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Laboratory and field evaluation of modulus-suction-moisture relationship for a silty sand subgrade
Transportation Geotechnics 19 (2019) 126–134
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Laboratory and field evaluation of modulus-suction-moisture relationship for a silty sand subgrade
T
⁎
Rizki Maretia Novi Barusa, Apiniti Jotisankasaa, , Susit Chaiprakaikeowa, Auckpath Sawangsuriyab a b
Department of Civil Engineering, Kasetsart University, Jatujak, Bangkok 10900, Thailand Bureau of Road Research and Development, Department of Highways, Bangkok 10400, Thailand
A R T I C LE I N FO
A B S T R A C T
Keywords: Small-strain shear modulus Soil-water retention curve Suction Spectral analysis of surface waves (SASW) Free-free resonant frequency (FFR) Compacted silty sand
A change in soil modulus in response to suction-moisture variation after compaction plays a vital role on modulus-based compaction control during earthwork construction. This study investigated the small-strain modulus-suction-moisture relationship for a silty sand subgrade using the laboratory free-free resonant frequency (FFR) and the in-situ spectral analysis of surface waves (SASW) in a trial section of highway construction project in Thailand. The post-compaction soil water retention curves (SWRCs) at different compaction states were investigated over the entire range of suction. Relationships between the SWRC parameters, i.e., air-entry suction, water-entry suction, residual suction etc., and as-compacted dry density and water content were obtained using the multiple-linear regression analysis. Such relationships are useful for the prediction of postcompaction suction in the field. The variation of SASW and FFR shear moduli with the suction stress, inferred from SWRCs, was found to be linear. A modified model was proposed, considering the combined effect of void ratio and the suction stress on the shear modulus, represented as Parameter A which was found to decrease as suction increased. The inclusion of suction stress and void ratio within the model variables yields better accuracy of prediction as compared to those models that considered either only suction or water content.
Introduction Long-term performance of compacted earthfill is highly related to its suction-moisture regime which can significantly affect the corresponding mechanical responses, especially the stiffness and deformation characteristics. Stiffness measurements in pavement engineering can be performed based on a variety of techniques namely resilient modulus (MR) tests using cyclic triaxial apparatus, in-situ automated plate load test [1–3], and non-destructive tests of small-strain modulus such as falling weight deflectometer (FWD), portable falling weight deflectometer (PFWD), light weight deflectometer (LWD), soil stiffness gauge (GeoGauge), spectral analysis of surface waves (SASW), intelligent vibratory roller compactors, etc [4–8]. More commonly adopted in pavement design and analysis, the resilient modulus (MR) tests normally involve up to some hundred cycles of loading, typically in the strain range from 10−2 to 10−1% [1–3]. However, in-situ resilient modulus determination involved relatively complicated test setup and time-consuming to carry out in the field. In contrast, wave propagation methods used for determining smallstrain modulus of geomaterials in a much smaller strain range of less ⁎
than 10−3%, were mainly employed for construction quality control/ assurance of compacted earthwork [4–7]. In general, the tests can be performed instantly during the earthwork construction, resulting in an increasing number of inspection points and a better control of compaction uniformity as well as a comparison with the mechanistic design parameters on the basis of strain-dependent modulus degradation curve [9,10]. Nevertheless, a limitation of modulus-based compaction control is that the modulus can be affected by suction-moisture conditions [11–17]. It has been generally recognized that without a proper understanding of suction and dry density influence on modulus, the field modulus measurements could be misleading and thus the target modulus may not be achieved. The soil-water retention curve (SWRC), a.k.a. soil-water characteristic curve (SWCC), representing the relationship between soil water content and suction, is generally regarded as one of the important fundamental properties of unsaturated soils in practice [18,19]. The SWRC can be used, directly or indirectly, to estimate the suction stress which represents the contributions of capillarity and adsorption water force on mechanical response of unsaturated soils such as shear strength [20–25], and modulus [11–17]. The SWRC is fundamentally related to
Corresponding author. E-mail address: [email protected] (A. Jotisankasa).
https://doi.org/10.1016/j.trgeo.2019.03.005 Received 30 November 2018; Received in revised form 17 March 2019; Accepted 21 March 2019 Available online 22 March 2019 2214-3912/ © 2019 Published by Elsevier Ltd.
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pore-size distribution of the soil, which is in turn influenced by various factors, such as soil structure and fabric [26,27], stress level and stress history [28–34], initial moisture content, initial dry density and gradation [35–43], deformability of the soil [44–46] etc. A number of SWRCs for different soil types have been reported in the literature along with some predictive models [47–52]. However, the test procedure adopted in most studies involved initial saturation of the compacted soil sample before gradually increasing suction from zero to the desired values, which is a conventional approach in the soil science discipline. Such test procedure does not mimic the field compaction condition, where the soil is unsaturated in its initial as-compacted state. It is very likely that the field condition follows the first wetting or first drying paths from the as-compacted state. This paper therefore investigates the effects of as-compacted moisture content and density on SWRCs of a silty sand subgrade from a highway construction project in Thailand [53], following a first wetting path and a first drying path over the whole range of suction (zero to 1,000,000 kPa). The small-strain shear moduli of the material having different suctions were investigated in the laboratory and in the field using the free-free resonant frequency (FFR) and the spectral analysis of surface waves (SASW) tests respectively, in order to develop the modulus-suction-moisture relationship for the compacted subgrade. Results from this study were used to improve the prediction model for shear moduli over the entire range of suction.
Fig. 1. Grain size distribution curve.
Two kinds of laboratory tests, SWRC tests and FFR tests, were carried out on statically compacted samples. A series of SASW tests were also performed in-situ at a test section of compacted subgrade layer over a period of two days, during which the water content condition of the test field was varied by spraying water and leaving the compacted layer to air-dry. The modification of the water condition of the subgrade in the field tests was intended to simulate a possible change in postcompaction suction of the subgrade due to rain or evaporation which could happen during quality control modulus tests in practice. Fig. 2 shows some photos of experimental setups for laboratory and field tests. Table 2 shows the test conditions adopted in this study. The initial conditions of the specimens and trial section were also compared with the standard Proctor compaction curve in Fig. 3. Since the as-compaction conditions (dry unit weight and moisture content) of the SWRC samples encompassed nearly all range of conditions encountered in FFR and SASW tests. This indicated the SWRCs could be used for analysis of FFR and SASW results. There were some SASW test locations that showed a slightly higher density that those of SWRC samples which could contribute to scatters in results as will be presented in subsequent sections.
Material and methods Material The material used in this study was a silty sand subgrade taken from a trial section of the Motorway No. 7 construction project in Chonburi province, Eastern part of Thailand [53]. The basic properties of the silty sand is summarised in Table 1. Fig. 1 shows the particle size distribution curve. The material was a reddish residual soil typically found in tropical countries and was classified as SM according to the unified soil classification system (USCS) and A-2-6 according to the American Association of State Highway and Transportation Officials (AASHTO). Both field and laboratory compaction were done to achieve a dry density approximately equivalent to a standard Proctor compaction effort. A bag sample was taken from the construction site and statically compacted to form specimens used in all laboratory tests. The static compaction was done in a compression machine at rate of 2 mm/min and the volume-controlled technique was used to obtain specimens of various densities. Only the material passing sieve No.4 (4.75 mm) was used when preparing the specimens to avoid erroneous results due to large particles inclusion in SWRC and FFR tests. In the field, the subgrade layer of the test section was compacted in three layers of 200 mm maximum lift thickness using a vibratory roller and a pneumatic tire roller.
Test procedures Soil-water retention curve (SWRC) tests The SWRCs were determined using the miniature tensiometer [54,55] for matric suctions less than 100 kPa, the pressure plate for matric suctions between 200 and 1500 kPa, and the isopiestic technique (salt solution equilibrium) for total suctions greater than 1500 kPa. In each compaction condition shown in Table 2, two samples were used to obtain the two paths, wetting and drying, of SWRCs. The soil samples were about 62 mm in diameter and 20 mm high. For the tensiometer method, the equilibrated suction, the weight and dimensions of each specimen were measured to acquire each data point of the SWRC at each stage of wetting or drying. Wetting was done by spraying very fine water droplets directly on to the sample’s upper face. At the final stage of wetting, the sample was soaked for 4–5 days to obtain the water content at zero suction. Drying was done by exposing sample’s upper face to air until the sample had the desired mass. The equilibration of suction throughout the sample was checked by measuring the suctions at both upper and lower faces, ensuring they were the same. For the pressure plate technique, the sample in post-compaction condition was equilibrated with matric suction in the order of 200, 800, and 1500 kPa. Afterwards, the sample was equilibrated with total suction in the order of 14029, 23645, 39370, 365622 kPa, using isopiestic technique with saturated solutions of BaCl2, KCl, NaCl, and NaOH respectively. For each suction equilibration step, a minimum curing period (5 days for pressure plate and 7 days for isopiestic technique) was allowed for so that the sample’s weight was practically constant
Table 1 Basic properties of silty sand. Test Grain size distribution Gravel ≤ 75 mm, % Sand ≤ 4.75 mm, % Silt ≤ 75 μm, % Clay ≤ 2 μm , % Specific gravity, Gs Atterberg Limits Liquid limit, LL, % Plastic limit, PL, % Plasticity index, PI Standard Proctor compaction test Maximum dry unit weight, kN/m3 Optimum water content, %
Properties
13.2 66.4 10.4 10.0 2.68 24.4 13.1 11.3 20.7 8.6
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Fig. 2. Photos of experimental setups of laboratory and in-situ tests; (a) suction measurement using tensiometer; (b) suction control using pressure plate apparatus; (c) suction control using isopiestic technique; (d) free-free resonant frequency (FFR) test and (e) spectral analysis of surface waves (SASW) test.
