Influence of environmental factors on the wetting front depth: A case study in the Loess Plateau

Engineering Geology 214 (2016) 1–10

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Influence of environmental factors on the wetting front depth: A case study in the Loess Plateau Ping Li a,b, Tonglu Li a,⁎, Sai K Vanapalli b a b

Department of Geological Engineering, Chang'an University, Xi'an 710054, China Department of Civil Engineering, University of Ottawa, Ottawa K1N6N5, Canada

a r t i c l e

i n f o

Article history: Received 25 February 2016 Received in revised form 15 September 2016 Accepted 19 September 2016 Available online 20 September 2016 Keywords: Unsaturated loess Wetting front depth Water content variation Environmental factors Soil temperature VADOSE/W

a b s t r a c t Reliable information on the wetting front depth and variation of water contents within the zone of wetting is required for addressing geotechnical problems in loess deposits such as estimation of the collapse deformation and assessment of the slope stability. For this reason, a field test was conducted at a site in the Loess Plateau of China to obtain data on soil water contents and temperatures at different depths for a period of one year. The variation of water contents was interpreted from the influence of environmental factors and soil temperature, and used to determine the maximum wetting front depth in the loess soils in the study region. In addition, a commercial software, VADOSE/W, was used to simulate the flow behaviour in unsaturated loess taking account of the influence of environmental factors. A reasonable agreement was found between the results of field investigations and numerical simulations. The study results are useful as they provide valuable information about the wetting front depth and water content variation in unsaturated loess in response to environmental factors. The field investigations and numerical simulations summarized in this paper can serve as a reference for future studies on other soils. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Loess soils are widely distributed in semi-arid and arid regions around the world; which include countries such as China, Russia, the United States, Argentina, France, Germany and New Zealand (Rogers et al., 1994). These soils are typically in a state of unsaturated condition and are susceptible to collapse (i.e. sudden decrease in soil volume) due to an increase in natural water content under practically unchanged vertical stress (Barden et al., 1973). The prerequisite conditions for collapse include: a soil fabric which is open and potentially meta-stable, an increase in water content that contributes to reduction of soil suction and destruction of bonding agents, and a relatively high level of total vertical stress (Barden et al., 1973). Li et al. (2016) presented a stateof-the-art review on the wetting-induced collapse mechanism with special reference to loess soils. In China, loess soils have deposited since 2.4 million years (i.e., 2.4 Ma) ago, forming the Loess Plateau extending an area of over 440,000 km2. Loess thicknesses are typically of 50 to 100 m while a thickness up to 300 m was found in Gansu, China (Zhou and Derbyshire, 2008). As per Smalley et al. (2001), Liu and his colleagues were the earliest to conduct large-scale investigations of loess stratigraphy. They divided the loess soils deposited in the Quaternary period (more than 2.4 Ma) into three formations; namely, ⁎ Corresponding author. E-mail addresses: [email protected] (P. Li), [email protected] (T. Li), [email protected] (S.K. Vanapalli).

http://dx.doi.org/10.1016/j.enggeo.2016.09.008 0013-7952/© 2016 Elsevier B.V. All rights reserved.

Wucheng, Lishi and Malan loess corresponding to early, middle and late Quaternary periods, respectively. The initially loose-structured wind-blown loess soils become stable with time and depth due to the increasing consolidation pressure. However, recently-deposited loess soils are susceptible to collapse upon wetting. The upper Lishi and Malan loess (typically, 10–20 m deep below the ground surface) are found collapsible upon wetting (Derbyshire, 2001; Dijkstra et al., 1994). It is difficult to estimate the collapse deformation of loess soils with a reasonable accuracy unless the wetting front depth is determined (Houston et al., 1988). In addition, rainfall-induced shallow landslides are major geo-hazards in loess regions. The rainfall-induced shallow failure of soil slopes is triggered by a matric suction decrease as a result of wetting (Crosta, 1998; Dai and Lee, 2001). A key issue in assessing this type of slope failure is reliable estimation of the matric suction variation within the zone of wetting (Trandafir et al., 2008). Limited research has focussed on the details of rainfall infiltration and advancement of the wetting front for understanding their effects on the unsaturated soil slope stability (Kim et al., 2004; Yeh et al., 2008; Trandafir et al., 2008; Cho, 2009). For these reasons, there is an urgent need to investigate the wetting front depth and water content variation within the wetted zone in loess soils. The wetting front depth is defined as the depth to which water contents have either increased due to introduction of water from external sources or decreased due to evaporation (Nelson et al., 2001). External sources include rainfall, irrigation, seepage from water lines, and others. The first conceptual model for estimating the depth of wetting front in

