CIVIL ENGINEERING 365 ALL ABOUT CIVIL ENGINEERING



AbstractSoil suction–based analyses are paramount to proper design of foundations in expansive soils, yet availability of field soil suction profiles from direct measurement is limited. A method was developed, using directly measured suction profiles obtained from sites across the US, by which routine geotechnical tests can be used to estimate soil suction to expand the database for estimation of field suction profiles. Herein, the expanded database is used to develop best-estimate clay soil suction envelopes for boundary conditions associated with covered or uncovered ground surface subjected to natural climatic surface flux. Where appropriate for site conditions, the proposed soil suction profile envelopes can be used with any suction-based heave/shrinkage analysis. Key features of the field suction envelopes, consistent with current popular approaches, include climate-dependent estimates for equilibrium suction at depth, depth to equilibrium (stable) suction, and variation in soil suction at the ground surface. Comparisons to existing soil suction envelope recommendations are made. Finally, a limited number of cases of developed/irrigated sites are presented for comparison to soil suction profiles obtained for natural climatic surface flux conditions.IntroductionSoil suction–based methods for computation of heave and shrinkage are based on sound fundamentals because they require input of the initial soil suction state as well as of the final soil suction state (Lytton and Woodburn 1973; Wray et al. 2005; Lytton 1994, 1997; Lytton et al. 2005; PTI 2004; Houston and Houston 2018; Vu and Fredlund 2004; Zhang 2004; Adem and Vanapalli 2015). However, the impacts of improper consideration of boundary conditions on initial and final soil suction profiles can be highly inaccurate estimates of volume change of expansive soil and associated high variability in heave or shrinkage estimates across geotechnical engineers. The solution to this problem is to develop a well-founded basis for obtaining initial suction conditions and for estimating the final, postwetting (and postdrying) soil suction. It is the objective of this study to increase the database of field soil suction profiles for expansive soil sites, and to expand on existing procedures for estimating initial and final field soil suction profiles for climatic flux boundary conditions. The database of field suction values is expanded primarily through the use of a substitute or surrogate for soil suction, based on water content and soil index properties. The advantage of the suction envelopes of this study is the benchmarking to field data, which is highly desirable given all of the complexities of deterministic unsaturated flow modeling (Cavalcante and Zornberg 2017; Houston et al. 2011; Houston and Welfert 2014). It was not possible for this study to include all conceivable boundary conditions that may ensue for every project, because postdevelopment data are very limited and typically restricted to forensic cases. The design suction profile parameters presented hold the restriction of being associated with clay profiles with a relatively deep groundwater table, natural climatic surface flux conditions, relatively flat natural topography, and absence of irrigation or surface water ponding or significant lateral/subsurface flow.The work presented here builds on the findings of others (Olaiz et al. 2018; Vann et al. 2018; Naiser 1997; Lytton 1997; Jayatilaka et al. 1992; Wray et al. 2005). Specific relationships presented herein are related to suction profile parameters that are generally familiar to practitioners, such as those adopted by the Post-Tensioning Institute (PTI) (2004, 2008): 1.Thornthwaite moisture index (TMI) versus the magnitude of equilibrium soil suction, ψe;2.TMI versus the depth to equilibrium (stable) soil suction, Dψe, commonly taken as the depth below which seasonal suction change is less than 0.2 log cycles (Naiser 1997; Lytton 1997); and3.TMI versus the variation in log of soil suction at the surface between seasonal wet (ψw) and dry (ψd) conditions, Δψ.The TMI values used in this study are based on estimates of the Thornthwaite (1948) moisture index values, consistent with recommendations in the AASHTO (2008), where nearest weather station data provide input for TMI computation (Olaiz et al. 2018).Fig. 1 depicts the referenced parameters and represents a typical one-dimensional (1D) flow soil suction envelope for a clay profile with deep groundwater table subjected only to climatic conditions, and where climatic conditions result in wet and dry seasons. A key to the use of Fig. 1–type suction envelopes is the existence of a more or less stable suction at depth