Effects of hysteresis on hydro-mechanical behavior of unsaturated soil

Accepted Manuscript Effects of hysteresis on hydro-mechanical behavior of unsaturated soil

Jaehong Kim, Woongki Hwang, Yongmin Kim PII: DOI: Reference:

S0013-7952(17)31303-0 doi:10.1016/j.enggeo.2018.08.004 ENGEO 4913

To appear in:

Engineering Geology

Received date: Revised date: Accepted date:

6 September 2017 29 July 2018 8 August 2018

Please cite this article as: Jaehong Kim, Woongki Hwang, Yongmin Kim , Effects of hysteresis on hydro-mechanical behavior of unsaturated soil. Engeo (2018), doi:10.1016/ j.enggeo.2018.08.004

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Effects of hysteresis on hydro-mechanical behavior of unsaturated soil Jaehong Kima, Woongki Hwangb, and Yongmin Kimc,* a

Department of Civil Engineering, Dongshin University, Naju, South Korea

b

Department of Civil and Environmental Engineering, Korea Maritime University, Busan, South Korea School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, Singapore,

PT

c,*

AC C

EP T

ED

MA

NU

SC

RI

[email protected]

ACCEPTED MANUSCRIPT

Abstract Hysteresis is a common feature in the hydraulic properties of unsaturated soils. At a given matric suction, the volumetric water content on a wetting curve is always lower than that on a drying curve. The hysteresis may affect the mechanical behavior and transient process in

PT

unsaturated soils. This study focuses on the hysteresis observed in soil- water retention curve (SWRC) tests in the laboratory and inferred from a semi-empirical equation for numerical

RI

implementations. Coupled hydro- mechanical finite element analyses, employing an initial

SC

drying, main drying, and main wetting curve as hydraulic properties of the soil, were

NU

performed to numerically study the effect of hysteresis on the hydro-mechanical behavior of unsaturated soil subjected to water infiltration. Numerical results show that the unsaturated

MA

soil exhibits lower soil strength and matric suction distributions when applying the main wetting curve as compared with other SWRCs. The hysteresis appears to affect the stress-

ED

strain behavior of the unsaturated soil during prolonged rainfall. Therefore, to predict the instability of the rainfall- induced soil slope more precisely, it is necessary to apply the

EP T

wetting curve of the SWRC, which shows the hydraulic characteristics of the slope surface. Keywords : Unsaturated soil; Soil-water retention curve; Hysteresis; Hydro- mechanical

AC C

behavior; Finite element analysis

ACCEPTED MANUSCRIPT

1. Introduction Traditional geotechnical engineering design is mostly based on the principle of saturated soil mechanics. However, embankments and soil slopes are usually in an unsaturated condition. Consequently, unsaturated soil mechanics are increasingly necessary

PT

to investigate subgrade soil. During wet seasons, water infiltration into soils leads to decreasing matric suction and then reduced shearing strength of the soil. A soil- water

RI

retention curve (SWRC), defining the relationship between the amount of water in the soil

SC

and matric suction, is an essential hydraulic property in constitutive modeling of unsaturated

NU

soils (Fredlund and Rahardjo, 1993). Because the SWRC depends on soil conditions (e.g., drying and wetting process), density, and external load (Nuth and Laloui, 2008), it may be

MA

preferable to use the retention curve in unsaturated soils. Two processes — the drying process, where pore-water in the soil is displaced by air as matric suction increase, and the wetting

ED

process, where pore-water is absorbed into the soil voids as matric suction decreases — are commonly adopted in transient processes. Therefore, the SWRC exhibits hysteretic behavior

EP T

during wetting and drying cycles, but the effect of the hysteresis has been ignored in the field. The initial drying curve has been frequently used as a hydraulic property in the transient

AC C

analysis, because it may require special techniques or apparatus to measure the hysteresis of SWRCs in laboratory tests. The main wetting curves can be inferred from theoretical equations using the initial drying curve that can be easily obtained through laboratory tests (Feng and Fredlund, 1999; Pham et al., 2003). This methodology is an alternative approach for numerical implementation to investigate hysteresis effects in geotechnical engineering problems. However, the appropriate hydraulic properties of soil (i.e., drying or wetting) should be used in accordance with the process that the soil experiences (Tami et al., 2004). The use of

ACCEPTED MANUSCRIPT

wetting curves for slope stability analyses under rainfall is more reasonable because the seepage process corresponds to wetting processes (Ebel et al., 2010; Borja et al., 2012). Many researchers have experimentally measured SWRCs to predict shear strength and permeabilities of unsaturated soils. Hydraulic properties of soil are required for

PT

addressing rainfall- induced slope instabilities (Nuth and Laloui, 2008; Rahardjo et al., 2012; Kim et al., 2016). Lu et al. (2010) proposed a relationship between suction stress, 𝜎 𝑠 =

RI

𝑆𝑒 (𝑝𝑎 − 𝑝𝑤 ), and effective degree of saturation, 𝑆𝑒 = (𝑆 − 𝑆𝑟 )/(1 − 𝑆𝑟 ), using the SWRC

SC

to describe the contribution of matric suction in assessing the shear strength of unsaturated

NU

soils, where, S is the degree of saturation, and 𝑆𝑟 is the residual degree of saturation. The hysteretic paths and characterization of SWRCs by different stress conditions cause solid

MA

skeleton deformations and coupled constitutive equations are required to describe water flow and solid deformations of unsaturated soils (Miller et al., 2008). Ebel et al. (2010) estimated

ED

infinite slope stability with three curves: the main drying, wetting, and mean (i.e.,

EP T

intermediate between the drying and wetting) curves. In this study, the appropriate use of the drying and wetting hydraulic properties to simulate the transient process is highlighted. The effect of hysteresis on the coupled hydro-

AC C

mechanical behavior of unsaturated soils in term of the stress-strain behavior, matric suction variation, and soil deformation under highly transient conditions was studied through coupled analyses with incorporation of the initial drying, main wetting, and main drying curves of the soil.

