Arab J Geosci DOI 10.1007/s12517-013-0915-4

ORIGINAL PAPER

Unsaturated characteristics of undisturbed expansive shale from Saudi Arabia Tamer Y. Elkady

Received: 5 October 2012 / Accepted: 11 March 2013 # Saudi Society for Geosciences 2013

Abstract The aim of this paper is to evaluate the soil water characteristic curves (SWCC) of undisturbed expansive shale identified at different locations of Kingdom of Saudi Arabia. The SWCCs were evaluated for suction ranging from 0.5 to 400 MPa. Based on test results, all SWCCs reveal a bimodal curve indicating the presence of two distinct pore size distributions referred to as small and large micropores. Volume change measurements were performed to evaluate void ratio–suction relationships which confirmed the expansive nature of shale. Similarities between measured SWCCs and void ratio–suction relations developed for expansive shale originating from same geological formation suggests the impact of geological and environmental conditions on the unsaturated behavior of shale samples. Finally, a modified approach based on Mckeen’s classification methodology was proposed to assess the swelling potential using bimodal SWCCs. The modified approach was used to assess the relative contribution of different micropores on the swelling potential of shale. Keywords Expansive soils . Soil water characteristic curves . Suction . Vapor equilibrium technique

Introduction Expansive soils are natural geological hazards that are identified in many parts of the world. These soils possess the unique property of volume change potential (shrinkage and

T. Y. Elkady (*) Department of Civil Engineering, College of Engineering, King Saud University and Cairo University, P.O. 800, Riyadh 11421, Kingdom of Saudi Arabia e-mail: [email protected]

swelling) in response to variation in moisture content. The effect of these soils is not dynamic in nature as in case of earthquakes, floods, or landslides; however, they are shown to be detrimental to light structure and pavements founded on these soils. Environmental conditions favoring the formation of expansive clays are arid and semi-arid climates that are typical in the Arabian Peninsula. Expansive soils were identified in several locations in Kingdom of Saudi Arabia that vary in their geological origin and swelling characteristics (Ruwaih 1987; Dhowian et al. 1990; Dhowian and Erol 1993; Abduljauwad and Al-Sulaimani 1993; Abduljauwad 1994; Azam 2003; Sabtan 2005; Aiban 2006). Expansive shales originating from sedimentary formations are considered one of the types of expansive soils identified in Kingdom of Saudi Arabia. Shale refers to fine-grained sedimentary rock formed by compression of successive layers of clay-rich sediment. Expansive shale extends from city of Al-Ghat in the central region of the Arabian Peninsula to the northwest areas of Tabuk and Tayma cities. Problems associated with expansive nature of these shales were documented in the technical literature (Dhowian and Erol 1993; Al-Mhaidib 2006; Dafalla and Al-Shamrani 2008; Dafalla and Shamrani 2011). Distribution of sedimentary rock formations in the Arab peninsula is shown in Fig. 1. Previous research conducted on expansive soils typically focused on geotechnical, physicochemical, and mineralogical characteristics. In the field, the active zone of expansive soils contributing to volume change is present in the vadose zone of the subsurface profile; therefore, modern research trends and applications have integrated principles of unsaturated soil mechanics in understanding and modeling the behavior of expansive soils. A key property required for the implementation of unsaturated soil principles is the soil water characteristic curve (SWCC). SWCC has been implemented in research related to groundwater infiltration studies (Dawoud and Ismail 2011; El-Hames and Al-Wagdany 2011), contaminant transport (Abderahim and Mohammed 2011; Barbour 1998), ground surface flux modeling (Wilson and Fredlund 2000),

Arab J Geosci

Fig. 1 Generalized map of sampling areas and distribution of sedimentary formations in Arab Peninsula

expansive soil-structure interaction (Zhang 2004; Abdelmalak 2007), and expansive soil classification using soil suction measurements (Mckeen 1992). SWCC defines the relationship between soil suction and water content (whether gravimetric, volumetric, or degree of saturation) as shown in Fig. 2a. Main parameters of the SWCC are the air entry value and the residual water content. Air entry value is defined as the suction above which air commence to enter the soil pores. The residual water content is defined by the inflection point on the SWCC (Fig. 2a) beyond which further reduction in suction is accompanied by insignificant change in water content. Furthermore, SWCC is considered as an estimation tool to obtain unsaturated soil properties such shear strength and hydraulic conductivity. Another attribute of the SWCC is that it is a measure of the ability of soil to retain water under different suction levels. The ability of fine-grained soils to retain water is directly related to its fabric which includes macropores, mesopores, and micropores (Mitchell 1993). Several researches have confirmed the dependence of SWCC shape on soil fabric and pore size distribution (Fredlund and Raharjo 1993; Vanapalli et al. 1998; Simms and Yanful 2002; Nowamooz and Masrouri 2010). Depending on the levels of pore size distribution, two types of