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saturated-unsaturated soil system was introduced by Lumb (1975). In Lumb's study, it was assumed that the soil is saturated near the ground surface and close to saturated down to a certain depth. Sun et al. (1998) extended Lumb's theory and proposed a generalised equation for estimating the wetting front depth. In Sun et al. study, it was suggested that a new infiltration zone forms and gradually progresses downwards when the ground surface moisture flux increases. This equation can estimate the wetting front depth reasonably in one-layered soil profiles (Yeh et al., 2008). Several other methods were proposed based on field and laboratory investigations (El-Ehwany and Houston, 1990; Leconte and Brissette, 2001; Trandafir et al., 2008; Yeh et al., 2008). The wetting front depth was commonly determined from artificial rainfall tests in the field or wetting column tests in the laboratory for various soil types (Zhang et al., 2000; Li et al., 2005; Singh et al., 2006; Tu et al., 2009). This is because the simplified conceptual models do not take account of many other factors which influence the wetting front depth (for example, Lumb, 1975 and Sun et al., 1998). Various factors, including soil properties, topographic features, rainfall intensity and duration, other climate factors (such as evaporation and atmospheric temperature) and land-use type (i.e. vegetation factors or cover type), influence the wetting front depth in loess soils. Several studies were performed to investigate the response of loess soils to varying rainfall intensity and duration, slope height and gradient, soil properties, type of land-use, respectively (De Roo and Riezebos, 1992; Gvirtzman et al., 2008; Zhao et al., 2012). For example, Zhao et al. (2012) conducted large-scale laboratory column tests and found that the influence of precipitation is typically within 1.6 m for loess soils from Changwu, China. Most of these studies focused on the influence of precipitation and land use, while few studies considered the comprehensive influence of environmental factors. In order to investigate the influence of environmental factors on the water contents in loess soils, a field test was undertaken at a site in the Loess Plateau of China. At the site, water contents and temperatures of the soils at different depths were measured for a period of one year. The variation of water contents was interpreted and used to determine the maximum wetting front depth in response to environmental factor. In addition, the flow behaviour in unsaturated loess was successfully simulated using a commercial software, VADOSE/W, in order to provide a reliable and more economical method for estimating the wetting front depth and water content variation under environmental factors. This study highlights the field investigation of soil water contents and temperatures over a long period of time, as well as the numerical modelling of the flow behaviour in unsaturated loess soils under environmental factors. 2. Site description Two key factors were considered for selecting a test site to undertake the field test. First, the site should be free of vandalism so that the instrumentation system would not be disturbed during the testing period.

Second, the soil at the site has to be a typical loess soil that is representative of the Loess Plateau. Considering these two factors, a site was selected at an abandoned school yard, in Zhengning County, Gansu, China (geographical location of the site in the map of China is shown in Fig. 1). As the study region is located in the central Loess Plateau, the soil at the site is representative of the Loess Plateau. The annual precipitation is less than 500 mm, while the annual evaporation can reach up to 1500 mm in the study region. This region has four distinct seasons and the atmospheric temperature typically varies from −20 to 35 °C. 2.1. Soil properties A well of 1 m in diameter and 10 m in depth was excavated at the site for installation of instruments. Along the depth, the soil of pale yellow color extending from the ground surface to about 8.5 m deep was classified as Malan loess. One layer of paleosol sandwiched between loess layers was identified from 8.5 to 10 m deep. Paleosol soil deposited during wet and warm periods has typically red-brown color and denser structure than loess soil which deposited during dry and cold periods. To characterize the soils at the site, soil samples were collected at integer depths (i.e. 1, 2, …, 10 m) during the excavation of the well for laboratory test program. In addition, one more sample was taken at a depth of 0.5 m. The physical properties determined from laboratory test program include: (i) bulk density, (ii) natural water content, (iii) Atterberg limits, and (iv) particle size distribution. The test results are shown in Fig. 2. From these results, it can be observed that the content of siltand clay-size particles increases with the depth; the dry density varies between 1.3 and 1.4 Mg/m3; the natural water content varies from 13 to 18%; both the plastic and liquid limits show small variations along the depth. 3. Instrumentation system The moisture probes and thermometers were used to measure the soil water contents and temperatures at specified depths, respectively. Before their installation, all the instruments were checked for proper functioning in the laboratory. 3.1. Moisture probe YT-DY-0101 moisture probes were used to measure soil water contents. The moisture probe has a high-frequency moisture detector that uses the principle of standing-wave to indicate the ratio of three or more substances (i.e. typically, soil particle, water and air) forming a mass of material. Each substance has a specific dielectric constant. The water content can be estimated from the change in dielectric constant value. The output of the moisture probe is volumetric water content calculated using the calibration coefficient provided by the manufacturer. However, the moisture probe needs to be recalibrated before using

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Fig. 2. Variations of soil properties with respect to depth: (a) Ps + c, the content of silt- and clay-size particles; (b) ρd, the dry density; (c) w0, the natural water content; (d) wP, the plastic limit; (e) wL, the liquid limit.

since various soil types have different dielectric constants. In other words, the calibration coefficient provided by the manufacturer is not a universal value that can be used for any soil type. After the moisture probe is recalibrated for a specific soil type, the outputs are typically within ± 2% of the true volumetric water content values. The moisture probe with a diameter of 50 mm and a total length of 200 mm has four needles that are 60 mm long. The needles can be either pushed or buried into the soil. All of the moisture probes were connected to an automatic data acquisition system, which was capable of recording and transmitting data to a computer through wireless internet connection. In other words, the data was remotely collected. The interval for data recording was set as 24 h.