2. Experimental Tests and Results 2.1 Apparatus and Samples

ACCEPTED MANUSCRIPT

Laboratory tests were conducted in an apparatus specially designed by Wayllace and Lu (2012) for measuring the hysteretic SWRC. The apparatus can measure the drying process as well as the wetting process of SWRCs by controlling air pressure applied to a saturated soil specimen, as shown in Fig. 1. The test takes approximately 40 days for the initial drying

PT

and main wetting processes in the case of weathered granite soil. In addition, the main drying and wetting curves were inferred from the methodology proposed by Feng and Fredlund

RI

(1999).

SC

Two weathered granite soils sampled from the Inje and Dogye areas in Korea were

NU

selected for the experimental program. These areas have experienced several landslide events during heavy rainfall. Specimens were prepared from reconstituted weathered granite to

MA

minimize difficulties associated with soil heterogeneity. Laboratory tests were conducted to estimate the index properties of the two soil specimens. The optimum water content, as

ED

determined by the Proctor compaction test, was 13.7%, corresponding to a maximum dry unit weight of 17.7 kN/m3 in the Inje weathered granite soil. The procedure for preparing soil

EP T

specimens included drying using an oven, crushing the soil particles, passing through a 2 mm sieve, and then mixing with the required amount of water to reach a specific water content.

AC C

The soil was then wrapped in polyethylene bags and stored in a room with constant temperature and humidity for 48 h to reach equilibrium. Grain size distribution curves and index properties of the two weathered granite soils are shown in Fig. 2 and Table 1, respectively.

2.2 Hysteretic Soil-Water Retention Curves (SWRCs) Hysteretic SWRCs represent different volume fractions of water under the same matric suction between the drying and wetting processes. This is attributed to the ink-bottle

ACCEPTED MANUSCRIPT

effect, pore- fluid contact-angle, and swelling and shrinking of the soil structure. Fig. 3 shows the experimental results of SWRCs for the two weathered granite soils (Inje and Dogye soils) obtained from the laboratory tests and the fitted curves by van Genuchten’s (1980) equation. The discrepancy was observed between the experimental data and the best fitted curves. It is

PT

due to the fact that the SWRCs seem to have bimodal characteristics, while the best fitted curves exhibit unimodal characteristics. The bimodal SWRC can be used to accurately

RI

estimate the permeability function and shear strength of soil (Zhai et al., 2017; Satyanaga and

SC

Rahardjo, 2018). However, an assumption can be made that only the unimodal SWRC was

NU

considered in this paper.

Fig. 4 shows the SWRC for silt obtained by Pham et al. (2003) for numerical

MA

implementations. Hydraulic properties and fitting parameters of SWCRs for the three soils

ED

are summarized in Table 2.

EP T

2.3 Estimation of Main Drying Curve

The initial drying curves of the SWRCs obtained from laboratory tests usually have

AC C

been used to estimate the permeabilities and shear strength of unsaturated soils caused by difficulties in measuring of hysteretic SWRCs. To overcome the difficulties, Feng and Fredlund (1999) proposed an equation to predict the main drying or wetting curve of the SWRC. Although the predicted drying curve is slightly overestimated at high matric suction, it has been proved that the curves predicted by the model are quite close to the measured results (Pham et al., 2003). Therefore, hysteretic SWRCs inferred from the equation of Feng and Fredlund (1999) for the weathered granite soils were used in this study. The Feng and Fredlund (1999) equation can predict either the drying curve or the

ACCEPTED MANUSCRIPT

wetting curve for boundary hysteretic SWRCs using the SWRC fitting equation. 𝜃𝑓 =

𝜃𝑓𝑠 ×𝑏+𝜃𝑓𝑟 ×𝑠𝑑

(1)

𝑏 +𝑠𝑑

where 𝜃𝑓 is the volumetric water content, 𝜃𝑓𝑠 and 𝜃𝑓𝑟 are the saturated and residual

PT

volumetric water contents, respectively, 𝑠 is the matric suction, 𝑑 is the parameter representing the slope at the inflection point of the curve, and both parameters 𝑑 and 𝑏

RI

control the air-entry value when 𝜃𝑓𝑠 and 𝜃𝑓𝑟 are constant. Two points on the boundary

SC

drying curve in Fig. 5 for the prediction can be obtained by Equations (2) and (3) as

𝑏 𝑤(𝜃𝑓𝑠 −𝜃1𝑑 ) 𝜃1𝑑 −𝜃𝑓𝑟

1/𝑑𝑤

}

− 𝑏𝑤 1/𝑑𝑤 ]

(2)

(3)

MA

𝑠2𝑑 = 𝑠1𝑑 − 2 [{

NU

𝑠1𝑑 ≈ (10𝑏𝑤 )1/𝑑𝑤

where 𝑠1𝑑 and 𝑠2𝑑 are the matric suctions at the inflection point of the curve and 𝑏𝑤 and

ED

𝑑𝑤 are the curve fitting parameters for the main boundary wetting curve. Equations (4) and

EP T

(5) can be used for calculating the soil suctions of two points on the boundary drying curve using the algebraic soil suction coordinate as,

AC C

|𝑠2𝑑 − 𝑠𝐸 | = |𝑠1𝑑 − 𝑠𝐸 | |𝑠1𝑑 − 𝑠𝐸 | = |𝑠𝐵 − 𝑠𝐶 |

(4) (5)

Through Equations (2) through (5) in a schematic manner, all the fitting curve parameters can be determined as shown in Table 3.