one end to diminish seismic energy loss due to the resonance in the hammer itself. An accelerometer was attached horizontally at the other end of the specimen to measure the transmitted wave in time domain which was then Fourier-transformed into frequency domain using a spectrum analyzer. The resonant frequency was observed as the frequency of the highest peak amplitude in the Fourier spectra. The FFR tests were carried out on the same sample to measure the resonant frequencies at different water content conditions along the drying path. The total mass of the sample after the FFR test was measured and the water content was calculated to estimate the suction during FFR tests using SWRCs in subsequent analysis.
before proceeding to the next suction state. The suction equilibrium was considered to be reached, once there was no measurable change in soil mass (measured to the precision of 0.01 gm) over several days. Curing periods of 7, 10 and 14 days were also tried which indicated negligible change in water content of less than 0.01%/day after the 5th to 7th day. Free-free resonant frequency (FFR) tests Free-free resonant frequency (FFR) tests were performed, due to its simplicity and reliability [56], to measure low-strain resonant frequency, and hence shear wave velocity and shear modulus of the compacted specimens using Eq. (1) and Eq. (2) respectively, where G0 = small-strain shear modulus, vs = shear wave velocity, ρ = soil density, fn = resonant frequency and L = sample length
vs = 2fn L
(1)
G0 = ρvs2
(2)
Spectral analysis of surface waves (SASW) tests SASW is an in-situ, low-strain, non-destructive test invented by University of Texas at Austin and has been successfully used to investigate shear wave velocity and shear modulus of various geotechnical and pavement sites since 1980 s [57–61], while in Thailand the technique was performed to investigate material stiffness of several dams [62–65]. The method uses a dispersive characteristic of Rayleigh waves to acquire a shear wave velocity profile of the tested site. In this study, the SASW tests were conducted at five locations, with 25-meter spacing between each location, along a test section of the same subgrade material in Motorway number 7 over a period of two days, during
In this study, the size of the cylindrical specimens was 50 mm in diameter by 100 mm in height and the specimens were statically compacted in order to acquire the maximum dry density as summarised in Table 2. Shear motion was performed by perpendicularly tapping one end of the hanged specimen with an in-house developed small hammer. The hammer was made by a wooden stick with an attached weight at Table 2 Testing conditions. Test
Soil-water retention curve (SWRC) Free-free resonant frequency (FFR) Spectral analysis of surface waves (SASW)
Range of as-compacted conditions
Moisture conditions during tests *
Percentage compaction (standard Proctor), %
Water content , %
90%, 95%, 100% 100% 97–105%
OMC%, OMC-3%, OMC + 3% OMC% OMC-1% to OMC-3%
* OMC = optimum moisture content 128
As-compacted, drying and wetting As-compacted and drying As-compacted, wetting and drying
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Fig. 3. Standard Proctor compaction curve and initial conditions of test specimens (SWRC & FFR) and test section (SASW).
which the water content of the test field was intentionally modified to various conditions as explained earlier. The common receiver midpoint (CRMP) array was used as the test configuration and the receiver spacings of 0.2, 0.4 and 1 m were applied to measure the shear wave velocity of the entire road structure. A 0.3-kg small hammer and a sledge hammer were used as seismic sources examining shallow and deep profiles respectively, while two 4.5-Hz geophones were used as receivers. The phase information was collected from the field using a spectrum analyzer and post-processions, a generating of dispersion curves and an iterative forward modelling to generate shear wave velocity profile, were performed using the WinSASW program developed by Joh in 1996 [61]. Sand cone tests were also conducted at the same location in order to obtain the initial dry density and the water content. In subsequent moisture conditioning stages, only the water content measurements were made using oven-drying at the nearby location to SASW tests. Where possible, field tensiometers were used to monitor suction at the site for suction less than 100 kPa. For suction higher than 100 kPa, SWRC were used to estimate suction based on water content measurement.
Fig. 4. SWRCs for samples compacted at optimum moisture content (OMC) and various compaction levels (90%, 95% and 100%); (a) degree of saturationsuction, (b) gravimetric water content-suction.
which is more representative of the in-situ moisture condition during typical modulus-based compaction control. The hysteresis behaviour of SWRC was not examined in the current study as only monotonic suction change was considered. The relationship between gravimetric water content, w , and logψ (Fig. 4b) appeared to be independent of compaction levels for the suction range between 10 and 20,000 kPa for samples compacted at the same water content (i.e. at the optimum water content). The uniqueness of w -logψ relationship over a certain range of suction agrees with findings of previous studies [71–73]. Fig. 5 shows a similar bimodality of the SWRCs for the samples compacted at dry of optimum (OMC-3%) at 95% and 100% compaction levels and wet of optimum (OMC + 3%) at 95% compaction. Interestingly, the w -logψ relationship is not unique for samples compacted at different water contents. The wet-of-optimum (OMC + 3%) sample had a much higher SWRC plotted terms of gravimetric water content and less bimodality. This could be attributed to the difference in the macroand micro-structures of the soils [73]. It is noted that the degrees of saturation observed for suction values higher than 100 MPa ranged between 10% and 45% and the projected degrees of saturation at suction of 1,000 MPa did not reach zero value in some samples. According to Fredlund [74], a soil without osmotic suction would be of zero moisture content once its total suction reached the value of 1,000 MPa. As a corollary, non-zero moisture content at 1,000 MPa suction would suggest that osmotic suction component may exist due to the presence of solutes in soil pores. However, the osmotic suction would not contribute to any gains in terms of mechanical behaviour in engineering practice [18]. This observation will be supported by additional interpretation in Section ‘Modelling of shear modulus-suction-water content relationships’.
Results and discussions Soil-water retention curves (SWRC) Fig. 4 shows the SWRCs for the samples compacted at optimum moisture content at different compaction levels (90%, 95% and 100%) together with the as-compaction conditions. The bi-modality of SWRCs in degree of saturation versus log suction (Sr − logψ ) plot (Fig. 4a) is more evident for samples with a lower compaction level and expected to be associated with the open aggregate structure of the less dense soil [27,66–69]. It is noteworthy that as the SWRCs were obtained in the post compaction condition (not the post-soaked condition), the curves are a combination of scanning curve, main wetting curve and main drying curve which could also contribute to the bimodality of the curve [70]. It is speculated that the turning point of SWRCs at around 10,000 kPa is associated with the suction level where the scanning curve converged with the primary drying curve. The suction history followed in the SWRC tests represents only a monotonic suction change 129
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S = S ∗ × Smax S∗ =
(4)
S1 − S2 S2 − S3 S3 − S4 + + 1 + (ψ/ ψb1 ψres1 )d1 1 + (ψ/ ψres1 ψb2 )d2 1 + (ψ/ ψb2 ψres2 )d3 (5)
+ S4 where
Si =
×
tanθi (1 + ri2 )ln(ψ/ ψia) (1 − ri2 tan2θi )
+ (−1)i
a2 (1 − ri2 tan2θi ) (1 + tan2θi ) + Sia; ri2 ln2 (ψ/ ψia) + 2 2 (1 + tan2θi ) (1 − ri tan θi )
i = 1, 2, 3, 4 ; (λ +λ) θi = − i − 12 i = hyperbolas rotation angles; ri = tan [(λi − 1 − λi )/2] = aperture angles tangents; a
( )
ψ λ 0 = 0 ; λi = arctan ⎧ (Sia − Sia+ 1)/ ⎡ln ψi +a1 ⎤ ⎫= desaturation slopes; i ⎨ ⎣ ⎦⎬ ⎩ ⎭ S1a = 1; S2a = Sres1; S3a = Sb ; S4a = Sres2 ; S5a = 0 ; a a a a a ψ1 = ψb1; ψ2 = ψres1; ψ3 = ψb2 ; ψ4 = ψres2 ; ψ5 = 106 ;
dj = 2exp ⎡1/ln ⎛ ⎢ ⎝ ⎣
ψja+ 1
⎞ ⎤ = weight factor; and j = 1, 2, 3 ⎥ ⎠⎦
ψja
Table 3 summarizes the parameters used to construct the fitting curves in Figs. 4 and 5. In order to find the correlation between the SWRC shape and as-compacted dry unit weight (γd ) and water content (w, %) , multiple linear regression analyses were performed for each SWRC fitting parameter to obtain the relationships as follows;
a = 0.0734 − 0.0303
γd γw
ψb1 = −2.371 + 1.142 Fig. 5. SWRCs for samples compacted at wet of optimum (OMC + 3%) and dry of optimum (OMC-3%) at 95% and 100% compaction levels; (a) degree of saturation-suction, (b) gravimetric water content-suction.