curves may emerge as shown in Fig. 2. Unimodal SWCCs (i.e., with two bending curves only) are associated with soil samples one level of pore size distribution (Fig. 2a); while bimodal SWCCs are obtained for soil samples with two distinct levels of the pore size distribution. The bimodal curve has four bends in the curve defining two air entry values and two residual gravimetric water contents with near horizontal or horizontal intermediate segment (Fig. 2b). Bimodal SWCCs are typically observed in case of structured soil such as aggregated loam (Smettem and Kirby 1990; Wilson et al. 1992; Durner 1994; Mallants et al. 1997) or soils with cracks (Abbaszadeh et al. 2010). Hence, accurate determination of the SWCC depends on using samples that represent in situ fabric. The technical literature comprises few researches related to the SWCC of expansive soils which basically utilized remolded samples (Li et al. 2007; Chao et al. 2008; Miao et al. 2002). Although these researches provide insight on the unsaturated behavior of expansive soils, the SWCC evaluated cannot be used in practical applications due to dissimilarity between soil fabric in the laboratory and field. There is very limited literature on the SWCC of undisturbed expansive shale samples (Chao et al. 1998). Due to scarcity of data and

Arab J Geosci Fig. 2 Main features of unimodal and bimodal SWCCs Gravimetric water content

Air entry value (AEV)

Residual water content (wres)

Residual suction (ψ r) 0.1

1

10 Suction (kPa)

100

1000

(a) Unimodal Curve

Gravimetric water content

(ψ b1, w b1)

(ψ i , wj)

(ψ b2, w b2)

(ψ res1, w res1)

(ψ res2, wres2) 0.1

1

10 Suction (kPa)

100

1000

(a) Bimodal Curve because past geological history and in situ fabric of expansive shale cannot be simulated in the laboratory, there is a need for the evaluation of SWCC of undisturbed expansive shale. The objective of this paper is to evaluate the SWCCs of undisturbed expansive shale obtained from different areas in Kingdom of Saudi Arabia. Information regarding pore size distribution and swelling characteristics as inferred from SWCC was discussed in detail. Furthermore, preliminary observations regarding SWCCs as related to geological origin were noted.

Geology Samples of expansive shale used in this study were obtained from the cities of Al-Ghat and Tabuk, and from Al-Qaliabah village. These expansive shales have different geological and environmental conditions. As such, it is expected that the type and amount of clay, degree of weathering, age, and the soil microstructure are among the differences between these shale samples.

The expansive shale from the city of Al-Ghat originates from the upper and middle Dhurma formation of the mesozoic age. This formation outcrops at several locations within the limits of the town at the foot of Jabal Tuwayq Mountain (Powers et al. 1966). In the field, the clayey shale of the Dhurma formation is overlain by quaternary fluvial deposits (sand, silt, and gravel) of variable thickness. The expansive shale encountered in Tabuk city and Al-Qaliabah village are part of the Tabuk formation which is part of the sedimentary paleozoic strata which outcrops in the hills outside and around the areas (Powers et al. 1966; Sabtan 2005). The clayey shale constitutes the upper 10 to 15 m of the formation which is covered by surfacial quaternary deposits or sandstone.

Material and testing methods Material sampling and characterization Samples of undisturbed expansive shale used in this study were obtained from the areas Al-Ghat, Tabuk, and Al-

