosmetic damage was correlated to 1.1-1.75” slab relative deflection and 1/300 angular distortion. Structural damage was found to occur at relative deflection larger than 3.5” and maximum angular distortion of 1/100 (Day, 1990, Skempton and MacDonald (1956), Marsh and Thoeny (1999)). The study of as-built floor levelness, however, suggests that these distress markers should be used with sound engineering judgement. Newly constructed slabs were found to exhibit on average 0.5” relative slab deflection and average angular distortion of 1/340. These values as-constructed values were found to be as large as 2.2” and 1/71 respectively, values corresponding to structural damage (Koenig, 1991, Marsh and Thoeny, 1999, Walsh, et al., 2001, Noorany et al., 2005).
Mitigation measures are employed to minimize potential soil movement and superstructure distress. They include 1) removal, replacement and recompaction, 2) chemical stabilization 3) passive moisture control with moisture barriers and 4) active moisture control. The economical feasibility of a mitigation measure depends on availability of material and expertise of mitigation team, as well as the timing of identification of the problem. In Arizona, active moisture control in the form of pad pre-wetting is the most commonly implemented mitigation method. The effectiveness of these methods remains to be quantified.
The literature review consensus message is that the depth of moisture migration, magnitude of suction variation with depth in open fields and below impermeable surfaces, the distance of horizontal moisture migration below a slab, and soil-slab system behavior (with or without mitigation measures) are highly dependent on 1) soil properties and 2) environmental and human imposed conditions around the edges of the structure. Geotechnical engineers are faced with the challenge of estimating design parameters for foundation system design purposes. In general, design guidelines provide a cookie cutter methodology developed based on a local experience in a geographic region, which may or may not be applicable to different soil and climatic conditions. When limited empirical data is available, numerical modeling of moisture flow through unsaturated soil can be performed to aid in selection of design parameters.
Numerical analysis of moisture flow through unsaturated soil involves implementation of unsaturated soil mechanics principles by solving Richards’ equation, a parabolic, stiff, advection- diffusion partial differential equation derived from mass conservation. Stability, convergence and time efficiency are problematic issues inherent to this class of problem. The currently implemented standard approach to solving the PDE follows a “method of lines”, also referred to as semi-discretization, where spatial derivatives are first approximated using a variety of (usually low order) finite difference or finite element schemes, and the resulting discrete system of ordinary differential equations (which also accounts for boundary conditions) is then solved using a time integrator. Three commonly used numerical software were reviewed: SVFlux, Vadose/W and Hydrus. It was concluded that numerical modeling of moisture flow through unsaturated soil is a very challenging and time consuming task, but it is helpful in identification of general moisture migration trends due to various soil and flux conditions.