All output ports were attached to the data acquisition system which was placed above the ground surface and 5 m away from the well. Besides the moisture probes, 22 thermometers were placed at the same depths as the moisture probes. The thermometer was placed in a glass bottle that was wax-sealed for keeping it in dry condition. The glass bottle was buried into the soil at a place that is approximately 0.1 m horizontally away from the well wall. After installation of all instruments for data collection, the well wall was treated for preventing lateral seepage and possible evaporation from influencing the measured values of soil water contents. The well wall was painted with straw-reinforced mortar, cement mortar and waterproof paint, successively. After all of the work in the well was completed, the well was covered with a concrete plate.

3.2. Thermometer

Output Ports

RC-3 thermometers were used to measure and record soil temperatures. The thermometer can continuously measure the temperature of surrounding environment from − 30 to 60 °C with ± 1 °C accuracy. Each thermometer is empowered by an external battery and is capable of recording 16,000 values for over one year. The interval for data recording was set as 6 h, considering the memory capability and functional period of the thermometer.

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3.3. Details of instrument installation The installation of instruments was undertaken following three steps; namely, (i) excavation and sampling, (ii) instrument installation, and (iii) well wall treatment. The well for instrument installation was excavated manually. A plumb line was used during the excavation to guarantee the verticality of the well. Both undisturbed and disturbed soil samples were collected at different depths during the excavation. The soil samples were stored in several humidity chambers for maintaining their natural water contents, and transported to the laboratory for determining their initial soil properties. In total, 22 moisture probes were pushed into the well wall at different depths. More moisture probes were placed within the top 2 m since it was reported that the loess soils within this range are more sensitive to environmental factors (Zhao et al., 2012). The spacing between the moisture probes was 0.1 m within the top 1 m and 0.2 m from 1 to 2 m. Below 2 m, the moisture probes were installed at integer depths (i.e. 3, 4, …, 10 m). Fig. 3 shows the schematic diagram of moisture probe distribution as well as the stratigraphic features of the site. The cables connecting the moisture probes and the output ports were fixed on the well wall through a plastic tube for protection purposes.

4 6 8 10 12 14 16 18 20 22

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4. Variation of soil water contents with respect to time The soils at specified depths were kept undisturbed and their volumetric water contents and temperatures were measured during the entire period of the one-year study, starting from January 1, 2013. In this paper, the results of field investigations are presented for determining the maximum wetting front depth and interpreting the water content variation under environmental factors. 4.1. Influence of environmental factors on soil water contents The variation of soil water contents with respect to time at several depths is presented in Fig. 4. The water contents below 4 m are not shown because they remained constant during the entire testing period. The daily-based data of climate factors, including precipitation, evaporation, relative humidity, atmospheric temperature and wind speed, during the testing period was collected from the local meteorology station. Since relative humidity, atmospheric temperature and wind speed influence the water contents in soils indirectly by means of controlling the rate of evaporation, only the information of precipitation and evaporation is shown for interpreting the variation of soil water contents (see Fig. 5). The study region had a low annual precipitation of about 300 mm in the year of 2013, while the annual evaporation was as high as 1400 mm, which confirms that the study region has an arid climate condition. The study region has four distinct seasons. In spring (from March to May), the daily amounts of precipitation and evaporation increased significantly. Both of them reached the maximum levels until summer (from June to August). The precipitation in spring and summer accounted for 35% and 47% of the annual amount, respectively; while the evaporation of both seasons were approximately the same. The water contents below 3 m were almost constant throughout the year. The water content at 2 m slightly increased from early spring (i.e. March) until the end of summer (i.e. August) and then decreased by the end of winter (i.e. February). Since the soil water contents between 2 and 3 m were not measured, the depth of wetting front could not be exactly determined. However, the water content changes at 2 m were less than 3% throughout the testing year, much lower than that within the top 1 m. Due to these reasons, the maximum wetting front depth in response to environmental factors in the study region was considered as 2 m. In other words, this is the zone in which soil water contents were sensitive to environmental factors. Typically, the changes in soil water content in response to environmental factors become less pronounced as the depth increases. To interpret the variation of water contents clearly, the wetted zone (i.e. the top 2 m) was divided into two subzones (i.e. the top subzone is the top 1 m and the bottom subzone is from 1 to 2 m deep). The soil water contents