+ 0.00245w
(R2 = 0.270)
+ 0.0768w
(R2 = 0.299)
γd γw
ψres1 = exp( −21.730 + 12.508
γd γw
(6a) (6b)
(R2 = 0.744)
− 0.0781w )
(6c) The bi-modal SWRC equations proposed by Gitirana and Fredlund [66] were used to construct the fitting curves in Figs. 4 and 5. Their model was chosen due to its major advantage in that the fitting parameters have clear physical meanings with independent properties. The degree of saturation, S , is a function of 10 parameters, 9 of which are the SWRC features and the other one is the suction, ψ .
S = f (ψb1, ψres1, Sres1, ψb2 , Sb, ψres2 , Sres2, a, Smax , ψ)
Sres1 = −0.680 + 0.411
γd γw
ψb2 = exp(20.237 − 5.281
Sb = −1.742 + 0.897
(3)
where ψb is the air-entry suction for drying path or water-entry suction for wetting path, ψres is the residual soil suction, Sres the residual degree of saturation, and a the sharpness of the transitions at bending points. The Subscripts 1 and 2 represent the two levels of soil structures. Sb is the degree of saturation at the air-entry of the second structure level. Smax is the maximum degree of saturation upon soaking the sample during wetting which can be less than 100%. Gitirana and Fredlund’s formulation uses four hyperbolas to model the bimodal feature of SWRC in log(ψ) − S coordinates. The degree of saturation is calculated as follows;
γd
(R2 = 0.670)
+ 0.0624w γd γw
(R2 = 0.417)
− 0.0127w )
ψres2 = exp( −24.023 + 17.739
γd γw
(6e)
(R2 = 0.850)
+ 0.0558w
γw
(6d)
+ 0.260w )
(6f)
(R2 = 0.705) (6g)
Sres2 = −0.190 + 0.146
Smax = 0.757 + 0.103
γd
+ 0.0004w
(R2 = 0.039)
+ 0.00193w
(R2 = 0.379)
γw
γd γw
;where γw is the water unit weight, and the term
(6h) (6i) γd γw
is unit-
Table 3 Curve fitting parameters for soil-water retention curves (SWRCs). Compaction condition
a
ψb1 (kPa)
ψres1 (kPa)
Sres1
ψb2 (kPa)
Sb
ψres2 (kPa)
Sres2
Smax
90% OMC 95% OMC 100% OMC 95% OMC-3 95% OMC+3 100% OMC-3
0.03 0.03 0.04 0.035 0.05 0.02
0.35 0.55 1 0.4 0.8 0.3
1.6 17 20 18 9 70
0.63 0.7 0.82 0.49 0.82 0.58
26,000 25,000 15,000 15,000 15,000 4,000
0.39 0.49 0.63 0.39 0.68 0.58
35,500 1,500,000 7,000,000 500,000 1,400,000 1,400,000
0.18 0.05 0.15 0.05 0.05 0.15
0.96 0.96 0.99 0.98 0.99 0.99
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independent. It can be seen the correlations linking compaction conditions with ψres1, Sres1, Sb , and ψres2 (Eq. (6c), (6d), (6f) and (6g)) were the more reliable ones (of R2 values between 0.670 and 0.850) and therefore these SWRC features were dependent on compaction conditions. However, correlations for other SWRC features, namely a , ψb1, ψb2 , Sres2 , and Smax (Eq. (6a), (6b), (6e), (6h), and (6i)) were less reliable (R2 ∼ 0.039 to 0.417), meaning that these SWRC features were less dependent on the compaction conditions. Based on Eqs. (4)–(6), the SWRC can be estimated from the routine field-based compaction control parameters (i.e. γd and w ), which can be used to estimate the suction or water content in a post-compaction state using either one of the two parameters. It is noted the variation in void ratios, e , with suction, ψ , during the SWRC tests were also determined but not presented here for brevity sake. All samples exhibited only a marginal volume change of less than 2% over the entire range of suction change, which was expected since the soil was of relatively low clay content. The variations e (ψ) and S (ψ) were used to find the trend lines for gravimetric water content (Fig. 4b and Fig. 5b) based on the following expression;
w=
S (ψ). e (ψ) Gs
Fig. 7. An example of resonant frequency acquired from FFR test.
(7)
The water contents during SWRC tests were predicted based on ascompacted properties (γd and w ) using the proposed relationships and compared with the measurements as shown in Fig. 6. A reasonable good agreement (R2 = 0.9437) was obtained with 95% confidence level corresponding to error range of ± 1.65%, indicating the satisfactory performance of the predictive model. This approach for predicting the SWRC based on the compaction conditions can be useful in practice, as knowledge of both suction and water content are important in characterizing the behaviour of unsaturated compacted soils [19–21].
Fig. 8. An example of shear wave velocity profile acquired from SASW test.
of shear modulus-suction-water content relationships’. Fifteen shear wave velocity profiles were acquired from SASW tests, three tests for each of five locations across the period of two days. The tests were used to investigate the soil modulus profile down to 1 m deep as shown in Fig. 8. However, only the shear wave velocities of the top 0.2 m were implemented in an establishment of modulus-suction correlation in Section ‘Modelling of shear modulus-suction-water content relationships’, because the soil moisture content was measured only at the top ground surface and it was the purpose of this study to investigate the upper part layer of pavement for quality control. The results indicate that the in-situ shear wave velocities ranged from 330 up to 510 m/s. The in-situ maximum shear moduli, determined using Eq. (2), ranged between 241 and 611 MPa. These numbers clearly suggest that the soil was well compacted at the site. The comparison between shear wave velocities from FFR and SASW are discussed in the following section.
Typical FFR and SASW test results Typical resonant frequency of the tested specimen was observed as the frequency of the highest peak amplitude in Fourier spectra as shown in Fig. 7. Four FFR tests were performed on identical samples having different soil moisture content, showing results in a range of resonant frequencies between 2178 and 3537 Hz, and therefore the shear wave velocity and shear modulus range between 436 and 707 m/s and 430–1059 MPa, respectively. The modulus noticeably increased with decreasing moisture content as will be discussed in Section ‘Modelling
Modelling of shear modulus-suction-water content relationships A number of semi-empirical models have been developed for describing modulus-suction-moisture relationships [11–17]. Most of the proposed models employed some forms of modified effective stresses or independent stress variables, taking into account the effects of net stress, suction, and degree of saturation. The influences of soil fabric, over-consolidation ratio, soil density, distribution of bulk water and menisci water, on modulus were considered in these models using some semi-empirical parameters. In this study, three modelling approaches were used to determine the relationships between unsaturated shear modulus, suction and water content/degree of saturation following Sawangsuriya et al. [11] due to their simplicity and practicality. Model 1 considers separately the influence of net stress and suction stress on the shear modulus, G0 , as in Eq. (8).
G0 = A × f (e )(σ0 − ua )n + CSr κψ
(8)
where f (e ) is the void ratio function proposed by Hardin [75], f (e ) = 1/(0.3 + 0.7e 2) ; A , n , C and κ are empirical parameters that can be determined experimentally. In this study, the tests involved only
Fig. 6. Comparison between predicted and measured moisture content. 131
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Fig. 10. Variation of A parameter with suction.