that can be treated as a fixed suction-based boundary condition for purposes of flow computations. Below the depth to equilibrium suction, the rate of change of suction with depth is very small, but the suction is not exactly constant because matric suction becomes zero (total suction equals osmotic) at the groundwater table. Below the depth of significant suction change, suction-induced soil movements are small, and often considered to be insignificant for engineering purposes. The more or less stable suction at depth is referred to herein as the equilibrium suction value, to be consistent with a large body of existing literature. The wet and dry soil suction envelope of Fig. 1 is common for arid to subhumid climates where the groundwater table is deep, and no shallow geologic flow-limiting or lateral flow conditions exist.Data CollectionAt several locations, a drilling, sampling, and laboratory testing program was conducted to develop the data set for determination of a soil suction surrogate (i.e., a soil index property–based estimate of suction). Where possible, borings at the selected locations extended to depths of 9 m. The drilling locations were selected where expansive soils were known to exist, and through coordination with geotechnical engineering firms, government agencies, and other companies. Undisturbed and disturbed samples of expansive soils were obtained. Field locations included Arizona, Colorado, Oklahoma, and Texas, and investigations included index properties, gradation, and swell tests, as well as soil suction measurement. The plasticity index (PI) of the clays for the study ranged from 15 to 81 and the percent fines ranged from 28% to 99%.At each field test site, total and matric soil suction measurements were made on the same soil specimens used for index testing and water content/degree of saturation measurements (Vann 2019). The WP4C (Meter Group, Pullman, Washington), a chilled-mirror-type device for determination of relative humidity, was used extensively for suction measurements. Several comparisons to measured soil suction values under field net total stress were made, confirming consistency, for the soils of this study with the WP4C (Olaiz 2017). Companion soil samples were tested for total suction at field moisture state and at saturated (soaked) state. The total suction under soaked conditions was taken to be the osmotic suction component (Miller and Wei 2018). Total suction values are reported herein. Atterberg limits, grain size distribution, and water content were obtained at a frequency of every 300 mm. Laboratory testing also included soil–water characteristic curve (SWCC) determination on undisturbed clays under field net total stress values, and ASTM D4546-14 (ASTM 2008) swell tests on undisturbed specimens at field stress level and moisture conditions.In addition to the drilled sites of this study, data from the files of agencies, companies, and consulting geotechnical engineers were collected for expansive soil locations throughout the US. Overall, hundreds of reports on expansive clays were made available for this study, although not all of these reports contained adequate data to appropriate depths for inclusion in the soil suction profile study. In particular, it was observed that soil testing beyond standard penetration test (SPT) and water content was generally quite limited at depths greater than about 3 m. The data mining ultimately provided more than 40 existing geotechnical engineering reports where sufficient information was available for assessment of soil suction, or soil suction surrogate profiles, to a depth adequate for identification of depth to essentially constant suction. In addition to the referenced geotechnical reports, literature containing expansive soil suction profiles was reviewed to increase the database. Once these data were compiled, further data mining was conducted, including information on soil types. All of the soils data from the drilled test sites and the data mining are tabulated by Vann (2019).Soil Suction SurrogateIt is common practice for a geotechnical investigation report to include considerable water content, gradation, and Atterberg limits data. In the characterization of an unsaturated soil site, it is the matric soil suction that is desirable, for two primary reasons: soil matric suction is a stress state variable controlling behavior, and soil suction is the most stable moisture-indicative parameter in typically variable field profiles. Matric suction is often obtained by subtraction of the osmotic component from the total suction value (Fredlund et al. 2012). As many researchers have determined, consideration of soil gradation and Atterberg limits alongside water content data allows the engineer to