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within the top subzone were more sensitive to environmental factors than the bottom subzone. The water contents at 0.2, 0.6 and 1 m showed an increase from mid-winter to early spring (i.e. from mid-January until the end of March). This increase which is considerable could not be well interpreted from the information of precipitation. It is because there was little precipitation in winter (i.e. as low as 11.3 mm), which was much less than the amount of evaporation during the same period. From early April to mid-July, the soil water contents at 0.2 and 0.6 m were almost constant or had a slight drop. This is attributed to the increasing precipitation and evaporation rates that balanced each other and resulted in negligible water content variation at the shallower depths (i.e. 0.2 and 0.6 m). However, the water content at 1 m decreased continuously at the same time due to the higher rate of evaporation than precipitation. In late summer (i.e. from mid-July to the end of August), the water contents within the top subzone had several sudden and dramatic increases which can be attributed to heavy rainfall events. However, they reduced rapidly once the rain stopped. In autumn, the water contents within the top subzone declined gradually due to significant decrease in precipitation. Compared to the top subzone, the soil water contents within the bottom subzone (i.e. between 1 and 2 m) showed much milder changes. For example, the values at 1.4 and 1.6 m practically remained constant from mid-winter to mid-summer (i.e. from January to mid-July). In late summer (i.e. August), dramatic increases observed in the water contents within the bottom subzone were also due to heavy rainfall events. The variation of soil water contents under the combined influence of precipitation and evaporation is rather complex as per the test results presented above. The rain water, soil water and water vapor can transform from one to another depending on various environmental factors and soil properties. The rain water infiltrates into the soil and flows downwards under the gravity effect and matric suction gradient. Typically, the water content in the topsoil increases rapidly after rainfall events, however, the response of water contents at the greater depths to precipitation are much slower. Also, the higher the rainfall intensity, the quicker the response of soil water contents. This can be inferred from the measured water content values within the top 1 m, which increased immediately and dramatically in response to the heavy rainfall events in July. When the rain water infiltrates into the soil, some of the water is absorbed and held by soil pores, especially the soil pores which are relatively small in size. The remainder of the water, however, flows downwards. It is difficult to remove the water from small size pores without high enough matric suction gradient. Once the rain stops, the increasing evaporation rate results in water content decrease in the topsoil and contributes to producing matric suction gradient that is opposite with precipitation and can induce upward water flow in the soil. Typically, the changes in the water contents at the shallower depths are larger than that at the greater depths. In the rainy season (i.e. from May to July as per Fig. 5), the advancement of the wetting front is a progressive process due to high rate of precipitation. Each rainfall event contributes to increasing the soil permeability within the wetted zone and promoting the wetting front depth. This can be inferred from the

P. Li et al. / Engineering Geology 214 (2016) 1–10

water content at 2 m, which increased to its maximum value after the rainy season. Evaporation contributes to inducing upward water flow in either liquid or vapor form in the soil. When the rain stops, the increasing temperature and decreasing relative humidity in the atmosphere transform the pore water in the topsoil into water vapor, which subsequently escapes from the soil (i.e. soil water evaporation). As the water content in the topsoil decreases, an opposite matric suction gradient generates and induces upward water flow in the soil. Based on this mechanism, the water contents at some depths (i.e. intermediate depths) would be in a state of dynamic stabilization in response to the varying precipitation and evaporation. The water contents at these depths remain constant for some time until significant changes in precipitation and evaporation arise. This reasoning can explain the test results of the water contents at 1.4 and 1.6 m which did not change much from January to mid-July; however, the water contents either above or below these depths (for example, 1 and 2 m) showed noticeable changes at the same time. 4.2. The effect of soil temperatures on soil water contents The variation of soil temperatures at several depths with respect to time is presented in Fig. 6. The daily temperature was determined by averaging the four measured values in a day. The variation of soil temperatures within the wetted zone (i.e. the top 2 m) is consistent with atmospheric temperature. Two important observations can be derived from these results. First, the soil temperatures at specified depths were higher than 0 °C over the testing period of one year. This means that the soils did not freeze in winter even though atmospheric temperatures reached as low as −16 °C. For this reason, the influence of freezethaw cycles on soil water contents could be neglected. Second, the soil temperatures at the shallower depths were higher than that at the greater depths in spring, summer and early autumn (i.e. from March to October). However, results with opposite trends were measured in late autumn and winter (i.e. from November to February). These observations suggest that the changes associated with the temperature gradient in the soil would contribute to the variation of water contents. The effect of soil temperature on its hydraulic properties is important such that ignoring the temperature effect would result in substantial errors in estimating the soil hydraulic properties (Hopmans and Dane, 1985). Temperature is experimentally proved to influence both the soil-water characteristic curve (i.e. SWCC) (Haridasan and Jensen, 1972; Hopmans and Dane, 1986; Jacinto et al., 2009; Wan et al., 2015) and unsaturated coefficient of permeability (Haridasan and Jensen, 1972; Constantz, 1982; Ye et al., 2013). The SWCC is the relationship between soil suction and water content (volumetric or gravimetric) or degree of saturation. Numerous studies have suggested that reliable determination or estimation of the SWCC is important for reliable