reached when the A parameter appeared constant thereafter. This trend can be expressed mathematically as follows;
marginal confining pressure, considering the waves travelling through the part of ground surface less than 0.20 m deep only in SASW test interpretation. Also in FFR tests, there was no net confining pressure. As a first approximate, the term Af (e )(σ0 − ua )n was assumed constant (D = Af (e )(σ0 − ua )n) and given the suction stress, σs = Sr κψ , (κ = 1) Lu & Likos [21], Eq. (8) can be rewritten as follows; (9)
Model 1 therefore simplifies to a linear relationship between the shear modulus and suction stress. As shown in Fig. 9, a reasonable goodness of fit was obtained for both G0 − ψ plot (R2 = 0.603) and G0 − σs plot (R2 = 0.612), and the values ofD and C in Eq. (9) based on curve fitting in Fig. 9b are 424.78 MPa and 6.1153 respectively. It should be noted that the linear equation appears curved in a semilogarithmic plot. The scatter in the results especially for the SASW data was expected since any variation in void ratio in the field and its influence on modulus were not directly taken into account in Eq. (9). It is also noteworthy that since the FFR tests were performed in the laboratory, while the SASW tests were carried out in the field, any discrepancy between the results could be due to the fundamental different conditions of the two tests, such as in-situ material variability, difference in state of compaction, presence of large grains in the field, soil structure, and different hydration rates in the lab and in-situ. Alternatively, Model 2 lumps together the influences of void ratio, net stress and the suction stress on the shear modulus as in Eq. (10);
G0 = A × f (e )[(σ0 − ua) + Sr κψ]n
(12a)
A = Amin ; forψ ≥ 20, 000kPa
(12b)
where A1 is the A parameter when suction equals 1 kPa, β represents the rate at which A parameter decreases with suction and Amin is the minimum value of A as suction exceeds 20,000 kPa. From the regression analysis, A1 = 115.5, β = 0.232 and Amin = 11.26. The parameter A represented the degree at which the function g (e , ψ, Sr ) contributed to the shear modulus, thus related to the fabric, distribution of bulk water, menisci water and adsorbed water. As shown in Fig. 10, an increase in suction gave rise to a reduction in Parameter A for suction below 20,000 kPa. A lower value of A indicates that there was a lesser contribution of the effective stress to the modulus as suction increased. The suction threshold of about 20,000 kPa would represent the range of suction where the menisci water started to disappear from the particle contacts, and surface adsorption water played a more significant role. Beyond this suction threshold, the Parameter A appeared to be constant. At such high suction, the water was in tightly adsorbed film regime, and it was the total suction, or total water potential, which was measured. In addition, the osmotic suction component, which may also be present, could also be contributing to the total potential, yet not providing any increase in modulus. This observation was in line with a few studies [71,76] which also investigated soil behaviour in a very high suction range. In contrast with Models 1 and 2, which incorporate suction and suction stress in the variables, an empirical relationship between shear modulus and water content, called Model 3 in this study, is also plotted as shown in Fig. 11 together with a 2nd order polynomial curve fitting. It is noted Model 3 can be more easily adopted in practice, since it does
Fig. 9. Go variations with (a) suction and (b) suction stress.
G0 = D + Cσs
A = A1 × ψ−β ; forψ < 20, 000kPa
(10)
In this model, assuming that(σ0 − ua)~0 , and introducing the function g (e , ψ, Sr ) = f (e )[Sr κψ]n , Eq (10) can be rewritten as follows;
G0 = A × g (e , ψ, Sr )
(11)
The A parameter was then determined by substituting the tested values of G0 and g (e , ψ, Sr ) in Eq. (11) at different suctions, as plotted in Fig. 10. The parameters, κ and n used were 1 and 0.2 according to Sawangsuriya et al. [11]. Interestingly, the obtained A parameter appeared to decrease non-linearly with logψ which could be described using a Power law, until a threshold of suction of about 20,000 kPa was
Fig. 11. Go variation with water content. 132
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(suction stress, void ratio), gave the most satisfactory curve fitting and the smallest standard error, as compared to Model 1, G0 = f (suction stress), and Model 3, G0 = f (water content). Model 2 lumped the effects of void ratio and suction stress together, using Parameter A. Parameter A decreased with suction according to a Power law until a threshold of 20,000 kPa suction was reached when it remained constant thereafter. The model can be used in practice to estimate the effects of post-compaction monotonic change in suction/moisture on the small strain shear modulus. Acknowledgements The first author is grateful to the scholarship provided by the Department of Civil Engineering and Faculty of Engineering, Kasetsart University. This research was also supported by Department of Highways, Ministry of Transports. Valuable assistance provided by the students and staffs at Geotechnical Division of Department of Civil Engineering, Soil Physics Laboratory of Department of Soil Science, Kasetsart University, and Department of Highways is gratefully acknowledged. Fig. 12. Comparison between predicted and measured small-strain shear modulus.
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.trgeo.2019.03.005.
not involve suction measurement which is much more difficult to conduct than water content test. However, the curve fitting parameters of Model 3 are purely empirical, depending on many factors such as soil types, plasticity, compaction level, etc, and thus their generalization to other materials and conditions would be less reliable. Fig. 12 compares the measured small-strain shear modulus and the predicted values from Models 1, 2 and 3, together with the 95% confidence levels. It is evident that Model 2 (R2 = 0.750) which considers the dependency of the parameter A with suction, gives a more satisfactory agreement with the measurement than Model 1 (R2 = 0.612) and Model 3 (R2 = 0.718). The standard error for G0 prediction using Model 2 was 79.5 MPa while that for Models 1 and 3 were 94.3 MPa and106 MPa respectively. It is noteworthy that as most previous studies involved a much lower range of suction in their tests than the current study, they understandably indicated A -parameters being independent on suction. The inclusion of suction stress and void ratio within model variable gives some improvement in accuracy of model prediction.
References [1] Sawangsuriya A, Edil TB, Benson CH. Effect of suction on resilient modulus of compacted fine-grained subgrade soils. Transportation Research Record 2101, TRB, National Research Council, Washington, D.C. 2009. p. 82–7. [2] Ng CWW, Zhou C, Yuan Q, Xu J. Resilient modulus of unsaturated subgrade soil: experimental and theoretical investigations. Can Geotech J 2013;50(2):223–32. https://doi.org/10.1139/cgj-2012-0052. [3] White DJ, Vennapusa PKR. In situ resilient modulus for geogrid-stabilized aggregate layer: a case study using automated plate load testing. Transp Geotech 2017;11:120–32. https://doi.org/10.1016/j.trgeo.2017.06.001. [4] Stokoe KH, Santamarina J. Seismic-wave-based testing in geotechnical engineering. GeoEng. 2000:1490–536. [5] Rathje EM, Wright SG, Stokoe KH, Adams A, Tobin R, Salem M. Evaluation of NonNuclear Methods for Compaction Control. Report No. FHWA/TX-06/0-4835-1. Texas Department of Transportation and the Federal Highway Administration. 2006. [6] Heitor A, Indraratna B, Rujikiatkamjorn C. Use of the Soil Modulus for Compaction Control of Compacted Soils. Singapore: Research Publishing; 2012. p. 1083–8. [7] Sawangsuriya A. Wave propagation methods for determining stiffness of geomaterials. In: Giovine Pasquale, editor. Wave Processes in Classical and New Solids. InTech; 2012. p. 157–200 Chapter 7. [8] Cacciola DV, Meehan CL, Baker WJ, Tehrani FS. A comparison of continuous compaction control measurements with localized in situ test results. Geotechnical Special Publication; 2018. p. 64–74. https://doi.org/10.1061/9780784481585.007. 2018-March (GSP 295). [9] Davich P, Labuz J, Guzina B, Drescher A. Small strain and resilient modulus testing of granular soils. Minnesota Department of Transportation; 2004. Final Report No. 2004-39. [10] Edil TB, Sawangsuriya A. Use of stiffness and strength for earthwork quality evaluation. ASCE, Geotechnical Special Publication. 149. 2006. p. 80–7. [11] Sawangsuriya A, Edil TB, Bosscher PJ. Modulus-suction-moisture relationship for compacted soils in post compaction state. J Geotech Geoenviron Eng 2009;135. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000108. [12] Tatsuoka F, Gomes Correia A. Importance of controlling the degree of saturation in soil compaction linked to soil structure design. Transp Geotech 2018. https://doi. org/10.1016/j.trgeo.2018.06.004. [13] Dong Y, Lu N, McCartney JS. Scaling shear modulus from small to finite strain for unsaturated soils. J Geotech Geoenviron Eng 2018;144(2). https://doi.org/10. 1061/(ASCE)GT.1943-5606.0001819. [14] Heitor A, Indraratna B, Rujikiatkamjorn C. The role of compaction energy on the small strain properties of a compacted silty sand subjected to drying–wetting cycles. Geotechnique 2015;65(9):717–27. https://doi.org/10.1680/geot.14.P.053. [15] Han Z, Vanapalli SK. State-of-the-art: prediction of resilient modulus of unsaturated subgrade soils. Int J Geomech 2016;16(4). https://doi.org/10.1061/(ASCE)GM. 1943-5622.0000631. [16] Yao Y, Zheng J, Zhang J, Peng J, Li J. Model for predicting resilient modulus of unsaturated subgrade soils in south China. KSCE J Civ Eng 2018;22(6):2089–98. https://doi.org/10.1007/s12205-018-1703-1. [17] Mancuso C, Vassallo R, d’Onofrio A. Small strain behavior of a silty sand in controlled-suction resonant column – torsional shear tests. Can Geotech J 2002;39(1):22–31. https://doi.org/10.1139/t01-076. [18] Fredlund DG. Unsaturated soil mechanics in engineering practice. J Geotech Geoenviron Eng 2006;132(3):286–321. https://doi.org/10.1061/(ASCE)1090-
Conclusion Understanding of how small-strain modulus of soil changes with suction and moisture variation after compaction is of great importance for accurate modulus-based compaction control. The small-strain modulus-suction-moisture relationship for a silty sand subgrade was studied using free-free resonant frequency (FFR) tests and in-situ spectral analysis of surface waves (SASW) tests in a trial section of a Motorway project in Thailand. The following conclusions can be drawn.