3. Coupled Hydro-mechanical Finite Element Model 3.1. Governing and Constitutive Equations

ACCEPTED MANUSCRIPT

A coupled model was used to investigate transient problems. It satisfies two equations: the balance of mass and balance of linear momentum for a solid skeleton (s), porewater (w), and pore-air (a). Owing to uncertainties in boundary conditions and material properties, the mathematical formulation was assumed to be small strain theory, isotropic

PT

homogeneous condition, and incompressibility of water. Consequently, the governing equations are expressed as 𝜕𝑆

SC

RI

−𝑛 𝜕𝑠 𝑝𝑤̇ + 𝑆 div 𝒗 = −div 𝒗 ̃𝑤 div𝝈 + 𝜌𝒈 = 0

(6) (7)

NU

where 𝑛 is the porosity, 𝑆 is the degree of saturation, 𝑠 = −𝑝𝑤 is the matric suction, 𝒗 is

MA

the velocity of the solid, 𝒗 ̃𝑤 = 𝑛𝑤 (𝒗𝑤 − 𝒗) is the superficial Darcy velocity, 𝒗𝑤 is the true seepage velocity, 𝝈 is the total Cauchy stress, 𝜌 is the total mass density of the solid, and

ED

𝒈 is the gravitational acceleration. For the unsaturated zone, the effective stress is calculated from the Bishop stress (1954) with the effective stress parameter (𝜒).

EP T

𝝈′ = 𝝈 − 𝑝𝑎 𝟏 + 𝜒 (𝑝𝑎 − 𝑝𝑤 )𝟏

(8)

where 𝜒 (= 𝑆𝑒 ) is the effective stress parameter, which varies from 0 for dry soils to 1 for

AC C

saturated soils, and 𝑝𝑤 is the pore-water pressure. In this equation, pore-air pressure (𝑝𝑎 ) remains equal to the atmospheric value, which is valid at the near-surface condition. The constitutive equation for unsaturated flow is given by the generalized Darcy’s law, relating to the relative velocity of the seepage (𝒗 ̃𝑤 ) with the hydraulic gradient as follows. 𝒗 ̃𝑤 = 𝑘 𝑤 (−∇𝑝𝑤 + 𝜌 𝑤𝑅 𝒈)

(9)

where 𝑘 𝑤 is the intrinsic permeability and 𝜌 𝑤𝑅 is the intrinsic mass density of water. In

ACCEPTED MANUSCRIPT

this equation, the intrinsic permeability depends on the degree of saturation and porosity. 𝑘 𝑤 = 𝑘𝑟𝑤 (𝑆)𝑘𝑠𝑤 (𝑛)

(10)

𝑘𝑟𝑤 (𝑆) = √ 𝑆 (1 − (1 − 𝑆 −m )m )2

(11) (12)

𝜂 𝑤 𝛿(𝑛0 )

𝑛𝑛 +∆𝜺 𝑣 1+∆𝜺 𝑣

, ∆𝜺𝑣 = 𝑡𝑟(∆𝜺)

(13)

RI

𝑛=

𝑙2 𝛿(𝑛)

PT

𝑘𝑠𝑤 (𝑛) =

SC

where 𝑘𝑟𝑤 (𝑆)is the relative permeability for unsaturated soils, 𝑘𝑠𝑤 (𝑛) is the saturated

NU

permeability, 𝑙 2 is the pore geometry parameter, 𝜂𝑤 is the dynamic viscosity of water, 𝛿(𝑛) is the Kozeny-Carman formula (Coussy, 2011) for representing the porosity-

MA

dependence of permeability, 𝑛0 is the initial porosity, and ∆𝜺𝑣 is the solid skeleton volumetric strain. The constitutive equation of the solid deformation is expressed by the

ED

effective Cauchy stress and strain through the tangent stress-strain tensor as (14)

EP T

𝝈′ = 𝒄𝑒 : 𝜺

where 𝒄𝑒 is the fourth-order tangent stress-strain tensor that depends on the specific

AC C

constitutive model for the solid, and 𝜺 is the small strain tensor for the solid. The SWRC relating to the dimensionless volumetric water content (𝜃) and matric suction (𝑠) provides an important constitutive relationship that is used for the balance of mass and the balance of linear momentum for a solid in the unsaturated zone. In this study, the following equation, as defined by van Genuchten (1980), was used. 𝑆 = 𝑆𝑟 + (1 − 𝑆𝑟 )[1 + (α𝑠) n ]−m

(15)

where the subscript 𝑟 indicates the residual value of the degree of saturation 𝑆; 𝑠 is the matric suction; and α, n, and m (= 1 − 1⁄n) are the curve fitting parameters for the SWRC.