qualitatively consider soil suction, facilitating application of unsaturated soil mechanics (Perera et al. 2005; Leroueil and Hight 2013; Nelson and Miller 1992). A soil suction surrogate is simply a statistically determined estimate of soil suction, based on commonly measured soil parameters.In this study, a soil suction surrogate for total suction was determined using 501 data points, obtained from the field test sites and Vann Engineering, Inc. reports, where adequate soil data, climatic data, and direct suction measurements were available. The search for a clay soil suction surrogate was initiated by accumulating the laboratory soil data from the drilled test sites, such as liquid limit (LL), plastic limit (PL), PI, water content (%), percent passing the #40 sieve (P40), percent passing the #200 sieve (P200), nearest weather station TMI, and WP4C total soil suction. A wide range of climatic conditions was included, and soil profiles were limited to expansive clay while covering a reasonable range in PI (15 to 81). Thus, the soil suction surrogate herein is only for field conditions and clay soils, and does not explicitly consider hysteresis. However, to the extent that hysteresis occurs in the field, hysteresis effects are embedded in the data and contribute to data scatter.To explore correlations between the collected variables and soil suction, the computer code Eureqa (Schmidt and Lipson 2009) was used, together with Minitab. Eureqa performs statistical analyses and uses an artificial intelligence program to sort through the data and to identify best-candidate predictive models. Follow-up statistical analyses were performed on best-candidate relationships using the program Minitab. Predictive models involving moisture content, liquid limit, plastic limit, plasticity index, percent passing the #200 sieve, TMI, and total soil suction were considered. The numerous relationships explored in arriving at a simple soil suction surrogate are presented in Vann et al. (2018) and Vann (2019). Here, only the final soil suction surrogate relationship is presented.Although it was anticipated that the surrogate equation would include the soil PL, the PL-based correlations had lower coefficient of correlation values, R2, compared to LL-based correlations. There is a strong correlation between PL and LL in general, but based on the authors’ experience, the LL is a relatively easier test to perform and typically has less scatter compared to PL determinations. The authors’ experience is consistent with Liu and Thornburn (1964), who found that the liquid limit had greater reproducibility than the plastic limit, and with Abbas (2018), who, for a series of tests across different laboratories, found the coefficient of variation (COV) of liquid limit to be substantially lower than the COV for plastic limit.The soil suction surrogate, shown in Fig. 2 and Eq. (1), was found to be most simply and reliably related to the ratio of water content (w) to LL. The data in Fig. 2 are given different symbols depending on the weighted plasticity index (W-PI) (the product of the percent passing the #200 sieve, as a decimal, and the PI), a parameter found by Houston et al. (2011) and Zapata et al. (2006) to correlate with soil expansivity. Eq. (1a) for soil suction surrogate is presented in terms of pF. Although kilopascals is the preferred unit for soil suction in general, the soil suction in pF (log to the base 10 of soil suction in centimeters of water) was also used in this study due to its extensive use in US geotechnical practice, particularly in expansive soil applications. Eq. (1b) provides the soil suction surrogate in log(kPa). The log of suction in kilopascals is approximately equal to suction in pF minus 1 {i.e., pF=3.0 corresponds to log [suction (kPa)] = 2.0} (1a) ψ(pF)=3.235(wLL)(−0.217)(1b) ψ(log(kPa))=[3.235(wLL)(−0.217)]−1The R2 of 0.61 and standard error, S, of 0.258 log cycles of suction are considered good, given known hysteresis for extreme wetting to extreme drying SWCCs of typically one order of magnitude for clays (Pham et al. 2003). Hysteresis effects under field conditions are likely reduced, because unsaturated soils at in situ moisture states have generally been found to lie on scanning curves between the extremes of laboratory wetting and drying SWCCs (Rocchi et al. 2018; Askarinejad et al. 2011; Iiyama 2016).The presented soil suction surrogate equation may be used by practitioners to arrive at a reasonable estimate of field soil suction values. However, Eq. (1) is proposed for use in practice only where direct soil suction measurements are not practical, or when using existing field data where suction measurements are not available. In this study, the suction surrogate allowed the use of