Arab J Geosci

Qaliabah. A generalized map of sampling areas is provided in Fig. 1. Al-Ghat city is located in the middle region of the Arab Peninsula (26° 32′ 42″N/43° 45′ 42″E), approximately 270 km northwest of Riyadh. Tabuk city and Qaliabah village are located in the northwest part of the Arab Peninsula (28° 23′ 24″ N/36° 34′ 23″ and 27° 58′ 29″ N/37° 57′ 7″E, respectively). Sampling activities were conducted in proximity to construction sites where structural problems associated with the expansive nature of the soil have been identified. Sampling was performed using open pits of depths ranging from 0.5 to 1.5 m below ground surface. All samples were transported in the laboratory for visual and geotechnical characterization. Al-Ghat shale is described as olive-green clayey shale with intercalations of sandstone of 15–30 cm in thickness. Tabuk shale obtained from the site was reddish gray clayey shale that has a thin bedded laminated structure with reddish hematite coating on the surface. The samples were platy shaped with thickness varying between 1 and 4 cm. Similar to Tabuk shale, Al-Qaliabah shale samples were platy-shaped greenish gray clayey shale with thin horizontal laminated beddings. For the purpose of geotechnical characterization, specimens of undisturbed shale were oven dried, pulverized, and tested for Atterberg limits, grain size distribution, and specific gravity. Summary of soil geotechnical characterization data is provided in Table 1.

Qaliabah shale), specimens were carefully trimmed using a handsaw. Specimens’ final dimensions were approximately 2 cm length by 2 cm width by 2 cm thick. For Al-Ghat shale, irregular clods of shale specimens were selected and carefully trimmed. As indicated from the previous procedure, final dimensions of specimens used in the test were not necessarily identical in shape or dimensions. Vapor equilibrium technique SWCCs were evaluated using the vapor equilibrium technique. The vapor equilibrium technique involves inducing or imposing total suction on a sample by controlling the relative humidity in the air space surrounding a given sample using aqueous solutions (Fredlund and Raharjo 1993; Delage et al. 2008; Taibi et al. 2011; Benchouk et al. 2012; Fredlund et al. 2012). Total suction in shale specimens were induced by the migration of the water molecules through the vapor phase from an aqueous solution of known water potential to the soil pores until equilibrium is attained. Total suction is defined as the state of free energy of soil water which can be measured in terms of partial vapor pressure (relative humidity) at equilibrium. The total suction is correlated to the relative humidity by Kelvin’s equation (Fredlund and Raharjo 1993): y¼


 RT un RT ln lnðRHÞ ¼ nwo wn n wo wn uno

Test sample preparation Testing was performed on specimens of expansive shale. Care was exercised in preparing these specimens so as not to disrupt or destroy the natural structure and fabric of shale samples. In case of platy-shaped shale samples (Tabuk and Table 1 Geotechnical characteristics of expansive shales Property

Tabuk shale

Al-Qaliabah shale

Al-Ghat shale

Initial water content (%) Liquid limit (%) Plastic limit (%) Plasticity index Shrinkage limit (%) Specific gravity Grain size distribution Sand (%) Silt (%) Clay (%) Unified soil classification system Swelling potential classification based on Chen (1988)

3.6 60 25 35 23 2.68

2.5 39 22 17 18.5 2.64

18 63 29 34 22 2.70

2 59 39 CH High

– 61.5 38.5 CL Low

3 22 75 CH High

where y =total suction; R=the constant for perfect gas (8. 31432 J mo−1 K−1); T=absolute temperature (in kelvin); n wo =The specific volume of water (i.e., reciprocal of density in meter cube per kilogram); ωυ =molecular mass of water vapor (18.016 kg/Kmol); uv =the partial pressure of soil water vapor (in kilopascal); uvo =the saturation pressure of pure water vapor (in kilopascal); and RH=relative humidity In this study, two types of aqueous solutions were used. Saturated salt solutions were used to impose total suction in the range of 3,000 to 300,000 kPa. Saturated salt solutions were prepared as a slushy mixture with distilled water and chemically pure salt as per ASTM E 104 (2007). To impose total suctions less than 3,000 kPa, solutions with known concentrations of sodium chloride were used. Several references in the technical literature provide information on different salt solutions and corresponding relative humidity. The aqueous solutions used in this study, corresponding relative humidity, and corresponding total suction are presented in Table 2. The laboratory setup of the vapor equilibrium technique included representative specimens of expansive shale placed on a rigid plastic screen above aqueous solutions placed at the base of air-tight non-reactive containers. Two specimens representative of each expansive shale formation was used

Arab J Geosci Table 2 Salt solutions used, corresponding relative humidity, and total suctions for the vapor equilibrium technique

Salt solution

Chemical formula

Sodium chloride salt solution

NaCl (0.1 M/L concentration)

Sodium chloride salt solution Sodium chloride salt solution Potassium sulfate Potassium nitrate Potassium chloride Sodium chloride Potassium iodide Sodium bromide Potassium carbonate Potassium acetate Lithium bromide