ACCEPTED MANUSCRIPT

Note that the appropriate equations and fitting parameters with clear physical meaning are required to represent SWRCs (Satyanaga et al., 2013). Leong and Rahardjo (1997), Sillers et al. (2001) observed that the parameters of the existing equations are not individually related to shape of the SWRC. In this study, 𝑆𝑟 in van Genuchten (1980) equation as shown in Table

PT

2 was treated as a fitting parameter rather than as a physical parameter of residual degree of

RI

saturation.

The failure behavior of soil can be described by the Drucker-Prager (DP) yield

SC

criterion.

2 √6𝑐′cos𝜙′ 3+𝛽sin𝜙′

,

𝐵𝜙 =

(16)

2 √6cos𝜙′ 3+𝛽sin𝜙′

,

−1 ≤ 𝛽 ≤ 1

ED

𝐴𝜙 =

1

𝑝 ′ = 3 tr𝝈′

MA

𝒔 = dev𝝈′ ,

‖𝒔‖ = √ 𝒔: 𝒔,

NU

𝑓 = 𝑓(𝝈′ , 𝑐 ′ , 𝜙′ ) = ‖𝒔‖ − (𝐴𝜙 − 𝐵 𝜙 𝑝 ′ ) = 0

where 𝒔 is the deviatoric stress (boldfaced symbol), 𝑝 ′ is the mean effective stress, 𝑐′ is

EP T

the effective cohesion, 𝜙′ is the effective friction angle, 𝛽 = −1 implies that the DruckerPrager model circumscribes the Mohr-Coulomb triaxial compression vertices, 𝛽 = 1 implies

AC C

that the Drucker-Prager model circumscribes the Mohr-Coulomb extension compression vertices, 𝑓 < 0 implies elastic behavior, and 𝑓 = 0

implies failure.

The plastic strain was not allowed in this study because the DP yield criterion was only used to detect slope failure at a given condition. When failure is detected by the DP yield criterion in the soil (𝑓 𝑡𝑟 > 0, where 𝑓 𝑡𝑟 is the trial failure function), catastrophic failure may be imminent. A progressive failure model can be incorporated into the finite element implementation that accounts for the evolution of slip surfaces in a partially saturated soil (Regueiro and Borja, 2001; Callari et al., 2010). Although it is beyond the scope of this paper,

ACCEPTED MANUSCRIPT contours of 𝑓 𝑡𝑟 in the soil slope with hysteretic SWRCs based on the DP yield criterion are presented to determine slope failure.

PT

3.2 Coupled Nonlinear Finite Element Formulation and Implementation In the coupled finite element analysis, the transient process of water flow changes

RI

equilibrium conditions of unsaturated soil, resulting in a volume change of the soil. The

SC

volume change alters the hydraulic properties of the soil and, thus, influences the transient process of water flow through the soil. The permeability function described in Equation 10 is

NU

a function of the volume change, such as porosity ( 𝑛 ), that is governed by the solid skeleton

MA

volumetric strain ( 𝜀𝑣 ). Therefore, the coupled processes affect the mechanical and hydraulic behavior of unsaturated soil interactively.

ED

The strong form of the coupled governing equations (Equations 6 and 7) can be expressed by coupling the nonlinear weak form of the unsaturated biphasic mixture after

EP T

integration by parts and the application of the divergence theorem (Hughes, 1987). In this case, the weighting functions of 𝒘 and 𝜂 are considered as variations of the displacement

AC C

and pore water pressure, respectively. ∫𝐵 [∇𝒘: (𝝈′ + 𝑆𝑒 𝑝𝑤 𝟏)]d𝑉 − ∫𝐵 𝜌𝒘 ∙ 𝒈d𝑉 − ∫Γ 𝒘 ∙ 𝒕𝜎 dΓ = 0 𝑡

𝜕𝑆

̃𝑤 d𝑉 − ∫Γ 𝜂 ∙ 𝑆 𝑤 dΓ = 0 ∫𝐵 −𝜂𝑛 𝜕𝑠 d𝑉 + ∫𝐵 𝜂 𝑆 div𝒗 d𝑉 − ∫𝐵 ∇𝜂 ∙ 𝒗 𝑠

(17)

(18)

where 𝒕𝜎 is the total traction on the solid traction boundary and 𝑆 𝑤 is the positive inward water seepage at the fluid flux boundary. Introducing shape functions for a mixed quadrilateral finite element formulation (Kim, 2010), after element assembly and application of boundary conditions, the coupled

ACCEPTED MANUSCRIPT

nonlinear first order ordinary differential equation can be expressed in matrix form as 𝑪(𝑫) ∙ 𝑫̇ + 𝑭𝐼𝑁𝑇 (𝑫) = 𝑭𝐸𝑋𝑇 (𝑫)

(19)

where 𝑪(𝑫) is a nonlinear ‘damping’ matrix, 𝑭𝐼𝑁𝑇 (𝑫) is a nonlinear internal ‘force’ vector, and 𝑭𝐸𝑋𝑇 (𝑫) is a nonlinear external ‘force’ vector. The time histories of solid skeleton

PT

displacement and pore water pressure are obtained by solving the above nonlinear finite

RI

element matrix equation via a fully- implicit time integration scheme (backward Euler) and

NU

SC

the Newton-Raphson method (Kim et al., 2012).