existing geotechnical engineering reports, containing water content and Atterberg limits data, to be used to expand the database of field soil suction profiles.Magnitude of Equilibrium SuctionA relationship between TMI and the magnitude of equilibrium soil suction, ψe, has been presented by PTI and is widely used by US practitioners (PTI 2004, 2008). The PTI (2004) TMI versus ψe relationship represents a culmination of data from Snethen (1977), Jayatilaka et al. (1992), Naiser (1997), Wray (1989), and McKeen (1981). Aside from these papers, other work has contributed to the development of a connection between TMI and ψe, such as Barnett and Kingsland (1999), Mitchell (2008), and Russam and Coleman (1961).The PTI correlation between TMI and ψe is not as strong as desired for practitioner use (R2 of 0.36). The work by Cuzme (2018) and Singhar (2018) supports that the correlation between TMI and ψe is relatively weak, and that the database for evaluation is limited. As noted by Cuzme (2018), Singhar (2018), and Saha et al. (2019), many non-climate-related factors affect ψe, including soil type, degree of homogeneity, layering in the soil profile, topography, soil weathering, and cracking. The current study used an expanded database to evaluate if stronger support can be provided for use in estimating a value of ψe from TMI, where soils suction measurements at depth are not available. The database was increased through the use of the soil suction surrogate, described previously, and also through the addition of field soil suction data collected as a part of this study. Sites from selected historical literature and from this study were combined in establishment of the TMI–equilibrium suction relationship. Literature data were selected based on the following criteria: (1) measured suction values; (2) adequacy of depth of sampling/testing to clearly establish equilibrium conditions, or beneath paved surface and well away from edges for a period of at least 5 years; (3) groundwater table depth greater than 9 m; and (4) natural climate surface flux boundary conditions. Where these criteria for field conditions could not be verified, some suction data from prior TMI versus equilibrium suction studies were not included here.The proposed relationship between TMI and the magnitude of equilibrium total soil suction, ψe, is depicted in Fig. 3 and described by Eq. (2) (2a) ψe(pF)=0.00002(TMI)2−0.0053(TMI)+3.9771(2b) ψe(log(kPa))=[0.00002(TMI)2−0.0053(TMI)+3.9771]−1As shown by the correlation coefficient, R2, and standard error, S, of 0.65 and 0.196, respectively, there appears to be reasonable statistical support for use of Eq. (2) in practice, where direct measurement of suction at depth is not possible. However, the relative flatness of the curve relating equilibrium suction to TMI is indicative of a relatively weak relationship, as borne out by field evidence wherein regional shifts in equilibrium suction, relative to TMI estimated values, are often required to match measured suction profiles (Walsh et al. 2009). Nonetheless, Eq. (2) represents an improved correlation in the TMI–ψe relationship compared to PTI (2004, 2008).Depth to Equilibrium SuctionDepth to equilibrium suction, Dψe, for relatively deep groundwater table sites and reasonably repeatable climate-driven surface boundary conditions is the depth below which soil suction values remain more or less stable, as depicted in Fig. 1. Given that the total suction must be equal to osmotic at the water table, below Dψe the suction is not constant with depth, but the rate of change of suction with depth is very gradual, and the suction is stable with time. A relationship between Dψe and TMI was developed using measured soil suction profiles and suction surrogate profiles from this study, together with literature data. The best-fit relationship between Dψe and TMI is given in Eq. (3). Fig. 4 shows that Eq. (3) yields a symmetric sigmoid plot, with depth to equilibrium suction generally increasing as climate becomes more arid, reaching a maximum depth of about 4.2 m at a TMI of −40. Only relatively flat uncovered clay sites subjected to natural climate surface flux conditions were used in the assessment of the depth to equilibrium suction (3) Dψe=1.617+2.6171+e(2.36+0.1612TMI)  mwhere Dψe = depth to equilibrium soil suction (m).While it seems likely that the soil type, and therefore clay soil LL, would impact Dψe, the authors investigated an LL-dependent correlation between TMI and Dψe, as depicted in Fig. 5. Specific consideration of LL in the estimation of depth to equilibrium suction results in only minor improvement, likely due to insufficient data that could be sorted on the basis of LL (Vann 2019). Therefore, for simplification, for expansive