NaCl (0.2 M/L concentration) NaCl (0.5 M/L concentration) K2SO4 KNO3 KCl NaCl KI NaBr K2CO3 CH3CO2K LiBr

to account for sample variability. Care was exercised during specimen placement such that they do not touch container walls to preclude the transfer of moisture for the condensate on the wall directly to tested samples. Containers containing tested specimens were stored in an insulated cooler during equilibration to minimize temperature fluctuations and its effect on the relative humidity. Temperature in the cooler was monitored using thermocouple connected to a data logger. Temperature variation was within ±0.5 °C. Samples’ equilibration time ranged from 20 to 35 days depending on the total suction applied. During the equilibration period, samples were weighed periodically to ensure that equilibrium has been attained. Samples were considered to reach equilibrium when the percentage difference between two consecutive sample weights does not exceed 0. 5 %. Sample weighing was performed as expeditiously as possible to minimize the absorption or adsorption of water to or from the samples. Furthermore, sample handling was performed using latex gloves to minimize soil water transfer due to hand contact. Weighing was performed using an electronic balance with a 0.0001 resolution. Final gravimetric water content (after equilibrium) was evaluated by oven drying samples at 105 °C. Volume measurements After equilibrium was attained under target suction, volume measurements on shale specimens were performed to determine volume change and void ratio corresponding to each suction level. Volume measurements technique was based on the principles of fluid displacement using kerosene (Mc Garry and Malafant 1987; Peron et al. 2006). Kerosene was used because of its immiscibility with water and non-polar characteristic resulting in filling pore air voids without altering shale specimens’ structure. Safety measures considered when performing the test included using latex gloves

Relative humidity (%) – – – 97.3 93.58 85.1 75.3 68.9 57.6 43.2 22.5 6.4

Total suction (kPa) 463 916 2,283 3,695 8,959 21,848 38,322 50,376 74,554 113,453 201,346 371,792

and eye glasses to avoid skin and eye contact as well as working in well ventilated rooms to avoid inhalation of vapors emitted. Furthermore, kerosene has a low flashpoint (between 38 and 65 °C); therefore, it was kept away from flame sources. All tests were performed at room temperature of 23 °C ± 2 where the density of kerosene (ρ k ) is 0. 79 g/cm3. Volume measurements were carried out in three stages. First stage involved submerging shale specimens in kerosene after weighing samples in the air (m1). The purpose of this stage was to saturate the air voids within the shale specimens. Initial trials revealed that saturation process took about 3–4 h. To expedite this stage and minimize air entrapment in the specimens, kerosene saturation was performed in a desiccator with vacuum applied in the headspace above the kerosene surface. This shortened the duration to about 1 h. Saturation was discontinued when air bubbles leaving the samples were not observed. In the second stage, kerosene-saturated specimens were then removed from the kerosene bath and excess kerosene on specimen surfaces were removed using blotted paper and then their mass in air was determined (m2). In the third stage, kerosene-saturated specimens were carefully re-submerged in a kerosene bath to avoid the entrapment of air bubbles and the submerged mass was recorded (m3). Samples were then oven dried at 105 °C to obtain the dry mass of the samples (m4). Based on the previous procedure, the total volume (V) and void ratio (e) were calculated using the following relationships: V ¼

ðm2  m3 Þ ρk

e¼

VV ¼ VS

ðm2 m1 Þ ρk ðm1 m3 Þ ρk

þ ðm1ρm4 Þ W

þ

ðm1 m4 Þ ρW

Arab J Geosci 22 Experimental Data- Al-Ghat Shale

20 Gravimetric water content (w, %)

Fig. 3 Total suction— gravimetric water content characteristic curves for expansive shale

Experimental Data - Tabuk Shale 18

Experimental data - Al-Qaliabah Shale

16

Fitted Curve

14 12 10 8 6 4 2

0 100.00

1,000.00

10,000.00

100,000.00

1,000,000.00

Suction (kPa)