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5

estimation of both the hydraulic and mechanical properties of unsaturated soils (van Genuchten, 1980; Fredlund et al., 1994; Vanapalli et al., 1996). The effect of temperature on the SWCC is primarily attributed to its influence on surface tension, entrapped air volume, angle of contact associated with the air-water-soil interphase, clay fabric and pore water chemistry. During the last half-century, a number of studies were conducted to develop equations for both the SWCC and matric suction taking account of the temperature effect, as summarized in Table 1. Philip and de Vries (1957) were among the first to present an equation for describing the change in the soil-water pressure head with temperature by considering only the temperature-dependence of surface tension (see Eq. (1)). Hopmans and Dane (1986) modified the Philip and de Vries (1957) theory by also considering the change of entrapped air volume due to thermal expansion (Eq. (2)). Grant and Salehzadeh (1996) extended the Philip and de Vries (1957) theory by introducing the wetting coefficient, which is temperature-sensitive and has pronounced effect on the SWCC (see Eq. (3)). Jacinto et al. (2009) developed a modified van Genuchten (1980) (i.e. VG) model which takes account of the influence of temperature and porosity (or dry density) on the SWCC (see Eq. (4)). Wan et al. (2015) found that the temperature effect is not only suction-dependent, but also dependent on the stress state in the soil. Based on the test results on bentonite, they modified the Fredlund et al. (1994) equation (see Eq. (5)). As per the studies summarized above, at a given water content, soil suction increases as temperature decreases, especially at high suction values. In other words, temperature decrease enhances the water retention/storage capacity of the soil. Due to this reason, water flows from high to low temperature zones due to the suction gradient generated as a result of the temperature gradient. For the scenario discussed in the present study, water could flow in either liquid or vapor form from the greater depths (high temperature zone) towards the shallower depths (low temperature zone) in late winter (i.e. from mid-January to early March), which contributed to the increase of the water contents at 0.2 and 0.6 m at that time. However, it is difficult to quantitatively assess how much the temperature effect contributes to the variation of soil water contents in summer. 5. Numerical simulation of the flow behaviour in unsaturated loess using VADOSE/W The most reliable information on the wetting front depth and water content variation should be obtained from field tests. However, it is rather cumbersome and expensive to measure soil water contents in the field over a long period of time. In addition, there are limitations of the presently available sensors for continuously measuring soil water content (or matric suction) in the field for a long time. For these reasons, more economical and simpler methods that can reasonably simulate the flow behaviour in unsaturated soils under environmental factors are desirable, especially for practicing engineers. Commercial software, such as VADOSE/W and SVFlux, are capable of simulating the flow behaviour taking account of not only the hydraulic properties of unsaturated soils but also their corresponding changes in response to environmental factors. Such techniques are useful and economical provided that a reasonable computational model is built with reasonable boundary conditions and soil parameters. VADOSE/W allows the accumulation of runoff in surface depressions and subsequent infiltration, and is able to predict soil water evaporation as a function of environmental factors (Gitirana et al., 2006). It has been used with increasing popularity during the last decade for predicting the infiltration and soil water evaporation (Weeks and Wilson, 2006), wetting front depth (Overton et al., 2006) and variations of soil water content or matric suction in response to environmental factors (Rajeev et al., 2012; Vanapalli and Adem, 2013). More recently, VADOSE/W was used to predict the infiltration in compacted loess which was used as a final cover material (Zhan, 2015). In the present study,

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Table 1 Summary of equations for describing the influence of temperature on the SWCC or matric suction. Source

Equation

Parameters

Philip and de Vries ∂h ¼ ð h Þðdσ Þ (1) σ dT ∂T (1957) ∂h dh dθ0 Hopmans and Dane ¼ ðσh Þðdσ Þ þ ðdθ Þ 0 Þð dT dT ∂T (1986) θ′= θ+ υ (2) β þT Grant and pcf ¼ pcr ð β0 þT rf Þ (3) 0 Salehzadeh (1996) Jacinto et al. (2009) w = wsat[1 + (s0/P0)1/(1−λ)]−λ (4) Wan et al. (2015)

w ¼ CðψÞ

wsat 0 þξðT−T 0 Þ m f ; ln ½eþðψ=ðη ; ln ðT−273ÞþεÞÞn g

(5)

h = the soil-water pressure head; σ = the surface tension at the air-water interface; T = temperature. θ′ = the apparent volumetric water content; θ = the volumetric water content; ν = the entrapped air content. pcf = the capillary pressure at temperature Tf; pcr = the capillary pressure at temperature Tr; Tr = the reference temperature; Tf = the observational temperature; β0 = the intercept of the linear relationship between ratios of capillary pressures to their temperature derivations and temperature. w = water content; wsat = the saturated water content; s0 = matric suction for the reference temperature and porosity; P0 and λ = fitting parameters. C(ψ) = the correction function; w0sat = the saturated water content at the reference temperature T0; ξ, η, ε, n and m = fitting parameters; ψ = matric suction; e = the base of natural logarithm.