• The
• •
post-compaction soil water retention curves (SWRCs) were found to be influenced by as-compacted dry densities and water contents. The SWRC features (e.g. water-entry suction, residual soil suction, etc.) were correlated with as-compacted dry density and water content, using multiple-linear regression analysis. These correlations were used for estimating post-compaction suctions of subgrade material in-situ. The relationship between gravimetric water content and suction appeared to be independent of compaction levels for the suction range between 10 and 20,000 kPa only for samples compacted at the same water content. The relationship was not unique for samples compacted at different water contents. Of all three predictive models used in this study, Model 2, G0 = f
133
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Experimental study on stress-dependent soil water characteristic curve of a recompacted expansive soil. Appl Mech Mater 2013:256–9. https://doi.org/10.4028/www.scientific.net/AMM.256-259.283. [33] Lynch K, Sivakumar V, Tripathy S, Hughes D. Development of a laboratory technique for obtaining soil water retention curves under external loading in conjunction with high capacity tensiometers. Géotechnique 2018. https://doi.org/10. 1680/jgeot.17.P.176. [34] Rostami A, Habibagahi G, Ajdari M, Nikooee E. Pore network investigation on hysteresis phenomena and influence of stress state on the SWRC. Int J Geomech 2015;15(5). https://doi.org/10.1061/(ASCE)GM.1943-5622.0000315. [35] Zhou W, Yuen K, Tan F. Estimation of soil-water characteristic curve and relative permeability for granular soils with different initial dry densities. Eng Geol 2014;179:1–9. https://doi.org/10.1016/j.enggeo.2014.06.013. [36] Mirzaii A, Yasrobi SS. Influence of initial dry density on soil-water characteristics of two compacted soils. Geotechnique Lett 2012;2:193–8. https://doi.org/10.1680/ geolett.12.00045. [37] Gallage CPK, Uchimura T. Effects of dry density and grain size distribution on soilwater characteristic curves of sandy soils. Soils Found 2010;50(1):161–72. https:// doi.org/10.3208/sandf.50.161. [38] Chen Y, Uchimura T. Soil-water characteristic curve for unsaturated soil at different dry densities Zhongnan Daxue Xuebao (Ziran Kexue Ban)/. J Central South Univ (Sci Technol) 2017;48(3):813–9. https://doi.org/10.11817/j.issn.1672-7207.2017. 03.032. [39] Hezmi MA, Saari R, Zahari MZ, Abdullah RA, Yunus NZM, Rashid ASA. Soil water characteristic curves of compacted kaolin for various initial moisture content. Jurnal Teknologi. 2015;76(2):39–44. https://doi.org/10.11113/jt.v76.5431. [40] Iyer K, Jayanth S, Gurnani S, Singh DN. Influence of initial water content and specimen thickness on the SWCC of fine-grained soils. 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Laboratory and field evaluation of modulus-suction-moisture relationship for a silty sand subgrade
T
⁎
Rizki Maretia Novi Barusa, Apiniti Jotisankasaa, , Susit Chaiprakaikeowa, Auckpath Sawangsuriyab a b
Department of Civil Engineering, Kasetsart University, Jatujak, Bangkok 10900, Thailand Bureau of Road Research and Development, Department of Highways, Bangkok 10400, Thailand
A R T I C LE I N FO
A B S T R A C T
Keywords: Small-strain shear modulus Soil-water retention curve Suction Spectral analysis of surface waves (SASW) Free-free resonant frequency (FFR) Compacted silty sand
A change in soil modulus in response to suction-moisture variation after compaction plays a vital role on modulus-based compaction control during earthwork construction. This study investigated the small-strain modulus-suction-moisture relationship for a silty sand subgrade using the laboratory free-free resonant frequency (FFR) and the in-situ spectral analysis of surface waves (SASW) in a trial section of highway construction project in Thailand. The post-compaction soil water retention curves (SWRCs) at different compaction states were investigated over the entire range of suction. Relationships between the SWRC parameters, i.e., air-entry suction, water-entry suction, residual suction etc., and as-compacted dry density and water content were obtained using the multiple-linear regression analysis. Such relationships are useful for the prediction of postcompaction suction in the field. The variation of SASW and FFR shear moduli with the suction stress, inferred from SWRCs, was found to be linear. A modified model was proposed, considering the combined effect of void ratio and the suction stress on the shear modulus, represented as Parameter A which was found to decrease as suction increased. The inclusion of suction stress and void ratio within the model variables yields better accuracy of prediction as compared to those models that considered either only suction or water content.
Introduction Long-term performance of compacted earthfill is highly related to its suction-moisture regime which can significantly affect the corresponding mechanical responses, especially the stiffness and deformation characteristics. Stiffness measurements in pavement engineering can be performed based on a variety of techniques namely resilient modulus (MR) tests using cyclic triaxial apparatus, in-situ automated plate load test [1–3], and non-destructive tests of small-strain modulus such as falling weight deflectometer (FWD), portable falling weight deflectometer (PFWD), light weight deflectometer (LWD), soil stiffness gauge (GeoGauge), spectral analysis of surface waves (SASW), intelligent vibratory roller compactors, etc [4–8]. More commonly adopted in pavement design and analysis, the resilient modulus (MR) tests normally involve up to some hundred cycles of loading, typically in the strain range from 10−2 to 10−1% [1–3]. However, in-situ resilient modulus determination involved relatively complicated test setup and time-consuming to carry out in the field. In contrast, wave propagation methods used for determining smallstrain modulus of geomaterials in a much smaller strain range of less ⁎
than 10−3%, were mainly employed for construction quality control/ assurance of compacted earthwork [4–7]. In general, the tests can be performed instantly during the earthwork construction, resulting in an increasing number of inspection points and a better control of compaction uniformity as well as a comparison with the mechanistic design parameters on the basis of strain-dependent modulus degradation curve [9,10]. Nevertheless, a limitation of modulus-based compaction control is that the modulus can be affected by suction-moisture conditions [11–17]. It has been generally recognized that without a proper understanding of suction and dry density influence on modulus, the field modulus measurements could be misleading and thus the target modulus may not be achieved. The soil-water retention curve (SWRC), a.k.a. soil-water characteristic curve (SWCC), representing the relationship between soil water content and suction, is generally regarded as one of the important fundamental properties of unsaturated soils in practice [18,19]. The SWRC can be used, directly or indirectly, to estimate the suction stress which represents the contributions of capillarity and adsorption water force on mechanical response of unsaturated soils such as shear strength [20–25], and modulus [11–17]. The SWRC is fundamentally related to
Corresponding author. E-mail address: [email protected] (A. Jotisankasa).
https://doi.org/10.1016/j.trgeo.2019.03.005 Received 30 November 2018; Received in revised form 17 March 2019; Accepted 21 March 2019 Available online 22 March 2019 2214-3912/ © 2019 Published by Elsevier Ltd.
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pore-size distribution of the soil, which is in turn influenced by various factors, such as soil structure and fabric [26,27], stress level and stress history [28–34], initial moisture content, initial dry density and gradation [35–43], deformability of the soil [44–46] etc. A number of SWRCs for different soil types have been reported in the literature along with some predictive models [47–52]. However, the test procedure adopted in most studies involved initial saturation of the compacted soil sample before gradually increasing suction from zero to the desired values, which is a conventional approach in the soil science discipline. Such test procedure does not mimic the field compaction condition, where the soil is unsaturated in its initial as-compacted state. It is very likely that the field condition follows the first wetting or first drying paths from the as-compacted state. This paper therefore investigates the effects of as-compacted moisture content and density on SWRCs of a silty sand subgrade from a highway construction project in Thailand [53], following a first wetting path and a first drying path over the whole range of suction (zero to 1,000,000 kPa). The small-strain shear moduli of the material having different suctions were investigated in the laboratory and in the field using the free-free resonant frequency (FFR) and the spectral analysis of surface waves (SASW) tests respectively, in order to develop the modulus-suction-moisture relationship for the compacted subgrade. Results from this study were used to improve the prediction model for shear moduli over the entire range of suction.
Fig. 1. Grain size distribution curve.