Results and discussions Soil water characteristic curves Fitted curves for experimental data depicting the relationship between total suction and gravimetric water content are shown in Fig. 3. Details regarding fitting equations and techniques used are provided in the next section. According to Fig. 3, SWCCs showed a bimodal curve which signifies the presence of dual-structure micropores referred to as small and large micropore series. Visual examination of curves indicated that the large micropores are represented by the SWCC ranging from 400 to 20,000 kPa; while the small micropore control the SWCC ranging between 20,000 to 106 kPa. The SWCC transition segments between the small and large microporosity depicted different trends. A near horizontal transition segment was observed for Tabuk and Al-Qaliabah SWCCs signifying the presence of gaps in microporosity in shale specimens. A sloped transition segment as depicted in Al-Ghat SWCC indicates the presence of intermediate pore sizes. It is observed that the SWCCs for Tabuk and Al-Qaliabah shale show similar trends with gravimetric water contents in close proximity to each other which were different from that deduced for Al-Ghat shale. These observed trends of SWCCs postulates the impact of geological and environmental conditions on shale fabric formations. Visual examination of test specimens revealed the presence of cracks in shale specimens subjected to suctions

less than 2,000 kPa. These cracks vary in thickness from hairline to about 0.1 mm as shown in Fig. 4. These cracks were formed as a result of the expansive nature of shale specimens limiting the ability of shale to absorb water (Zhang and Fredlund 2004; Fredlund et al. 2010; Abbaszadeh et al. 2010). This is realized in the form of a plateau of constant gravimetric water content for suctions less than 2,000 kPa. Based on the previous observation, a threshold suction at which cracks will demonstrate appreciable impact on the SWCC can be defined. The threshold suction corresponds to the suction below which gravimetric water content show no appreciable change due to the presence of cracks. From Fig. 3, the threshold suctions for Al-Ghat and Tabuk shale are about 2,000 kPa; while the threshold suction for Al-Qaliabah shale was identified around 3,500 kPa. Finally, it should be noted that the limiting suction does not define the point of cracking initiation as it may occur somewhere along the transitional segment of the SWCCs. Curve fitting of bimodal SWCC Two approaches were adopted in this study to fit the experimental data of SWCC of expansive shales. The first approach involved fitting the bimodal SWCC using unimodal SWCCs functions as described by Burger and Shackelford (2001a, b). This involved partitioning the bimodal curves into two unimodal curves representing small and large micropore series (Fig. 3) and fit the data for each curve using Fredlund and Xing (1994) unimodal function.

Fig. 4 Cracks developed in shale specimens during SWCC determination (ψ=916 kPa)

Al-Ghat Shale

Tabuk Shale

Al-Qaliabah Shale

Arab J Geosci Table 3 Fitted parameters of Fredlund and Xing (1994) SWCC function Shale type

Al-Ghat Tabuk Qaliabah a

Small micropore SWCC af1, kPa

nf1

mf1

2,395 2,824 5,469

255 1.78 2.479

0.093 0.723 0.624

Large micropore SWCC ψb1, kPa

ψres1a, kPa

1,890 1,500 3,980

4,000 30,000 21,000

R2

af2, kPa

nf2

mf2

ψb2, kPa

ψres2a, kPa

R2

0.9953 0.9499 0.9930

89,879 124,177 77,689.4

5.672 428.31 3.89

0.604 0.2861 1.484

74,857 158,489 50,376

200,000 158,489 150,000

0.9955 0.9982 0.9911

Parameter value was obtained from the curve and not optimized in the regression analysis

In this approach, partitioning was performed by visually defining coordinates of the joining point (ψj, wj) between which the upper and lower SWCC segments. The Fredlund and Xing equations used in development of the fitted curves in terms of gravimetric water content are as follows: 3 8 2 > > > w > 4h  b1 nf 1 imf 1 5 y  yj > > > < ln expð1Þþ ay f1 2 3 wðy Þ ¼ > > > w > b2 nf 2 imf 2 5 y  y j > C ðy Þ4 h  > > : ln expð1Þþ y

The function proposed by Fredlund and Gitirana was rewritten in terms of gravimetric water content as follows: w¼

þ

wi ¼

af 2

  ln 1 þ yy res2  C ðy Þ ¼ 1   106 ln 1 þ y res2

Where w=gravimetric water content; y =suction; wb1 = water content corresponding to the air entry value of large micropores; wb2 =water content corresponding to the air entry value of small micropores, y res2 =suction corresponding to residual water content for small micropores; and af1, af2, nf1, nf2, mf1, mf2 =equation parameters. It should be noted that the correction factor C(ψ) proposed by Fredlund and Xing (1994) was originally introduced to force the fitted SWCC curve to a limiting point of coordinates (106, 0). In performing regression analysis for the large micropore SWCC, it was observed that including C(ψ) reduced the regression analysis accuracy; therefore, it was not included in the analysis. The second fitting approach involves using bimodal function developed by Fredlund and Gitirana (2004) which assumes the bimodal SWCC comprising of four hyperbolas.