clay sites, the relationship between TMI and Dψe in Eq. (3), as shown in Fig. 4, is suggested.Change in Soil Suction at the Ground SurfaceOf particular importance in estimation of a design soil suction envelope is the change in soil suction that occurs at the ground surface, Δψ. The Australian standard, AS 2870 (Australian Standard 2011) and PTI (2008) make recommendations for Δψ for use with design soil suction profiles. The change in the log of suction at the ground surface is often assumed to be equally distributed about the value of equilibrium suction at depth. However, in this study, consistent with Aubeny and Long (2007), a shift in Δψ to the dry or wet side of equilibrium suction, depending on the TMI, was found. The study of Δψ requires that suction data be available across multiple seasons and multiple years at a given site, resulting in limited data for evaluation.Seven data points, based on measured or surrogate suction profiles from uncovered sites, were included in the study of Δψ as follows: (1) four sites from this study, one with directly measured suction values and three using the soil suction surrogate; and (2) three sites from the literature having direct suction measurements (Wray 1989; Fityus et al. 2004). Suction data were available at these sites for durations up to 9 years, but some sites had suction data for only 2 years. Therefore, future augmentation of this data set is desirable.Fig. 6 provides the best-fit curve of Δψ, generally supporting recommendations from various studies and codes, shown in Fig. 6 for reference. An R2 value of 0.92 was obtained for Eq. (4), relating Δψ to TMI. It is recommended that Eq. (4) be used only in the range of TMI of −60 to +30 and that the recommendation of McManus et al. (2004), that the change in suction at the surface be no lower than 1 log cycle (1.0 pF), be considered for regions more humid than TMI=30(4) Δψ (in pF  or  log(kPa))=1.2109e−0.005TMIΔψ=change in log suction at the ground surfaceThe change in log of suction at the ground surface increases as the TMI become more negative, such that Δψ is greater for arid regions than for humid regions, as expected.Aubeny and Long (2007) introduced a climate parameter, r, that is the percentage of the total anticipated change in log of soil suction at the surface, Δψ, comprising the wet side of the suction envelope. Typical values of r were shown to be 0.25, 0.5, and 0.75, characteristic of humid, semiarid, and arid climates, respectively. Aubeny and Long cite unequal durations of wet and dry seasons and nonlinearly decreasing hydraulic conductivity with increase in soil suction as reasons for asymmetry of the suction envelope. Eq. (5) is the relationship between r and TMI obtained from this study, and thus are values from direct field measurements and surrogate suction profiles. As shown in Fig. 7, the field data determined values of r match reasonably well with r values proposed by Aubeny and Long, which were obtained by reasoning and analyses (5) Establishment of Suction EnvelopesWhile it is reasonable that the initial soil suction profile be measured at a time just prior to construction, in the absence of a large regionally appropriate database of postconstruction profiles, the final soil suction profile for climatic surface flux boundary conditions may be best estimated through use of soil suction envelopes. The suction envelopes are established using the following parameters: (1) equilibrium suction, ψe, (2) depth to equilibrium suction, Dψe, (3) change in log of suction at the ground surface, Δψ, and (4) climate parameter, r. In addition to these parameters, it is important to establish the shape of the suction envelope.In this study, unsaturated flow model simplifications proposed by Mitchell (1980) and Naiser (1997) were used in determination of the shapes of soil suction envelopes, consistent with an approach taken by Lytton et al. (2005). The simplified flow analyses were used here only as a rational basis for establishment of the shape of the wet and dry suction profiles, and to facilitate interpolation between available field profile points. The key suction envelope parameters (previously listed) are established for any given TMI from the field data–based relationships presented herein.Normalized suction envelopes, for TMI of −60 to 20, are shown in Fig. 8. The soil suction, in log(kPa) [Fig. 8(a)] or pF [Fig. 8(b)], is normalized such that ψ/ψe=1 at the value of equilibrium suction. The normalized depth term, z/Dψe, is 1 when z=Dψe. The suction envelopes of Fig. 8 are extended to a normalized depth of 2.0. The curves of Fig. 8 are unit-dependent due to the use of the log scale for soil suction, which is necessary given the wide range in soil suction encountered for