4. Effect of Hysteresis on Hydro-mechanical Behavior of Unsaturated Soil

MA

To investigate the variation of vertical displacements, pore-water pressure, vertical effective stresses and corresponding strains, and suction stress on a soil column under rainfall,

ED

a series of numerical simulations was carried out in the three weathered granite soils. The coupled hydro- mechanical finite element model simulates the behavior of soil deformations

EP T

depending on the seepage force. In particular, the different hydraulic properties may affect numerical results in accordance with the initial drying curve, main wetting curve, and main

AC C

drying curve. Table 4 indicates the soil properties used in numerical analyses. By applying these parameters of Table 4, it is possible to confirm the compressibility of the sandy soil due to rainfall infiltration through the algorithm of the study. At the same time, a seepage analysis of the unsaturated soil can be performed. Fig. 6 shows the boundary conditions and finite element mesh of the soil column. The soil was discretized using mixed quadrilateral finite elements (Q9P4) employing continuous biquadratic displacement 𝒖 (nine-noded) and bilinear pore-water pressure 𝑝𝑤 (four-noded). A groundwater table (𝑝𝑤 = 0) was assumed to be at the bottom of the soil

ACCEPTED MANUSCRIPT

column and initial matric suction was assumed to be hydrostatic as an ideal initial condition. The infiltration rate (𝑆 𝑤 ) was applied to the top surface of the soil column. The dimensions of the numerical model in coupled analyses were 1 m in width and 3 m in height for the soil column. The numerical simulation was performed using a 30-element mesh for all soil

PT

column tests.

RI

The initial drying curve, which is generally used as a hydraulic property of unsaturated soil, cannot simply represent the transient process in unsaturated soil subject to

SC

infiltration. The hysteresis of the SWRCs in Figs. 3–5 may lead to various hydraulic

NU

properties and the different deformations of the soil due to water infiltration. Fig. 7 shows the vertical displacements that occurred at the surficial element of the

MA

soil column due to water infiltration. The deformation of the soil column applied by the main wetting curve was smaller than those of the soil columns applied by the initial and main

ED

drying curve. The results confirmed the fact that the soil under the wetting process exhibits

EP T

more stiffness, whereas the soil under the drying process exhibits less stiffness. All the soils have the same mechanical properties, but with the different saturated volumetric water contents and initial porosity. Note that the saturated volumetric water content (𝑉𝑤⁄𝑉 ) and the

AC C

porosity (𝑉𝑣 ⁄𝑉) are the same in a saturated condition. The initial porosity of each sample was implemented to the coupled analyses as shown in Table 2 and 3. In this case, therefore, the vertical displacement of soils depends on the saturated volumetric water content. The negative term of vertical displacement represents settlements as shown in Fig. 7. The higher initial saturated volumetric water content gave the larger initial vertical displacement and vice versa. This could be attributed to the assumption that water is incompressible. Because all soils have the same elastic modulus and Poisson’s ratio, the larger the saturated volumetric water content, the smaller the compressibility due to the higher volumetric water content in

ACCEPTED MANUSCRIPT

the same volume. Thus, the vertical displacement of the silt was larger than that of other soils. In addition to the vertical displacement, elastic deformation occurred in a short per iod at the beginning of rainfall and there was no additional deformation afterward, because only elastic behavior was considered without consideration of plastic deformation.

PT

For the difference of hysteretic SWRCs in the same soil, water flow quickly passes through the soil column applied by the main wetting curve because the soil deformation with

RI

the main wetting curve was the smallest among them. Note that variations of the unsaturated

SC

permeability function for the three boundary curves mainly depend on the saturated

NU

volumetric water content and porosity as indicated in Equations (10) through (12). The fitting parameters also affect the permeability function, but these effects are not discussed in this

MA

study. Fig. 8 shows the variation in the hydraulic conductivity depending on the degree of saturation with time according to three different SWRCs. The hydraulic conductivity of the

ED

silty soil becomes getting wetter with time as shown in Fig. 8. The soil column implemented by the main wetting curve showed a wide range of hydraulic conductivity during rainfall.

other cases.

EP T

This means that matric suction decreased because more water soaked into the soil than in

AC C

Fig. 9 shows the distribution of pore-water pressure at the last time step. As the trend of contours is similar to that of the other soils (e.g., Dogye and Inje soils), other plots are omitted. The contours of pore-water pressure in the Dogye soil implemented by the initial drying curve exhibited lower water infiltration on the surficial layer of the soil column than other cases. This showed a shallow wetting band depth from the surface, because the initial drying curve had a high air-entry value. On the other hand, similar distributions of pore-water pressure appeared in the soil column when using the main drying and wetting curves with lower air-entry value.

ACCEPTED MANUSCRIPT

For the distribution of effective vertical stress and strain of the soil column, the contours tended to be similar, but there were discrepancies. The discrepancies in terms of the effective vertical stress, vertical strain, and suction stress in the silty soil column were graphically investigated to clarify the effect of hysteretic SWRCs. These values were

PT

obtained at the right corner element of the surficial layer. Fig. 10 shows the reduction in vertical effective stresses in the element due to seepage force. Because the soil with the initial

RI

drying curve had a high air-entry value, decreasing trends of the vertical effective stress were

SC

similar to each curve, but the initial value of the effective vertical stress depended on the applied initial seepage force. The water infiltration wetted the soil faster in the main wetting

NU

curve that had a low value of air-entry value. The variation in vertical strains with the main

MA

drying curve was higher than that of other soil curves (Fig. 11). The smallest vertical strain was observed for the main wetting curve. Fig. 12 shows the variation in suction stresses,

ED

𝑆𝑒 𝑝𝑤 , which is equal to [1 + (α𝑠)n ]−m 𝑝𝑤 and related to the unsaturated shear strength. The plotting of the suction stress tended to be similar to the variation in the vertical effective

al., 2010).