w1  w2 w2  w3  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid1 þ 1 þ y y b1 y res1 1 þ y y res1 y b1 

w3  w4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid3 þ w4 1 þ y y b2 y res2 

    tan θi 1 þ ri2 ln yya

ð1 þ tan2 θi Þ ð1  ð1  ri2 tan2 θi Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 ð1  ri2 tan2 θi Þ  ri2 ln2 ðy =y ai Þ þ þ wai ð1 þ tan2 θi Þ i

ri2 tan2 θi Þ

þ ð1Þi 

where i=1, 2, 3, 4; w=gravimetric water content; θi =hyperbolas rotation angles=−(li-1 +li)/2; ri =aperture angles tangents=tan [(l  a  i-1

−l  i)/2]; li ¼

desaturation slopes ¼ arctan wi  waiþ1 ln y aiþ1 y ai ; wa1 ¼ ws ; wa2 ¼ wres1 ; wa3 ¼ wb2 ; wa4 ¼ wres2 ; wa5 ¼ 0 ; y a1 ¼ y b1 ; y a2 ¼ y res1 ; y a3 ¼ y b2 ; y a4 ¼ y res2 ; y a5 ¼ 106 ; dj =weight factor for w1, w2, w3, w and smooth curves ¼ 2 h 4.that produces . continuous i exp 1 ln y ajþ1 y aj , j=1, 2, 3. Non-linear, least square regression analysis for both procedures were performed using Microsoft Excel® spreadsheet and Solver (Brown 2001) to obtain best fit parameters of experimental data for all three expansive shale. Fitted curves of experimental data are shown in Fig. 3. Results of regression analysis including key features (i.e., air entry value and residual water content, and fitting parameters) for expansive shales are summarized in Tables 3 and 4. Based on the regression analyses performed in this study the following can be noted. From a mathematical point of

Table 4 Fitted parameters of Gitirana and Fredlund (2004) SWCC function Shale type

ψb1 (kPa)

wres1a (%)

ψres1a (kPa)

wb2a (%)

ψb2a (kPa)

wres2 (%)

ψres2 (kPa)

Al-Ghat Tabuk Qaliabah

2,099.3 958.22 3,571

11 2.44 4.03

4,000 40,000 20,000

6 2.46 4.03

65,000 75,000 55,000

1.45 0.375 0.261

201,000 200,083 199,996

a

Parameters value was obtained from the curve and not optimized in the regression analysis.

α

R2

0.011 0.15 0.32

0.9971 0.9719 0.9961

Arab J Geosci Fig. 5 Plot of variation of void ratio versus total soil suction for expansive shale samples

0.50 0.45

Al-Ghat Shale

0. 40

Tabuk Shale

Al-Qalaibah Shale

Void ratio

0.35

R² = 0.7489

0.30

0.25 R² = 0.318

0.20 0. 15 0.10

R² = 0.9262 0.05

0.00 2

2.5

3

3.5

4

4.5

5

5.5

6

Suction (log kPa)

view, the Fredlund and Xing function is easier to implement than the Gitirana and Fredlund function. From a statistical point of view, partitioning the bimodal curves into two curves reduces the number of data points (i.e., degree of freedom of the regression analysis) which, in turn, erodes reliability of regression analysis. Therefore, it is recommended to use the partitioning approach when there is enough data points to adequately perform the regression analysis Variation of void ratio with total suction Volume measurements were performed to evaluate the variation of void ratio (e) with suction. These measurements were performed on specimens subjected to suctions greater than 3,000 kPa. Shale specimens subjected to suction less than 3,000 kPa tended to be highly fissile; therefore no volume change measurements were performed. Based on these measurements, semilogarithmic plots depicting the relationships between void ratio (e) and suction for all expansive shale are shown in Fig. 5. From this figure, it was observed that there is a trend of decreasing void ratio with increase in suction which is a typical characteristic of expansive soils. Linear, least square regression analyses were performed to develop linear relationships for void ratio–suction data for all expansive shales as shown in Fig. 5. Different degrees of scatter were observed for void ratio–suction relationship which is attributed to the spatial variations in fabric and pore size distribution between specimens used in this study. Specifically, the spatial variability in specimen pore size distribution for Tabuk shale samples was higher than that for Al-Ghat and Al-Qaliabah shale samples. Another observation is that the values void ratios for Tabuk and Al-Qaliabah shale are in comparable range strengthening the premise that soils originating same geological formation may have similar microstructure.