Two kinds of laboratory tests, SWRC tests and FFR tests, were carried out on statically compacted samples. A series of SASW tests were also performed in-situ at a test section of compacted subgrade layer over a period of two days, during which the water content condition of the test field was varied by spraying water and leaving the compacted layer to air-dry. The modification of the water condition of the subgrade in the field tests was intended to simulate a possible change in postcompaction suction of the subgrade due to rain or evaporation which could happen during quality control modulus tests in practice. Fig. 2 shows some photos of experimental setups for laboratory and field tests. Table 2 shows the test conditions adopted in this study. The initial conditions of the specimens and trial section were also compared with the standard Proctor compaction curve in Fig. 3. Since the as-compaction conditions (dry unit weight and moisture content) of the SWRC samples encompassed nearly all range of conditions encountered in FFR and SASW tests. This indicated the SWRCs could be used for analysis of FFR and SASW results. There were some SASW test locations that showed a slightly higher density that those of SWRC samples which could contribute to scatters in results as will be presented in subsequent sections.
Material and methods Material The material used in this study was a silty sand subgrade taken from a trial section of the Motorway No. 7 construction project in Chonburi province, Eastern part of Thailand [53]. The basic properties of the silty sand is summarised in Table 1. Fig. 1 shows the particle size distribution curve. The material was a reddish residual soil typically found in tropical countries and was classified as SM according to the unified soil classification system (USCS) and A-2-6 according to the American Association of State Highway and Transportation Officials (AASHTO). Both field and laboratory compaction were done to achieve a dry density approximately equivalent to a standard Proctor compaction effort. A bag sample was taken from the construction site and statically compacted to form specimens used in all laboratory tests. The static compaction was done in a compression machine at rate of 2 mm/min and the volume-controlled technique was used to obtain specimens of various densities. Only the material passing sieve No.4 (4.75 mm) was used when preparing the specimens to avoid erroneous results due to large particles inclusion in SWRC and FFR tests. In the field, the subgrade layer of the test section was compacted in three layers of 200 mm maximum lift thickness using a vibratory roller and a pneumatic tire roller.
Test procedures Soil-water retention curve (SWRC) tests The SWRCs were determined using the miniature tensiometer [54,55] for matric suctions less than 100 kPa, the pressure plate for matric suctions between 200 and 1500 kPa, and the isopiestic technique (salt solution equilibrium) for total suctions greater than 1500 kPa. In each compaction condition shown in Table 2, two samples were used to obtain the two paths, wetting and drying, of SWRCs. The soil samples were about 62 mm in diameter and 20 mm high. For the tensiometer method, the equilibrated suction, the weight and dimensions of each specimen were measured to acquire each data point of the SWRC at each stage of wetting or drying. Wetting was done by spraying very fine water droplets directly on to the sample’s upper face. At the final stage of wetting, the sample was soaked for 4–5 days to obtain the water content at zero suction. Drying was done by exposing sample’s upper face to air until the sample had the desired mass. The equilibration of suction throughout the sample was checked by measuring the suctions at both upper and lower faces, ensuring they were the same. For the pressure plate technique, the sample in post-compaction condition was equilibrated with matric suction in the order of 200, 800, and 1500 kPa. Afterwards, the sample was equilibrated with total suction in the order of 14029, 23645, 39370, 365622 kPa, using isopiestic technique with saturated solutions of BaCl2, KCl, NaCl, and NaOH respectively. For each suction equilibration step, a minimum curing period (5 days for pressure plate and 7 days for isopiestic technique) was allowed for so that the sample’s weight was practically constant
Table 1 Basic properties of silty sand. Test Grain size distribution Gravel ≤ 75 mm, % Sand ≤ 4.75 mm, % Silt ≤ 75 μm, % Clay ≤ 2 μm , % Specific gravity, Gs Atterberg Limits Liquid limit, LL, % Plastic limit, PL, % Plasticity index, PI Standard Proctor compaction test Maximum dry unit weight, kN/m3 Optimum water content, %
Properties
13.2 66.4 10.4 10.0 2.68 24.4 13.1 11.3 20.7 8.6
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Fig. 2. Photos of experimental setups of laboratory and in-situ tests; (a) suction measurement using tensiometer; (b) suction control using pressure plate apparatus; (c) suction control using isopiestic technique; (d) free-free resonant frequency (FFR) test and (e) spectral analysis of surface waves (SASW) test.
one end to diminish seismic energy loss due to the resonance in the hammer itself. An accelerometer was attached horizontally at the other end of the specimen to measure the transmitted wave in time domain which was then Fourier-transformed into frequency domain using a spectrum analyzer. The resonant frequency was observed as the frequency of the highest peak amplitude in the Fourier spectra. The FFR tests were carried out on the same sample to measure the resonant frequencies at different water content conditions along the drying path. The total mass of the sample after the FFR test was measured and the water content was calculated to estimate the suction during FFR tests using SWRCs in subsequent analysis.
before proceeding to the next suction state. The suction equilibrium was considered to be reached, once there was no measurable change in soil mass (measured to the precision of 0.01 gm) over several days. Curing periods of 7, 10 and 14 days were also tried which indicated negligible change in water content of less than 0.01%/day after the 5th to 7th day. Free-free resonant frequency (FFR) tests Free-free resonant frequency (FFR) tests were performed, due to its simplicity and reliability [56], to measure low-strain resonant frequency, and hence shear wave velocity and shear modulus of the compacted specimens using Eq. (1) and Eq. (2) respectively, where G0 = small-strain shear modulus, vs = shear wave velocity, ρ = soil density, fn = resonant frequency and L = sample length
vs = 2fn L
(1)
G0 = ρvs2
(2)
Spectral analysis of surface waves (SASW) tests SASW is an in-situ, low-strain, non-destructive test invented by University of Texas at Austin and has been successfully used to investigate shear wave velocity and shear modulus of various geotechnical and pavement sites since 1980 s [57–61], while in Thailand the technique was performed to investigate material stiffness of several dams [62–65]. The method uses a dispersive characteristic of Rayleigh waves to acquire a shear wave velocity profile of the tested site. In this study, the SASW tests were conducted at five locations, with 25-meter spacing between each location, along a test section of the same subgrade material in Motorway number 7 over a period of two days, during
In this study, the size of the cylindrical specimens was 50 mm in diameter by 100 mm in height and the specimens were statically compacted in order to acquire the maximum dry density as summarised in Table 2. Shear motion was performed by perpendicularly tapping one end of the hanged specimen with an in-house developed small hammer. The hammer was made by a wooden stick with an attached weight at Table 2 Testing conditions. Test
Soil-water retention curve (SWRC) Free-free resonant frequency (FFR) Spectral analysis of surface waves (SASW)
Range of as-compacted conditions
Moisture conditions during tests *
Percentage compaction (standard Proctor), %
Water content , %
90%, 95%, 100% 100% 97–105%
OMC%, OMC-3%, OMC + 3% OMC% OMC-1% to OMC-3%
* OMC = optimum moisture content 128
As-compacted, drying and wetting As-compacted and drying As-compacted, wetting and drying
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Fig. 3. Standard Proctor compaction curve and initial conditions of test specimens (SWRC & FFR) and test section (SASW).
which the water content of the test field was intentionally modified to various conditions as explained earlier. The common receiver midpoint (CRMP) array was used as the test configuration and the receiver spacings of 0.2, 0.4 and 1 m were applied to measure the shear wave velocity of the entire road structure. A 0.3-kg small hammer and a sledge hammer were used as seismic sources examining shallow and deep profiles respectively, while two 4.5-Hz geophones were used as receivers. The phase information was collected from the field using a spectrum analyzer and post-processions, a generating of dispersion curves and an iterative forward modelling to generate shear wave velocity profile, were performed using the WinSASW program developed by Joh in 1996 [61]. Sand cone tests were also conducted at the same location in order to obtain the initial dry density and the water content. In subsequent moisture conditioning stages, only the water content measurements were made using oven-drying at the nearby location to SASW tests. Where possible, field tensiometers were used to monitor suction at the site for suction less than 100 kPa. For suction higher than 100 kPa, SWRC were used to estimate suction based on water content measurement.
Fig. 4. SWRCs for samples compacted at optimum moisture content (OMC) and various compaction levels (90%, 95% and 100%); (a) degree of saturationsuction, (b) gravimetric water content-suction.
which is more representative of the in-situ moisture condition during typical modulus-based compaction control. The hysteresis behaviour of SWRC was not examined in the current study as only monotonic suction change was considered. The relationship between gravimetric water content, w , and logψ (Fig. 4b) appeared to be independent of compaction levels for the suction range between 10 and 20,000 kPa for samples compacted at the same water content (i.e. at the optimum water content). The uniqueness of w -logψ relationship over a certain range of suction agrees with findings of previous studies [71–73]. Fig. 5 shows a similar bimodality of the SWRCs for the samples compacted at dry of optimum (OMC-3%) at 95% and 100% compaction levels and wet of optimum (OMC + 3%) at 95% compaction. Interestingly, the w -logψ relationship is not unique for samples compacted at different water contents. The wet-of-optimum (OMC + 3%) sample had a much higher SWRC plotted terms of gravimetric water content and less bimodality. This could be attributed to the difference in the macroand micro-structures of the soils [73]. It is noted that the degrees of saturation observed for suction values higher than 100 MPa ranged between 10% and 45% and the projected degrees of saturation at suction of 1,000 MPa did not reach zero value in some samples. According to Fredlund [74], a soil without osmotic suction would be of zero moisture content once its total suction reached the value of 1,000 MPa. As a corollary, non-zero moisture content at 1,000 MPa suction would suggest that osmotic suction component may exist due to the presence of solutes in soil pores. However, the osmotic suction would not contribute to any gains in terms of mechanical behaviour in engineering practice [18]. This observation will be supported by additional interpretation in Section ‘Modelling of shear modulus-suction-water content relationships’.