EP T

stress, because the suction stress is proportional to the effective stress of saturated soils (Lu et

AC C

Unsaturated soil slopes may fail and/or undergo plastic deformation due to heavy rainfall. Although the coupled finite element model cannot incorporate the plasticity scheme, one should check whether the soil slope has reached failure (𝑓 𝑡𝑟 > 0) or not (𝑓 𝑡𝑟 < 0) by using the Drucker-Prager (DP) yield criterion. Linear isotropic elasticity was used as the constitutive model for the soil, and a post- localization failure model was not implemented. Homogeneous and isotropic soil slopes were assumed for the coupled finite element analysis. Fig. 13 shows the unsaturated soil slope geometry and boundary conditions to investigate instability of the soil slope by using the hysteretic SWRCs. The slope has an angle of 40 

ACCEPTED MANUSCRIPT

with the initial groundwater table and a slope height of 20 m. Soil properties related to unsaturated soils, such as hydraulic conductivity and strength parameters, are summarized in Tables 2–4. Fig. 14 shows the distribution of the trial failure criterion ( 𝑓 𝑡𝑟 > 0 ) on the

PT

unsaturated soil slope. A surficial wetting band depth occurred on the soil slope due to rainfall

RI

infiltration and then matric suction decreased. Therefore, the 𝑓 𝑡𝑟 contour on the slope with the main wetting curve exhibited the worst slope condition at the toe and surficial elements of

SC

the slope (Fig. 14b). The matric suction decreased in the areas of the slope due to infiltration,

NU

resulting in decreases in the shear strength. These contours indicate that the soil slopes implemented by the wetting curve tended to be weaker than those of other hysteretic SWRCs.

MA

Note that progressive failure analyses are needed to make possible the development of plastic

ED

deformation and/or failure starting at the toe and crest of slopes.

EP T

5. Conclusion

The appropriate use of the soil- water retention curve (SWRC) is of particular interest

AC C

with respect to slope stability because the hydraulic property of the soil is required for solving transient conditions. The influence of hysteretic SWRCs is apparent and affects the distribution of pore-water pressure, effective stress, strain, and suction stress in unsaturated soil. However, the initial drying curve has been frequently used by many researchers and engineers due to difficulties associated with the equipment and time in laboratories to evaluate the hysteresis. For hysteretic SWRCs, the main drying or wetting curve can be easily obtained using the schematic manner to avoid time-consuming and costly procedures. Through the coupled

ACCEPTED MANUSCRIPT

finite element analyses, the effects of hysteresis on the hydro- mechanical behavior of unsaturated soil in terms of the vertical displacement, effective stress, strain, and suction stress were investigated. As a result, it was found that the unsaturated soil exhibited lower soil strength and matric suction distributions in hydro-mechanical analyses when using the

PT

main wetting curve rather than those of other branches of SWRCs. Failure was considered to have occurred during rainfall when plastic strains were

RI

developed on the cohesionless soil slope. Therefore, a methodology with the incorporation of

SC

the coupled analysis by linking the elastic deformation and seepage is needed for addressing

NU

the field simulation more rigorously than the staggered analysis. Combined with the numerical analysis, these observations give insight into the influence of hysteresis on the

MA

hydro- mechanical behavior of unsaturated soil. Therefore, the wetting curve of SWRCs should be considered to accurately interpret the instability of the slope due to rainfall

AC C

EP T

ED

infiltration.

ACCEPTED MANUSCRIPT

References Bishop, A. W. 1954. The use of pore water coefficients in practice, Géotechnique 4, 148– 152. Borja, R.I., Liu, X., White, J.A. 2012. Multiphysics hillslope preceses triggering landslides.

PT

Acta Geotechnica 7, 261–269.

RI

Callari, C. and Armero, F. and Abati, A. 2010. Strong discontinuities in partially saturated

SC

poroplastic solids. Computer Methods in Applied Mechanics and Engineering 199,

NU

1513–1535.

Coussy, O. 2011. Poromechanics, John Wiley and Sons, New York.

MA

Ebel, B.A., Loague, K., Borja, R.I. 2010. The impacts of hysteresis on variably saturated hydrologic response and slope failure. Environmental Earth Sciences 61 (6), 1215–1225.

ED

Feng, M. and Fredlund, D.G. 1999. Hysteretic influence associated with thermal conductivity

EP T

sensor measurements. Proceeding from Theory to the Practice of Unsaturated Soil Mechanics, in association with 52nd Canadian Geotechnical Conference & Unsaturated

AC C

Soil Group, Regina, pp. 14:2:14–14:2:20. Frdlund, D.G., Rahardjo, H. 1993. Soil mechanics for unsaturated soils. John Wiley and Sons Inc., New York.

Hughes, T.J.R. 1987. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Dover, New Jersey. Kim, J. 2010. Plasticity modeling and coupled finite element analysis for partially-saturated soils. Ph.D. Thesis, University of Colorado at Boulder, US. Kim, J., Jeong, S., Regueiro, R.A. 2012. Instability of partially saturated soil slopes due to

ACCEPTED MANUSCRIPT

alternation of rainfall pattern. Engineering Geology, 147–148, 28–36. Kim, Y., Jeong, S., and Kim, J. 2016. Coupled infiltration model of unsaturated porous media for steady rainfall. Soils and Foundations 56 (6), 1073–1083. Leong E.C. and Rahardjo H. (1997) A review of soil–water characteristic curve equations.