Assessment of swelling characteristics of expansive shale The swelling potentials of expansive shales were assessed according to the classification methodology developed by Mckeen (1992). This methodology provides qualitative characterization of the swelling potential based on the slope of a straight line fitted through SWCC data points on linear plot with the x-axis representing the logarithmic of suction as illustrated in Fig. 6. This slope is termed the suction index and is defined as “Δψ/Δw”. Table 5 defines five categories as proposed by Mckeen for the classification of expansive soils based on suction index. Based on initial examination of the plots in Fig. 6, it is apparent that no one line can be fitted to all data points as assumed by Mckeen due to the bimodal nature of measured SWCCs. Nevertheless, SWCC data was segmented into two data sets representing the small (≤20,000 kPa) and large (>20,000 kPa) micropore series and a straight line was fitted through each series independently as shown in Fig. 6. This approach was used to assess the relative contribution of each level of microporosity to the swelling potential of expansive shale. For Al-Ghat shale, the computed suction index for the small micropore series was −17.06. According to Mckeen’s classification, this small micropore series have low contribution to swelling potential of shale. However, suction indices indicative of high swelling potential (−7.50) was observed for the large micorpores. On the other hand, Al-Qaliabah and Tabuk shales indicate that each micropore series have similar suction indices (ranging between −19.36 and −26.24) signifying equal contribution of levels of microporosity to swelling potential which is categorized as low. The aforementioned classifications of swelling potential are in close agreement with Chen (1988) classifications provided in Table 1.

Arab J Geosci Fig. 6 Computed suction index for expansive shale samples

6 y = -17.063x + 5.3323 R² = 0.97

5

y = -16.37x + 5.6829 R² = 0.9773

small micropore

Suction (log kPa)

4

3

y = -19.768x + 5.3745 R² = 0.9957 y = -26.236x + 5.1466 R² = 0.9873

y = -19.316x + 5.1845 R² = 0.9832

y = -7.5036x + 4.6408 R² = 0.7052

2 Al-Ghat Shale 1

large micropore

Tabuk Shale

Al-Qaliabah Shale 0 0.00

0.05

0.10

0.15

0.20

Gravimetric water content (g/g)

Summary and conclusions A laboratory program was devised to bridge the gap in knowledge regarding the soil water characteristic curves of expansive shale in Kingdom of Saudi Arabia; namely AlGhat, Tabuk, and Al-Qaliabah. Test results showed that SWCC for all expansive soil have a bimodal form which was attributed to presence of two pore size distribution level. In absence of data, the SWCCs presented herein can be used as a first estimate in studies related to ground surface flux and water infiltration modeling. Curve fitting analyses were performed using two techniques: (1) two unimodal Fredlund and Xing functions and (2) Gitirana and Fredlund bimodal SWCC function. Analyses revealed that both techniques provided a good fit to experimental data; however, the bimodal SWCC function was proven to be mathematically cumbersome. Furthermore, it was recommended, from a statistical point of view, that fitting using two unimodal functions require enough data points in order not to compromise the accuracy of the regression analysis. Furthermore, test results preliminary substantiates the premise that geological history and environmental conditions may have an impact on shale characteristics. Tabuk and Al-Qaliabah shale originating from the same geological formation show similar appearances of SWCC with close

Table 5 Mckeen’s expansive clay classification categories Category

Swell potential

Suction index “Δψ/Δw”a

I II III IV V

Very high High Moderate Low Non-expansive

Less than −6 −6 to −10 −10 to −13 −13 to −20 Greater than −20

a

Δψ=log kilopascal, Δw=gram per gram

range in gravimetric water content. Moreover, void ratios evaluated for both Tabuk and Al-Qaliabah shales were in close range. Additional testing will be further needed to statistically substantiate these findings. The swelling potentials of expansive shale were evaluated using Mckeen’s classification methodology and measured SWCCs. Modification to the original classification methodology was proposed to account for the bimodal nature of SWCCs. This proposed technique was considered beneficial in evaluating the contribution of the different microporosity to the swelling potential of expansive shale. Acknowledgments This paper is a part of a research project supported through NPST program by King Saud University, project no. 11BUI1901-02. The authors would like to thank the technicians and staff of Bugshan Research Chair in Expansive Soils for their help and support.

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