Results and discussions Soil-water retention curves (SWRC) Fig. 4 shows the SWRCs for the samples compacted at optimum moisture content at different compaction levels (90%, 95% and 100%) together with the as-compaction conditions. The bi-modality of SWRCs in degree of saturation versus log suction (Sr − logψ ) plot (Fig. 4a) is more evident for samples with a lower compaction level and expected to be associated with the open aggregate structure of the less dense soil [27,66–69]. It is noteworthy that as the SWRCs were obtained in the post compaction condition (not the post-soaked condition), the curves are a combination of scanning curve, main wetting curve and main drying curve which could also contribute to the bimodality of the curve [70]. It is speculated that the turning point of SWRCs at around 10,000 kPa is associated with the suction level where the scanning curve converged with the primary drying curve. The suction history followed in the SWRC tests represents only a monotonic suction change 129
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S = S ∗ × Smax S∗ =
(4)
S1 − S2 S2 − S3 S3 − S4 + + 1 + (ψ/ ψb1 ψres1 )d1 1 + (ψ/ ψres1 ψb2 )d2 1 + (ψ/ ψb2 ψres2 )d3 (5)
+ S4 where
Si =
×
tanθi (1 + ri2 )ln(ψ/ ψia) (1 − ri2 tan2θi )
+ (−1)i
a2 (1 − ri2 tan2θi ) (1 + tan2θi ) + Sia; ri2 ln2 (ψ/ ψia) + 2 2 (1 + tan2θi ) (1 − ri tan θi )
i = 1, 2, 3, 4 ; (λ +λ) θi = − i − 12 i = hyperbolas rotation angles; ri = tan [(λi − 1 − λi )/2] = aperture angles tangents; a
( )
ψ λ 0 = 0 ; λi = arctan ⎧ (Sia − Sia+ 1)/ ⎡ln ψi +a1 ⎤ ⎫= desaturation slopes; i ⎨ ⎣ ⎦⎬ ⎩ ⎭ S1a = 1; S2a = Sres1; S3a = Sb ; S4a = Sres2 ; S5a = 0 ; a a a a a ψ1 = ψb1; ψ2 = ψres1; ψ3 = ψb2 ; ψ4 = ψres2 ; ψ5 = 106 ;
dj = 2exp ⎡1/ln ⎛ ⎢ ⎝ ⎣
ψja+ 1
⎞ ⎤ = weight factor; and j = 1, 2, 3 ⎥ ⎠⎦
ψja
Table 3 summarizes the parameters used to construct the fitting curves in Figs. 4 and 5. In order to find the correlation between the SWRC shape and as-compacted dry unit weight (γd ) and water content (w, %) , multiple linear regression analyses were performed for each SWRC fitting parameter to obtain the relationships as follows;
a = 0.0734 − 0.0303
γd γw
ψb1 = −2.371 + 1.142 Fig. 5. SWRCs for samples compacted at wet of optimum (OMC + 3%) and dry of optimum (OMC-3%) at 95% and 100% compaction levels; (a) degree of saturation-suction, (b) gravimetric water content-suction.
+ 0.00245w
(R2 = 0.270)
+ 0.0768w
(R2 = 0.299)
γd γw
ψres1 = exp( −21.730 + 12.508
γd γw
(6a) (6b)
(R2 = 0.744)
− 0.0781w )
(6c) The bi-modal SWRC equations proposed by Gitirana and Fredlund [66] were used to construct the fitting curves in Figs. 4 and 5. Their model was chosen due to its major advantage in that the fitting parameters have clear physical meanings with independent properties. The degree of saturation, S , is a function of 10 parameters, 9 of which are the SWRC features and the other one is the suction, ψ .
S = f (ψb1, ψres1, Sres1, ψb2 , Sb, ψres2 , Sres2, a, Smax , ψ)
Sres1 = −0.680 + 0.411
γd γw
ψb2 = exp(20.237 − 5.281
Sb = −1.742 + 0.897
(3)
where ψb is the air-entry suction for drying path or water-entry suction for wetting path, ψres is the residual soil suction, Sres the residual degree of saturation, and a the sharpness of the transitions at bending points. The Subscripts 1 and 2 represent the two levels of soil structures. Sb is the degree of saturation at the air-entry of the second structure level. Smax is the maximum degree of saturation upon soaking the sample during wetting which can be less than 100%. Gitirana and Fredlund’s formulation uses four hyperbolas to model the bimodal feature of SWRC in log(ψ) − S coordinates. The degree of saturation is calculated as follows;
γd
(R2 = 0.670)
+ 0.0624w γd γw
(R2 = 0.417)
− 0.0127w )
ψres2 = exp( −24.023 + 17.739
γd γw
(6e)
(R2 = 0.850)
+ 0.0558w
γw
(6d)
+ 0.260w )
(6f)
(R2 = 0.705) (6g)
Sres2 = −0.190 + 0.146
Smax = 0.757 + 0.103
γd
+ 0.0004w
(R2 = 0.039)
+ 0.00193w
(R2 = 0.379)
γw
γd γw
;where γw is the water unit weight, and the term
(6h) (6i) γd γw
is unit-
Table 3 Curve fitting parameters for soil-water retention curves (SWRCs). Compaction condition
a
ψb1 (kPa)
ψres1 (kPa)
Sres1
ψb2 (kPa)
Sb
ψres2 (kPa)
Sres2
Smax
90% OMC 95% OMC 100% OMC 95% OMC-3 95% OMC+3 100% OMC-3
0.03 0.03 0.04 0.035 0.05 0.02
0.35 0.55 1 0.4 0.8 0.3
1.6 17 20 18 9 70
0.63 0.7 0.82 0.49 0.82 0.58
26,000 25,000 15,000 15,000 15,000 4,000
0.39 0.49 0.63 0.39 0.68 0.58
35,500 1,500,000 7,000,000 500,000 1,400,000 1,400,000
0.18 0.05 0.15 0.05 0.05 0.15
0.96 0.96 0.99 0.98 0.99 0.99
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independent. It can be seen the correlations linking compaction conditions with ψres1, Sres1, Sb , and ψres2 (Eq. (6c), (6d), (6f) and (6g)) were the more reliable ones (of R2 values between 0.670 and 0.850) and therefore these SWRC features were dependent on compaction conditions. However, correlations for other SWRC features, namely a , ψb1, ψb2 , Sres2 , and Smax (Eq. (6a), (6b), (6e), (6h), and (6i)) were less reliable (R2 ∼ 0.039 to 0.417), meaning that these SWRC features were less dependent on the compaction conditions. Based on Eqs. (4)–(6), the SWRC can be estimated from the routine field-based compaction control parameters (i.e. γd and w ), which can be used to estimate the suction or water content in a post-compaction state using either one of the two parameters. It is noted the variation in void ratios, e , with suction, ψ , during the SWRC tests were also determined but not presented here for brevity sake. All samples exhibited only a marginal volume change of less than 2% over the entire range of suction change, which was expected since the soil was of relatively low clay content. The variations e (ψ) and S (ψ) were used to find the trend lines for gravimetric water content (Fig. 4b and Fig. 5b) based on the following expression;
w=
S (ψ). e (ψ) Gs
Fig. 7. An example of resonant frequency acquired from FFR test.
(7)
The water contents during SWRC tests were predicted based on ascompacted properties (γd and w ) using the proposed relationships and compared with the measurements as shown in Fig. 6. A reasonable good agreement (R2 = 0.9437) was obtained with 95% confidence level corresponding to error range of ± 1.65%, indicating the satisfactory performance of the predictive model. This approach for predicting the SWRC based on the compaction conditions can be useful in practice, as knowledge of both suction and water content are important in characterizing the behaviour of unsaturated compacted soils [19–21].
Fig. 8. An example of shear wave velocity profile acquired from SASW test.
of shear modulus-suction-water content relationships’. Fifteen shear wave velocity profiles were acquired from SASW tests, three tests for each of five locations across the period of two days. The tests were used to investigate the soil modulus profile down to 1 m deep as shown in Fig. 8. However, only the shear wave velocities of the top 0.2 m were implemented in an establishment of modulus-suction correlation in Section ‘Modelling of shear modulus-suction-water content relationships’, because the soil moisture content was measured only at the top ground surface and it was the purpose of this study to investigate the upper part layer of pavement for quality control. The results indicate that the in-situ shear wave velocities ranged from 330 up to 510 m/s. The in-situ maximum shear moduli, determined using Eq. (2), ranged between 241 and 611 MPa. These numbers clearly suggest that the soil was well compacted at the site. The comparison between shear wave velocities from FFR and SASW are discussed in the following section.