VADOSE/W was used to simulate the flow behaviour and predict the maximum wetting front depth in unsaturated loess taking account of the influence of environmental factors. The flow behaviour in response to environmental factors in two months, representing winter and summer seasons, respectively, were simulated using VADOSE/W. Case A (i.e. August) represents summer season and Case B (i.e. January) represents winter season. The temperature effect on the hydraulic properties (i.e. the SWCC and unsaturated coefficient of permeability) was only taken into account in Case B. This is because the daily amounts of precipitation and evaporation reached their relatively low levels in January, such that the influence of precipitation and evaporation on the soil water contents was expected to be less in January. In addition, the temperature gradient within the zone of wetting that can induce upward water flow was the highest in January (see Fig. 6). Furthermore, the water contents within the wetted zone were relatively high in August due to several heavy rainfall events in July. This means that the soil suction values were relatively low during this period and the temperature effect was less significant under such a scenario. The input information of VADOSE/W includes (i) soil properties for simplified thermal model, including the SWCC, permeability function, thermal conductivity, heat capacity; (ii) climate factors, including daily precipitation, atmospheric temperature, relative humidity and wind speed; (iii) vegetation factors, including the leaf area index (LAI), plant moisture limiting point and root depth; (iv) flux boundary conditions and ground water level (GWL) (Geo-Slope International, 2010). 5.1. Computational model One-dimensional model of a 4-m-thick loess column was set up in VADOSE/W taking account of the maximum wetting front depth determined from the field test (i.e. 2 m). For both cases, the loess column was divided into three layers based on the variations in initial water content and soil temperature (see Table 2). Average values of initial water

content and soil temperature of each layer were determined from the available data. For Case A, the same SWCC was used for the three layers; however, different SWCCs were assigned to the three layers in Case B. In addition, a temperature gradient was imposed in the loess column in Case B by maintaining three layers with different temperatures. The deeper the layer, the higher the temperature.

5.2. Soil properties for simplified thermal model Since the measured SWCCs of the loess soil at the site corresponding to different testing temperatures were not available, the modified VG model developed by Cai et al. (2010) was employed to estimate the temperature-dependent SWCCs. Cai et al. (2010) extended the work of Grant and Salehzadeh (1996) and modified the simplified VG model (i.e. the residual water content is assumed as zero). The modified VG model can estimate the SWCC at any temperature and dry density from a reference SWCC. This model was chosen because it takes advantage of the Grant and Salehzadeh (1996) work which considered both the temperature-dependence of surface tension and changes in the wetting coefficient induced by the temperature variation. In addition, this model is easy to be used by following a simple procedure. The model was validated for a Malan loess soil in Wang et al. (2008) study, a good agreement was found between the measured and estimated results (see Fig. 7). The soil samples tested by Wang et al. (2008) were collected from Xi'an, China, which is about 100 km southeast and has the geological characteristics as same as that of the test site. Therefore, the model parameters reported in Cai et al. (2010) study for Malan loess soil were directly used in this study. The model is shown in Eq. (6), where, s = matric suction at temperature T; θw = volumetric water content at matric suction s; θs = saturated volumetric water content; a, b = curve fitting parameters. As per Jacinto et al. (2009), a, b and θs were represented as functions of temperature and dry density (see Eqs. (7)–(9)). The SWCC at the reference temperature and dry density should be known before estimating the curves at other values of

Table 2 The initial properties and hydraulic properties of loess soil layers for both cases. Layer

Depth (m)

θi (%) for Case A

Parameters for Case A

θi (%) for Case B

Ti (°C) for Case B

Parameters for Case B

①

0–0.8

32.3

θs = 31.7% a = 8.81 b = 1.39 ksat = 2.35 × 10−6 m/s

22.8

1.6

②

0.8–1.5

21.1

18.4

4.1

③

1.5–4

26.3

25.8

6.7

θs = 38.9% a = 12.4 b = 1.43 ksat = 1.94 × 10−6 m/s θs = 37.6% a = 11.6 b = 1.42 ksat = 2.01 × 10−6 m/s θs = 36.2% a = 10.8 b = 1.42 ksat = 2.08 × 10−6 m/s

θi = the initial volumetric water content; Ti = the initial soil temperature; ksat = the saturated coefficient of permeability.

P. Li et al. / Engineering Geology 214 (2016) 1–10

40 5 15 25 35

30

5 15 25 35

Vol. water content (%)

Vol. water content (%)

40

7

20

10

30

20 Case A Case B-L1

10

Case B-L2 Case B-L3

0 0.1

0 1

10

100

1

10

100

1000

Matric suction (kPa)

1000

Matric suction (kPa)