field conditions.Example Heave ComputationsThe following example demonstrates how to use the soil suction surrogate and the estimated soil suction envelopes for estimating expected heave under 1D flow conditions. The surrogate path method (SPM) (Singhal 2010; Houston and Houston 2018) is used here in the computation of heave. However, the soil suction surrogate and estimated soil suction envelopes can be used with any desired suction-based method for estimating heave.The SPM is a total stress equivalent path approach, coupled with oedometer swell tests and soil suction values—a general method also used by Fredlund and Rahardjo (1993) and Nelson et al. (2015). In the SPM, a proportionality factor, Rw (the ratio of the final suction to the initial matric suction value), is used to interpolate ASTM D4546-14, Method B, swell strains for suction values between the initial suction and full wetting (matric suction of zero). The swell index, CH, is the slope of the swell strain versus the log of equivalent total stress along the total stress surrogate path. It is assumed that no swell occurs at constant volume swell pressure, σocv, such that the full wetting swell strain, εob, at overburden stress, σob (or overburden plus structural load, as appropriate), is (6) The partial wetting heave strain (εpw), realized in going from the initial suction value to the final suction value, is (7) (8) where  σp=σob+Rw(σocv−σob)A hypothetical site in San Antonio is used here for example heave computations. The TMI for the San Antonio site is −15. For simplicity in presenting example computations, osmotic suction is assumed to be negligible, such that total suction values are equal to matric suction values. The normalized design suction envelopes developed in this study (Fig. 8) are used in establishment of final suction profile conditions, taking the wet arm of the estimated design suction envelope as the final suction profile for assumed conditions of wetting under natural seasonal fluctuations at the ground surface. Although shrinkage can be computed using the dry arm of the suction envelope, for this example, where the initial soil suctions are relatively dry, wetting is the critical case for design. The initial suction values, ψi, used in the example are established by computation of the suction surrogate based on initial water content and LL [Eq. (1)]. As an alternate to using the soil suction surrogate for establishment of initial suction values, direct measurement of initial suction can be made.Laboratory and field data on samples from depth, z, and layers of thickness, Δz, are presented in Table 1. The load-back swell pressure, σlb, is obtained from the oedometer swell test by loading the fully wetted specimen back to original height. In this example, the swell pressure for overburden stress conditions, σocv, is estimated from the load-back value (Nelson et al. 2006) as (9) σocv=σob+λ(σlb−σob)where λ = proportionality constant, taken to be 0.7 in this example (Olaiz 2017).Table 1. Example heave computationTable 1. Example heave computationz/Δz (m)wi (%)LLσoba (kPa)σlb (kPa)σocv (kPa)εob (%)CH (%/log cycle)ψi(pF)/(kPa)ψf(pF)/(kPa)Rwσp (kPa)εpw (%)ΔH (mm)0.3/0.6511.1524.3226.7160.02.651.694.52/3,3113.76/5750.17311.207.81.0/0.615.46214.2238.9171.53.002.774.37/2,3443.93/8510.36711.066.41.5/0.517.26521.3248.0180.02.052.214.32/2,0894.01/1,0230.49990.572.92.0/0.7516.35928.4215.1159.02.172.904.28/1,9054.07/1,1750.621090.483.63.0/0.7525.78842.6301.0223.52.753.824.22/1,6604.14/1,3800.831930.241.83.5/0.524.78649.7310.7232.42.013.004.24/1,7384.16/1,4450.832010.190.94.0/0.525.78856.8333.0250.11.953.034.22/1,6604.18/1,5140.912330.090.5The magnitude of equilibrium (stable) suction, ψe, was determined to be 4.22 pF, using the average soil suction surrogate values below the estimated depth to equilibrium, Dψe. The value of Dψe was estimated as 2.89 m from Fig. 4 [Eq. (3)] for a TMI of −15. Alternatively, the equilibrium suction value could be estimated from Fig. 3, although this is not recommended where field measurements of suction or suction surrogate are available. The normalized plots of Fig. 8 were used to establish the wet arm of the design suction envelope for the San Antonio site, as shown by the final suction values, ψf, in Table 1. To use the equation form of the suction envelopes of Fig. 8, rather than reading values directly from the normalized plots, parameters Δψ=1.3  pF [Eq. (4)] and climate parameter r=0.426 [Eq. (5)] are also needed.Once the initial and final field suction profiles are determined, the partial wetting strain, εpw, is determined using the SPM [Eqs. (7) and (8)]. The partial wetting strain is the strain realized in going from the initial suction value to the final suction value, and is therefore