Typical FFR and SASW test results Typical resonant frequency of the tested specimen was observed as the frequency of the highest peak amplitude in Fourier spectra as shown in Fig. 7. Four FFR tests were performed on identical samples having different soil moisture content, showing results in a range of resonant frequencies between 2178 and 3537 Hz, and therefore the shear wave velocity and shear modulus range between 436 and 707 m/s and 430–1059 MPa, respectively. The modulus noticeably increased with decreasing moisture content as will be discussed in Section ‘Modelling
Modelling of shear modulus-suction-water content relationships A number of semi-empirical models have been developed for describing modulus-suction-moisture relationships [11–17]. Most of the proposed models employed some forms of modified effective stresses or independent stress variables, taking into account the effects of net stress, suction, and degree of saturation. The influences of soil fabric, over-consolidation ratio, soil density, distribution of bulk water and menisci water, on modulus were considered in these models using some semi-empirical parameters. In this study, three modelling approaches were used to determine the relationships between unsaturated shear modulus, suction and water content/degree of saturation following Sawangsuriya et al. [11] due to their simplicity and practicality. Model 1 considers separately the influence of net stress and suction stress on the shear modulus, G0 , as in Eq. (8).
G0 = A × f (e )(σ0 − ua )n + CSr κψ
(8)
where f (e ) is the void ratio function proposed by Hardin [75], f (e ) = 1/(0.3 + 0.7e 2) ; A , n , C and κ are empirical parameters that can be determined experimentally. In this study, the tests involved only
Fig. 6. Comparison between predicted and measured moisture content. 131
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Fig. 10. Variation of A parameter with suction.
reached when the A parameter appeared constant thereafter. This trend can be expressed mathematically as follows;
marginal confining pressure, considering the waves travelling through the part of ground surface less than 0.20 m deep only in SASW test interpretation. Also in FFR tests, there was no net confining pressure. As a first approximate, the term Af (e )(σ0 − ua )n was assumed constant (D = Af (e )(σ0 − ua )n) and given the suction stress, σs = Sr κψ , (κ = 1) Lu & Likos [21], Eq. (8) can be rewritten as follows; (9)
Model 1 therefore simplifies to a linear relationship between the shear modulus and suction stress. As shown in Fig. 9, a reasonable goodness of fit was obtained for both G0 − ψ plot (R2 = 0.603) and G0 − σs plot (R2 = 0.612), and the values ofD and C in Eq. (9) based on curve fitting in Fig. 9b are 424.78 MPa and 6.1153 respectively. It should be noted that the linear equation appears curved in a semilogarithmic plot. The scatter in the results especially for the SASW data was expected since any variation in void ratio in the field and its influence on modulus were not directly taken into account in Eq. (9). It is also noteworthy that since the FFR tests were performed in the laboratory, while the SASW tests were carried out in the field, any discrepancy between the results could be due to the fundamental different conditions of the two tests, such as in-situ material variability, difference in state of compaction, presence of large grains in the field, soil structure, and different hydration rates in the lab and in-situ. Alternatively, Model 2 lumps together the influences of void ratio, net stress and the suction stress on the shear modulus as in Eq. (10);
G0 = A × f (e )[(σ0 − ua) + Sr κψ]n
(12a)
A = Amin ; forψ ≥ 20, 000kPa
(12b)
where A1 is the A parameter when suction equals 1 kPa, β represents the rate at which A parameter decreases with suction and Amin is the minimum value of A as suction exceeds 20,000 kPa. From the regression analysis, A1 = 115.5, β = 0.232 and Amin = 11.26. The parameter A represented the degree at which the function g (e , ψ, Sr ) contributed to the shear modulus, thus related to the fabric, distribution of bulk water, menisci water and adsorbed water. As shown in Fig. 10, an increase in suction gave rise to a reduction in Parameter A for suction below 20,000 kPa. A lower value of A indicates that there was a lesser contribution of the effective stress to the modulus as suction increased. The suction threshold of about 20,000 kPa would represent the range of suction where the menisci water started to disappear from the particle contacts, and surface adsorption water played a more significant role. Beyond this suction threshold, the Parameter A appeared to be constant. At such high suction, the water was in tightly adsorbed film regime, and it was the total suction, or total water potential, which was measured. In addition, the osmotic suction component, which may also be present, could also be contributing to the total potential, yet not providing any increase in modulus. This observation was in line with a few studies [71,76] which also investigated soil behaviour in a very high suction range. In contrast with Models 1 and 2, which incorporate suction and suction stress in the variables, an empirical relationship between shear modulus and water content, called Model 3 in this study, is also plotted as shown in Fig. 11 together with a 2nd order polynomial curve fitting. It is noted Model 3 can be more easily adopted in practice, since it does
Fig. 9. Go variations with (a) suction and (b) suction stress.
G0 = D + Cσs
A = A1 × ψ−β ; forψ < 20, 000kPa
(10)
In this model, assuming that(σ0 − ua)~0 , and introducing the function g (e , ψ, Sr ) = f (e )[Sr κψ]n , Eq (10) can be rewritten as follows;
G0 = A × g (e , ψ, Sr )
(11)
The A parameter was then determined by substituting the tested values of G0 and g (e , ψ, Sr ) in Eq. (11) at different suctions, as plotted in Fig. 10. The parameters, κ and n used were 1 and 0.2 according to Sawangsuriya et al. [11]. Interestingly, the obtained A parameter appeared to decrease non-linearly with logψ which could be described using a Power law, until a threshold of suction of about 20,000 kPa was
Fig. 11. Go variation with water content. 132
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(suction stress, void ratio), gave the most satisfactory curve fitting and the smallest standard error, as compared to Model 1, G0 = f (suction stress), and Model 3, G0 = f (water content). Model 2 lumped the effects of void ratio and suction stress together, using Parameter A. Parameter A decreased with suction according to a Power law until a threshold of 20,000 kPa suction was reached when it remained constant thereafter. The model can be used in practice to estimate the effects of post-compaction monotonic change in suction/moisture on the small strain shear modulus. Acknowledgements The first author is grateful to the scholarship provided by the Department of Civil Engineering and Faculty of Engineering, Kasetsart University. This research was also supported by Department of Highways, Ministry of Transports. Valuable assistance provided by the students and staffs at Geotechnical Division of Department of Civil Engineering, Soil Physics Laboratory of Department of Soil Science, Kasetsart University, and Department of Highways is gratefully acknowledged. Fig. 12. Comparison between predicted and measured small-strain shear modulus.
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.trgeo.2019.03.005.
not involve suction measurement which is much more difficult to conduct than water content test. However, the curve fitting parameters of Model 3 are purely empirical, depending on many factors such as soil types, plasticity, compaction level, etc, and thus their generalization to other materials and conditions would be less reliable. Fig. 12 compares the measured small-strain shear modulus and the predicted values from Models 1, 2 and 3, together with the 95% confidence levels. It is evident that Model 2 (R2 = 0.750) which considers the dependency of the parameter A with suction, gives a more satisfactory agreement with the measurement than Model 1 (R2 = 0.612) and Model 3 (R2 = 0.718). The standard error for G0 prediction using Model 2 was 79.5 MPa while that for Models 1 and 3 were 94.3 MPa and106 MPa respectively. It is noteworthy that as most previous studies involved a much lower range of suction in their tests than the current study, they understandably indicated A -parameters being independent on suction. The inclusion of suction stress and void ratio within model variable gives some improvement in accuracy of model prediction.
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Conclusion Understanding of how small-strain modulus of soil changes with suction and moisture variation after compaction is of great importance for accurate modulus-based compaction control. The small-strain modulus-suction-moisture relationship for a silty sand subgrade was studied using free-free resonant frequency (FFR) tests and in-situ spectral analysis of surface waves (SASW) tests in a trial section of a Motorway project in Thailand. The following conclusions can be drawn.
• The
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post-compaction soil water retention curves (SWRCs) were found to be influenced by as-compacted dry densities and water contents. The SWRC features (e.g. water-entry suction, residual soil suction, etc.) were correlated with as-compacted dry density and water content, using multiple-linear regression analysis. These correlations were used for estimating post-compaction suctions of subgrade material in-situ. The relationship between gravimetric water content and suction appeared to be independent of compaction levels for the suction range between 10 and 20,000 kPa only for samples compacted at the same water content. The relationship was not unique for samples compacted at different water contents. Of all three predictive models used in this study, Model 2, G0 = f
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