temperature and dry density. θw ¼ h

a ¼ a0

1þ

θs
s b i1−1=b

ð6Þ

a

 n C 1 T þ C 2 T ln T þ C 3 ρ0 C 1 T 0 þ C 2 T 0 ln T 0 þ C 3 ρ

ð7Þ

b ¼ b0 þ λb ðT−T 0 Þ þ κ b ðρ−ρ0 Þ

ð8Þ

θs ¼ θs 0 þ λθ ðT−T 0 Þ þ κ θ ðρ−ρ0 Þ

ð9Þ

where, T0 and ρ0 = the reference temperature and dry density; a0 and b0 = fitting parameters a and b at the reference temperature and dry density; θ0s = saturated volumetric water content at the reference temperature and dry density; C1, C2 and C3 = constants; n, λθ, κθ, λb, κb = fitting parameters. The model parameters for Malan loess soil are summarized in Table 3. In the present study, the soil dry density was determined as 1.3 Mg/ m3 (i.e. average value of the 4-m-thick loess column) in both cases. The initial soil temperature was determined as 15 °C in Case A, and the values for the three layers in Case B are summarized in Table 2. VADOSE/W provides several well-known SWCC models for inputting the SWCC information, including the VG model. The SWCC fitting parameters, as summarized in Table 2, were directly input in VADOSE/ W (see Fig. 8). It is observed that there are considerable differences among the SWCCs due to the temperature effect. At a given water content, the lower the soil temperature, the higher the matric suction. It is therefore concluded that temperature decrease enhances the water retention/storage capacity of the soil. The VG function (Eq. (10)) was used to estimate the permeability function in VADOSE/W once the SWCC and saturated coefficient of permeability are specified. 
 2 1− αsn−1 ð1 þ αsn Þ−m k w ¼ ks  m ð1 þ αsn Þn 2

ð10Þ

Table 3 The SWCC model parameters for Malan loess soil (from Cai et al., 2010). Parameters θ0s Loess 37.1 Parameters λb Loess −2.85 × 10−3

a0 13.2 κθ 3.02 × 10−4

b0 1.42 κb −4.20 × 10−4

n 1.96 C1 1.16 × 10−2

λθ −5.35 × 10−3 C2 −1.84 × 10−3

Fig. 8. The SWCCs corresponding to different temperatures used in the numerical simulation study.

where, kw = coefficient of permeability at matric suction s; ks = saturated coefficient of permeability; α, n, m = curve fitting parameters. The saturated coefficient of permeability of the loess soil at the site was measured in the laboratory at 20 °C (i.e. room temperature), as 2.55 × 10−6 m/s. The values at other temperatures were estimated from the varying water viscosity (Haridasan and Jensen, 1972), as summarized in Table 2. The permeability functions under various temperatures are shown in Fig. 9. It is observed that coefficient of permeability decreases significantly with the increasing matric suction, especially in the suction range from 10 to 100 kPa. As matric suction increases to around 100 kPa, coefficient of permeability decreases to the order of 10−10 m/s. In other words, the soil can be considered as impermeable when soil suction is reaching 100 kPa. The temperature-dependence of permeability function should be consistent to that of the SWCC. However, the variation of permeability function with respect to temperature, as shown in Fig. 9, is not as noticeable as that of the SWCC (see Fig. 8). This could be attributed to one of the figures being plotted on a semi-logarithmic scale while the other is plotted on a double-logarithmic scale. The frozen and unfrozen thermal conductivities and volumetric heat capacities are assumed as constant with respect to temperature in the simplified thermal model in VADOSE/W. This is reasonable especially for the two cases in the present study since there was no ice formed during both months (i.e. August and January). These parameters were determined as suggested by Geo-Slope International (2010).

5.3. Boundary conditions The daily-based data of climate factors (including precipitation, relatively humidity, atmospheric temperature and wind speed) in both months (i.e. August and January) was collected from the local meteorology station (see Fig. 10). The daily precipitation was assumed to be distributed in a sinusoidal form within the second half of the day (i.e. from

1.E-05

Permeability coef. (m/s)

Fig. 7. Comparison between the measured SWCC data and estimated curves using the Cai et al. (2010) model (the Malan loess soil has a dry density of 1.2 × 109 Mg/m3, from Cai et al., 2010).

Case A Case B-L1 Case B-L2 Case B-L3

1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 1

10

100

1000

Matric suction (kPa) C3 −2.99 × 10−1

Fig. 9. The permeability functions corresponding to different temperatures used in the numerical simulation study.

8

P. Li et al. / Engineering Geology 214 (2016) 1–10

Case A (August) Pre. (mm)

2

Case B (January) 4

(a)

1

(e)

2

0

0 0

10

20

30

100

0 100

RH (%)

20

50 Max. Min.

Max. Min.

0

0 0

10

20

30

30

0

AT (°C)

10

20

30

20

(g)

(c) 20

0 Max. Min.

Max. Min.

10

-20 0

10

20

30

6

WS (m/s)

30

(f)

(b) 50

10

0

10

20

30

10

20

30

10

(h)

(d) 4

5

2

0 0

10

20

30

0

Time (day)

Time (day)

Fig. 10. The information of climate factors for both cases: (a) precipitation in August; (b) relative humidity in August; (c) atmospheric temperature in August; (d) wind speed in August; (e) precipitation in January; (f) relative humidity in January; (g) atmospheric temperature in January; (h) wind speed in January (Pre. = precipitation; RH = relative humidity; AT = atmospheric temperature; WS = wind speed).