PT

Journal of Geotechnical and Geoenvironmental Engineering. 123 (12), 1106–1117.

SC

unsaturated soil. Water Resources Research, 46 (5).

RI

Lu, N., Godt, J. W., Wu, D. T. 2010. A closed‐ form equation for effective stress in

NU

Miller, G. A., Khoury, C. N., Muraleetharan, K. K., Liu, C., Kibbey, T. C. 2008. Effects of soil skeleton deformations on hysteretic soil water characteristic curves: experiments and

MA

simulations. Water Resources Research, 44 (5).

Nuth, M. and Laloui, L. 2008. Advances in modelling hysteretic water retention curve in

ED

deformable soils. Computers and Geotechnics 35, 835–844.

EP T

Pham, H.Q., Fredlund, D.G. and Barbour, S.L. 2003. A practical hysteresis model for the soilwater characteristic curve for soils with negligible volume change. Géotechnique 53 (2),

AC C

293–298.

Rahardjo, H., Satyanaga, A., Leong, E.C. 2013. Effect of flux boundary conditions on porewater pressure distribution in slope. Engineering Geology 165, 133–142. Regueiro, R.A. and Borja, R.I. 2001. Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity. International Journal of Solids and Structures 38, 3647–3672. Satyanaga, A., Rahardjo, H., Leong, E.C. and Wang, J.Y. 2013. Water Characteristic Curve o f Soil with Bimodal Grain-size Distribution. Computer and Geotechnics, 48, 51–61.

ACCEPTED MANUSCRIPT

Satyanaga, A. and Rahardjo, H. 2018. Unsaturated Shear Strength of Soil with Bimodal Soilwater Characteristic Curve. Géotechnique. Sillers W.S., Fredlund D.G., Zakerzadeh, N. (2001). Mathematical attributes of some soil– water characteristic models. Geotechnical and Geological Engineering, 19, 243–283.

RI

barriers. Geotechnical Testing Journal 27 (2), 173–183.

PT

Tami, D., Rahardjo, H., Leong, E.C., Fredlund, D.G. 2004. A physical model for capillary

SC

van Genuchten, M. 1980. Closed- form equation for predicting the hydraulic conductivity of

NU

unsaturated soils. Soil Science Society of America Journal 44 (5), 35–53. Wayllace, A. and Lu, N. 2012. A transient water release and imbibitions method for rapidly

MA

measuring wetting and drying soil water retention and hydraulic conductivity functions. Geotechnical Testing Journal, 35 (1), 103–117.

ED

Zhai, Q., Rahardjo, H., Satyanaga, A. and Priono (2017) Effect of bimodal soil- water

AC C

230, 142–151.

EP T

characteristic curve on the estimation of permeability function. Engineering Geology,

ACCEPTED MANUSCRIPT

List of figures

Fig. 1. Schematic diagram of apparatus for soil-water retention curve (SWRC) tests. Fig. 2. Grain size distribution curves for the Inje and Dogye weathered granite soils.

Fig. 4. Hysteresis of SWRCs for the silt (Pham et al., 2003).

PT

Fig. 3. Drying and wetting curves of SWRC from laboratory tests; a) Inje weathered granite soil; b) Dogye weathered granite soil.

RI

Fig. 5. Main drying curve of SWRC inferred from the main wetting curve of SWRC by Feng and Fredlund (1999); a) Inje weathered granite soil; b) Dogye weathered granite soil.

SC

Fig. 6. Finite element mesh and boundary conditions for the rainfall infiltration analysis. Fig. 7. Comparisons of vertical displacements for the three difference soils at the surficial soil element

NU

Fig. 8. Variations in hydraulic conductivities with respect to the hysteresis of SWRCs in the silt.

MA

Fig. 9. Distribution of pore-water pressure (kPa) with respect to the hysteresis of SWRCs in the Dogye weathered granite soil; a) Initial drying curve; b) Main drying curve; c) Main wetting curve.

ED

Fig. 10. Variations in vertical effective stresses at the right corner element of the surficial layer in the silt. Fig. 11. Variations in vertical strain at the right corner element of the surficial layer in the silt.

EP T

Fig. 12. Variations in suction stresses at the right corner element of the surficial layer in the silt.

AC C

Fig. 13. Finite element mesh and boundary conditions for a typical unsaturated soil slope subjected to rainfall infiltration. Fig. 14. Distribution of Drucker-Prager failure criterion (kPa) in the silt slope; a) Main drying curve of SWRC; b) (a) Main wetting curve of SWRC

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

Fig. 1. Schematic diagram of apparatus for soil-water retention curve (SWRC) tests.

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

Fig. 2. Grain size distribution curves for the Inje and Dogye weathered granite soils.

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

(a) Inje weathered granite soil

(b) Dogye weathered granite soil Fig. 3. Drying and wetting curves of SWRC from laboratory tests

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

Fig. 4. Hysteresis of SWRCs for the silt (Pham et al., 2003).

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

(a) Inje weathered granite soil

(b) Dogye weathered granite soil Fig. 5. Main drying curve of SWRC inferred from the main wetting curve of SWRC by Feng and Fredlund (1999).

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

Fig. 6. Finite element mesh and boundary conditions for the rainfall infiltration analysis.