reduced compared to the fully wetted swell strains, εob, reported in Table 1. The partial wetting strains, εpw, and the incremental contribution to heave for each layer, ΔH, are provided in Table 1. Once the partial wetting strain profile is generated, the 1D heave is estimated by summing the ΔH values. For this example San Antonio site, the estimated heave is 23.9 mm.Impact of Nonclimatic Boundary ConditionsSuction under Covered AreasThe preceding discussions have addressed parameters required for establishment of soil suction envelopes for uncovered sites subjected to seasonal fluctuations only. The soil suction surrogate was also used to evaluate suction profiles at the 12 available covered sites, where adequate laboratory data to considerable depth were available. In all cases, the sites were relatively flat and covered with an asphalt or concrete pavement for at least 5 years, with the perimeter of the pavement subjected to natural climatic conditions only. Fig. 9 is a typical suction surrogate profile for locations at least 10 m inward from the edge of pavement. Additional suction profiles for covered areas can be found in Vann (2019). A key feature of all 12 suction profiles beneath covered areas is the relatively vertical plot of soil suction, with soil suction approximately equal to the equilibrium suction at depth. This finding is useful in selection of a final soil suction profile for design where heave/shrinkage is to be computed for a zone beneath paved surfaces, because the final suction profile, throughout the zone of suction change, basically seeks the equilibrium suction, ψe, as a final suction condition. Where suction measurements are not available, Fig. 3 can be used to establish the final suction conditions for paved locations well away from the edge of the paved surface. Alternatively, and preferably, site-specific suction measurement at depth can be made to obtain ψe.Developed and Irrigated SitesDevelopment might, in general, be expected to increase the depth to constant suction, and perhaps change the equilibrium suction value itself, because there is typically an increase of water applied to a developed site. Postdevelopment data are very limited and typically restricted to forensic cases. Fig. 10 shows equilibrium suction values for eight developed/irrigated site suction profiles gleaned from this study.Whether heavy or moderate residential, including forensic, or agricultural irrigation occurs at a site does not appear to form a basis for modification to the ψe versus TMI relationship obtained for sites subjected only to natural climate. However, as shown in Fig. 11, heavy irrigation or ponding of water near the surface, such as occurs often in forensic cases, can result in depth of wetting greater than that determined for seasonal fluctuations alone.Although insufficient field data were available to fully investigate design envelopes for irrigated sites, in general, available data suggest that some irrigation and development, with proper control of site water, may occur with little impact on the suction envelope parameters Dψe and ψe, relative to those obtained for seasonal fluctuation. However, heavy irrigation, particularly that associated with residential development and very green and dense vegetation (and near-surface water ponding), can result in a final suction profile that is wet of the wet arm of the suction envelopes established for seasonal fluctuation conditions, and with greater depth of wetting compared to climate-driven conditions. These facts speak strongly to the importance of adherence to geotechnical engineering recommendations for control of site water.Limitations of Climate-Driven Suction EnvelopesSite conditions will arise that preclude the use of the design suction envelopes presented herein. Shallow impeding layers (e.g., relatively unweathered bedrock or zones of calcium carbonate development), particularly within the depth of seasonal suction fluctuation (Fig. 4), may cause deviations from Figs. 1 and 8-type suction profiles. In addition, a significant source of on-site or off-site water (e.g., lateral flow source or surface ponding) would likely preclude the use of Fig. 8 suction envelopes. In all cases, site-specific geotechnical and hydrological investigation is required to determine whether site conditions are consistent with the assumptions implicit in adoption of suction envelopes of Fig. 8.Where site-specific unsaturated flow modeling is required to obtain design suction envelopes, such as where conditions extend significantly beyond seasonal fluctuations only, the suction design envelopes presented herein can be used as a means of calibrating the flow model to field-observed suctions. Similarly, flow model–based methods for