12:00 to 24:00). The solar radiation was estimated in VADOSE/W by considering the latitude of the test site (i.e. 35.5°). The vegetation factors (including the leaf area index, plant moisture limiting point and root depth) were determined by considering the local climate condition. The growing season in the study region is between March 15 and October 15. The leaf area index function was estimated based on a standard shaped function for a “good” quality 2.0

1.0

(a)

grass in Case A, while a "poor" quality grass in Case B (Tratch et al., 1995). The roots were assumed from a depth of 0.05 m on the first day of the growing season to the maximum depth of 0.3 m in three months. The root zone distribution was assumed as triangular, which describes a decreasing root uptake of water with depth (Fredlund et al., 2012). The plant moisture limiting factor is a function of matric suction, which is 1.0 at low matric suction value, and 0.0

(b)

Case A Case B

(c)

0.8

1.0

Root depth (m)

Limiting factor

Leaf area index

1.5

0.6

0.4

-0.1

-0.2

0.5 0.2

0.0

0

200

Time (day)

400

0.0

0

500

1000

1500

Matric suction (kPa)

-0.3 50

100

150

200

Time (day)

Fig. 11. The information of vegetation factors: (a) the leaf area index function, (b) the plant moisture limiting function and (c) the root depth function.

P. Li et al. / Engineering Geology 214 (2016) 1–10

is zero when the wilting point of plants is reached (Fredlund et al., 2012). The defaults for the limiting value and wilting point were suggested to be 100 and 1500 kPa, respectively (Tratch et al., 1995). The vegetation factors are shown in Fig. 11.

5.4. Numerical simulation results The estimated variation of water contents with respect to time at several depths in August (Case A) and January (Case B) is shown in Fig. 12. In Case A, since the daily amounts of precipitation were relatively low even though it rained many times, the water contents at 0.2 and 0.6 m decreased throughout the month due to the relatively high rate of evaporation. However, the reducing trends at 1 and 1.4 m showed a characteristic of delay. The greater the depth, the slower the response of soil water content. The value at 2 m was almost constant, and the water contents below 2 m did not change all the month (i.e. from 2.2 to 4 m, the node spacing was set as 0.2 m). In Case B, the influence of evaporation on the water contents at the shallower depths (i.e. 0.2 and 0.6 m) was still noticeable. However, the values at 0.2 and 0.6 m started to grow halfway, until the end of the month. This behaviour could be attributed to the temperature gradient which induces upward water flow in the soil. Correspondingly, the water contents from 1 to 1.6 m decreased at approximately the same time. The value at 2 m showed little increase and the water contents from 2 to 2.4 m (i.e. 2.2 and 2.4 m) had minor fluctuations (less than 0.5%). The values below these depths (i.e. from 2.6 to 4 m) were constant throughout the month. Since quite small changes were observed in the water contents below 2 m, the maximum wetting front depth was determined as 2 m. It is worth mentioning that soil water content shows a slower and weaker response to the temperature gradient in comparison to precipitation or evaporation from the modelling results.

9

Besides the consistency between the results of field investigations and numerical simulations with respect to the wetting front depth, a comparison was also made between the measured and estimated volumetric water contents, as shown in Fig. 13. There is a reasonable agreement between the two sets of data (R2 = 0.92 and R2 = 0.93 for Case A and Case B, respectively). The results suggest that the computational model set in VADOSE/W can simulate the flow behaviour in unsaturated loess taking account of environmental factors well and hence can be used to estimate the maximum wetting front depth.

6. Conclusions In the present case study, soil water contents and temperatures at different depths were measured for a period of one year at a site in the Loess Plateau of China. The test results were used to determine the maximum wetting front depth in the loess soils in the study region taking account of the influence of environmental factors, which was 2 m. The other objective was to understand the influence of environmental factors on the variation of soil water contents within the zone of wetting. The results show that the soil water contents are significantly influenced by environmental factors, especially the precipitation and evaporation. The effect of soil temperature on the hydraulic properties is important, especially at high suction values. The temperature effect contributes partially to the variation of water contents, especially in winter season. The commercial software, VADOSE/W, was used to simulate the flow behaviour in unsaturated loess taking account of environmental factors. The numerical modelling approach is more economical and simpler for use in practice. A reasonable agreement was found between the results of field investigations and numerical simulations. The conclusions drawn from this study are useful as they provide valuable information about the wetting front depth and variation of water contents in unsaturated loess in response to environmental factors.

Case A (August)

30

35

Predicted vol. water content (%)

Vol. water content (%)

35

25

20

0.2 m 1.0 m 1.6 m 3.0 m

15 0

5

10

(a)

0.6 m 1.4 m 2.0 m 15

20

25

25 Case A (August) R2=0.93

20

15

30

(a)

Time (day)

30

15

20

25

30

35

Measured vol. water content (%) 0.2 m 1.0 m 1.6 m 3.0 m

30

35

0.6 m 1.4 m 2.0 m

Case B (January)

Predicted vol. water content (%)

Vol. water content (%)

35

25

20

25 Case B (January) R2=0.92

20

15

15

(b)

30

0

5

10

15

20

25

30

Time (day)

Fig. 12. Estimated variation of soil water contents with respect to time at several depths: (a) Case A, August; (b) Case B, January.

(b)

15

20

25

30

35

Measured vol. water content (%)

Fig. 13. Comparison between the measured and estimated water content values: (a) Case A, August; (b) Case B, January.

10

P. Li et al. / Engineering Geology 214 (2016) 1–10

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