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

Fig. 7. Comparisons of vertical displacements for the three difference soils at the surficial soil element

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

Fig. 8. Variations in hydraulic conductivities with respect to the hysteresis of SWRCs in the silt.

(a) Initial drying curve

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

(b) Main drying curve

(c) Main wetting curve

AC C

EP T

ED

MA

Fig. 9. Distribution of pore-water pressure (kPa) with respect to the hysteresis of SWRCs in the Dogye weathered granite soil.

NU

SC

RI

PT

(kPa)

ACCEPTED MANUSCRIPT

Time (hr)

AC C

EP T

ED

MA

Fig. 10. Variations in vertical effective stresses at the right corner element of the surficial layer in the silt.

NU

Time (hr)

SC

RI

PT

(%)

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

Fig. 11. Variations in vertical strain at the right corner element of the surficial layer in the silt.

NU

SC

RI

PT

(kPa)

ACCEPTED MANUSCRIPT

Time (hr)

AC C

EP T

ED

MA

Fig. 12. Variations in suction stresses at the right corner element of the surficial layer in the silt.

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

Fig. 13. Finite element mesh and boundary conditions for a typical unsaturated soil slope subjected to rainfall infiltration.

NU

SC

RI

PT

ACCEPTED MANUSCRIPT

AC C

EP T

ED

MA

(a) Main drying curve of SWRC

(b) Main wetting curve of SWRC Fig. 14. Distribution of Drucker-Prager failure criterion (kPa) in the silt slope.

ACCEPTED MANUSCRIPT

List of tables

Table 1. Index properties for the two soils. Table 2. Soil-water retention curve fitting parameters for the three soils predicted by van Genuchten (1980).

PT

Table 3. Soil-water retention curve fitting parameters for the three soils predicted by Feng and Fredlund (1999).

AC C

EP T

ED

MA

NU

SC

RI

Table 4. Material properties used in numerical analyses.

ACCEPTED MANUSCRIPT

Table 1. Index properties for the two soils. Inje

Dogye

Specific gravity, G s

2.64

2.63

Maximum dry unit weight,  d max ( kN / m3 )

17.7

-

Minimum dry unit weight,  d min ( kN / m3 )

13.2

-

Coefficient of uniformity, Cu

10.17

9.27

Coefficient of gradation, Cc

1.32 19.85 12.54

1.47 12.17 16.18

AC C

EP T

ED

MA

NU

SC

USCS Classification

7.19  10-7 SW

RI

Plastic limit, PL ( % ) Plastic index, PI ( % ) Saturated hydraulic conductivity, k s ( m / s )

PT

Index property

4.76  10-7 SW

ACCEPTED MANUSCRIPT

Table 2. Soil-water retention curve fitting parameters for the three soils predicted by van Genuchten (1980).

Inje Dogye

𝜃𝑟

𝑆𝑟

0.422 0.400 0.418 0.387 0.369 0.352

0.067 0.067 0.032 0.032 0.077 0.077

0.159 0.168 0.077 0.083 0.209 0.219

α (1/kPa) 0.231 0.404 0.100 0.643 0.031 0.070

n

m

𝑛0

2.083 2.125 1.469 1.353 2.332 2.352

0.520 0.529 0.319 0.261 0.571 0.575

0.422 0.400 0.418 0.387 0.369 0.352

AC C

EP T

ED

MA

NU

SC

RI

Pham et al. (2003)

Drying Wetting Drying Wetting Drying Wetting

𝜃𝑠

PT

SWRC

ACCEPTED MANUSCRIPT

Table 3. Soil-water retention curve fitting parameters for the three soils predicted by Feng and Fredlund (1999).

Pham et al. (2003)

𝜃𝑓𝑟

0.400 0.400

Predicted main drying curve Measured main wetting curve Predicted main drying curve Measured main wetting

0.067 0.067

𝑏 36.6 9.4

𝑑 1.75 1.5

𝑛0 0.400 0.400

0.381 0.387 0.352

0.044 0.057 0.077

14.9 5.6 910

0.76 0.75 1.79

0.381 0.387 0.352

0.352

0.077

280

1.87

0.352

Pham et al. (2003)

29  106 , 7  106

MA

NU

Intrinsic permeability, l 2 ( m2 )

Seepage force, Sw ( m / sec )

Dynamic viscosity of water,

w

( Pa  s )

2700, 1000, 1.2

7.19  10-14

7.2  10-7

10-3

2700, 1000, 1.2

4.76  10-14

4.8  10-7

10-3

1.00  10-14

1.1  10-7

10-3

ED

Dogye

29  106 , 7  106 29  106 , 7  106

2700, 1000, 1.2

EP T

Inje

AC C

Soil property

Lame parameters, ,  (Pa)

Intrinsic mass density for solid, water, and air, sR  ,  wR ,  aR ( kg / m3 )

SC

Table 4. Material properties used in numerical analyses.

PT

Dogye

𝜃𝑓𝑠

RI

Inje

SWRC Predicted main drying curve Measured main wetting curve

Strength parameters, c (Pa),  (  ),  5.0  103 , 30, -1 (TC) 5.0  103 , 30, -1 (TC) 5.0  103 , 30, -1 (TC)

ACCEPTED MANUSCRIPT

Highlights Estimation of hysteresis of soil-water retention curve (SWRC)



Coupled hydro-mechanical finite element analyses



Role of hysteretic SWRCs in the transient condition.



Emphasis on the hysteresis effect

AC C

EP T

ED

MA

NU

SC

RI

PT