estimation of suction profile parameters, such as Saha et al. (2019), could be calibrated to field data of this study.ConclusionsDirect measurement of initial soil suction profiles is preferred, where possible and practical. However, where suction measurements are not available, routinely collected data can be used, via the soil suction surrogate, to establish the beginning point for field wetting or drying of expansive soil sites. The final soil suctions will depend on the surface boundary conditions, which are challenging to numerically simulate. Boundary conditions for unsaturated flow must be appropriately considered when estimating initial and final soil suction profiles for design. The field suction profiles of this study are related to two common boundary condition cases for expansive soil design: (1) uncovered sites, subject to seasonal fluctuations only; or (2) interior of covered sites, protected from surrounding seasonal fluctuation suction swings at the edge of a pavement. An underlying assumption in use of climate boundary conditions is that appropriate measures have been taken to protect against ponding of water at the ground surface and lateral flow of water from on or off site; use of seasonally driven suction change assumes that protections have been put in place against major accidental subsurface leaks. Case 1 corresponds to structures located close to the edge of a paved (covered) surface, or roadways with a narrow shoulder, such that seasonal variations occur under the pavement edge. Case 2 corresponds to structures that are set back from the edge of the pavement some substantial distance, or to roadway lanes protected by a paved shoulder or vertical moisture barrier that is as wide or deep as the edge moisture-change distance. For Case 1, the maximum heave or shrinkage will be associated with suction change from the initial measured state to the wet side (heave) or dry side (shrinkage). For covered areas (Case 2), the heave or shrinkage would be calculated for change in suction from the initial state to the final suction state, taken to be the equilibrium (stable) suction value. Because climate, as represented by nearest weather station TMI, has a reasonably good correlation with suction envelope parameters, TMI correlations can often be used to approximate final soil suction profiles for design. However, suction envelope parameters are influenced by factors beyond climate, such as soil type and soil layering, and the correlation between equilibrium suction and TMI was found in this study to have an R2 of 0.65. Therefore, it is recommended that the equilibrium (stable) suction, at depth, be determined by direct suction measurement, and that this measured equilibrium suction value be considered for use as a regional shift for purposes of estimation of design suction envelopes, as suggested by Walsh et al. (2009).In dealing with developed sites, it is typical in the US that development results in wetting of soils compared to conditions at time of construction. Based on the limited developed site data of this study, with good control of site water to avoid excessive wetting, it appears that the final wet suction profiles might reasonably be expected to be the wet envelope obtained in this study for seasonal fluctuation conditions. However, field data also show that poor control of site water may be associated with increased depth of wetting compared to climate-driven ground surface boundary conditions (Fig. 11). A locally obtained database of suction profiles for developed sites, where available, may be helpful in the establishment of final suction profiles, provided boundary conditions for the database are similar to those for the case at hand. Unsaturated flow modeling could also be used to augment selection of design suction envelopes for developed sites. Although unsaturated flow modeling can be used to address certain what-if scenarios with respect to impact of nonclimatic conditions on final soil suction profiles, such modeling undertakings represent a considerable challenge (Naiser 1997; Houston and Welfert 2014; Wray et al. 2005). Where numerical flow models are employed, it is recommended that the field measurement–based suction envelopes of this study be considered, along with any other site-specific data, as one approach to calibrate such models.Data Availability StatementAll data, models, and code generated or used during the study appear in the published article.AcknowledgmentsThis work is based in part on research funded by the National Science Foundation under Award No. 1462358. The opinions, conclusions, and interpretations are those of the authors and not necessarily the National Science Foundation. 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