J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44 DOI: 10.1007/s12204-017-1796-6

Hydraulic Properties Analysis of the Unsaturated Cracked Soil CAO Ling1,2∗ (

),

ZHANG Hua1 (

), CHEN Yong1 (

)

(1. College of Civil Engineering & Architecture, China Three Gorges University, Yichang 443002, Hubei, China; 2. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)

© Shanghai Jiao Tong University and Springer-Verlag Berlin Heidelberg 2017 Abstract: Morphological parameters of cracks significantly affect the hydraulic conductivity of cracked soil. A laboratory test was conducted to study the hydraulic properties of cracks. The dynamic development of cracks in soil during drying and wetting was measured in the test. Based on the test results, the relationships between the morphological parameters and the soil water content were quantified. According to the fractal model, the soil-water characteristic curve (SWCC) and permeability functions for the cracked soil were predicted based on the dynamical development process of the cracks. A crack-pore dual media model was established to simulate the ponding infiltration in the unsaturated cracked soil. The variations of the pore water pressure in different part of the fractal model are quite different due to the impact of the cracks. This result illustrates that the prediction of the hydraulic properties for the cracked soil is reasonable. Key words: expansive soil, seepage, fractal model, soil-water characteristic curve (SWCC), crack-pore media CLC number: TU 443 Document code: A

0 Introduction It is well recognized that the cracks can break the integrality of the soil and reduce its strength. Another main effect of cracks is that the pathways provided by cracks significantly increase the hydraulic conductivity of the soil. As such, it is easier for the cracked soil slopes to slip or collapse during rainy seasons[1-2] . It is necessary to determine the stability including the effects of cracks during the saturated-unsaturated seepage analysis. This has been done in previous studies[3-6] . For the cracked soil, the water retention ability and the hydraulic conductivity change with the soil water content. Soil-water characteristic curve (SWCC) and coefficient of permeability function are often used to determine these hydraulic properties. In geotechnical engineering, much attention has been given to the water retention curves and permeability functions for the soil matrix[3-4] . In view of the hydraulic properties of crack medium, scholars pay more attention to the numerical simulation. But cracks in soils are randomly distributed and hard to describe. The constitutive relaReceived date: 2015-09-10 Foundation item: the National Natural Science Foundation of China (No. 51409149), the Science Research Key Project of Hubei Provincial Department of Education (No. D20151201), and the Science Research Foundation of Yichang Science and Technology Bureau (No. A14302-a10) ∗E-mail: [email protected]

tionships of complex and random crack networks need more research. The SWCC has been studied for a long time and used to predict the soil hydraulic conductivity. However, for the cracked soil, it is a crack-pore dual media. Zhang and Fredlund[5] showed that the SWCCs for discontinuous material depend on the pore distribution. They assumed that the crack network system and the pore network system both follow lognormal distribution. The SWCC with double-peak specificity can then be obtained by combining the estimated SWCCs of the two systems. The similar way for SWCC was proposed by other researchers[6]. However, the theory is based on rock mechanics, because the pore size distribution of the cracks is invariable. During the repetitive rainfall-evaporation process, the morphological characteristic of cracks changes with the water content, and the hydraulic conductivity of this deformable medium is not a constant. The conductivity changes with the morphological characteristic of the cracks and the suction of the soil. Hence, the study of SWCC and permeability function for the unsaturated cracked soil based on the dynamical development process of cracks is a challenging problem. In this paper, a reasonable way is found to simulate the whole process from crack initiation to coalescence under the alternate rainfall-evaporation condition in laboratory. Finally, a crack-pore dual media seepage example is presented to prove the SWCCs and permeability functions for the unsaturated cracked soil.

36

1 Development Process of the Cracks in Drying and Wetting Cycles 1.1 Experiment Both laboratory and field experiments were conducted to study the development of desiccation cracks[7-9] . A laboratory experiment has been conducted to simulate the alternate rainfall-evaporation condition and to investigate the dynamic development of the cracks during the drying and wetting cycles. This experiment focuses on the development of surface cracks. Based on the test results, the relationships between the crack morphological parameters and the water content during the drying-wetting cycle have been developed. Firstly, some past soil samples were prepared with 32% water mass fraction by using the local dry soils. Hereinafter, w represents the water mass fraction. The past was sealed in the moisturizing cylinder, and the soil and water were kept to equilibrate. Based on the designed dimensions of the soil sample and the dry density (ρd = 1.44 g/cm3 which is close to the natural dry density), the weight of the past for every one sample was calculated. Half of the past was put into an iron plat with a size of 29.5 cm × 39.5 cm after 24 h. The past was compressed into a cuboid of 1.5 cm thick with a jack. The soil sample surface was then roughened with a brush, and the second layer was compacted by the same method. Then, a soil sample with the size of 29.5 cm × 39.5 cm × 3 cm was finished. Electric fan generated a steady wind to simulate the evaporation process and to accelerate the development of cracks. The initial drying process was completed when the weight of the soil sample was at a constant for 3 h. Then, the electric fan was turned off and water was sprayed onto the dry and cracked soil samples to simulate the rainfall process. The wetting process was ceased, when the soil surface was covered with water and the water mass fraction rose back to about 32%. This was the end of the first wetting-drying cycle. The cycle was repeated with the same procedures seven times, so as to simulate the continuous rainfallevaporation process under the natural condition. A fixed digital camera took photographs at the appointed time so as to record the evolution progress of the soil cracks. At the beginning of drying process, images of the soil surface were recorded at short intervals (about 5 min). At the end of the drying process, longer intervals (30 min) were adopted to take the crack images. In the wetting process, images were taken every 30 s. During this photographic session, all curtains in the laboratory were drawn and only the indoor light was on. In this way, the brightness of the light was the same throughout the session. Two identical samples with the same initial water content, dry density and dimensions were prepared to ensure the camera area consistence

J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44

and the soil sample stay in the fixed position: one for capturing images of the cracks, and the other for the measurement of water content. The typical geotechnical properties of the soil are summarized as follows: Gs = 2.72, ws = 15.3%,

wL = 69.65%, Ip = 39.7,

wP = 29.95%, δef = 52%,

where Gs , wL , wP , ws , Ip and δef represent specific gravity, liquid limit, plastic limit, shrinkage limit, plasticity index and free swelling rate, respectively. The soil has weak expansibility. 1.2 Results In each cycle, the development process of the cracks can be divided into three stages. In Stage 1, the water content decreases slowly with only a few cracks developing. In Stage 2, the development of the cracks accelerates, while the water content continues to decrease. In Stage 3, the development of the cracks tends towards equilibrium. At the end of the first cycle, only a few major cracks appeared. With subsequent cycles, more cracks appeared but the crack width became smaller. The number of cracks did not change substantially after five drying-wetting cycles. Thus, it may be inferred that the effect of drying-wetting cycles on soil cracking is limited during the former few cycles. In this study, only the results from the sixth cycle represent the longterm effect of the rainfall-evaporation cycle on the soil cracks. Figures 1 and 2 show the crack development from the sixth cycle. The intersections of the crack network and the area of the cracks change with the water content obviously. A Matlab-based photo-processing program was used to characterize the morphological properties of the cracks at different stages. After cutting, binarization and bridging, the photographs were converted into binaryzation images of the same size as the original cracks, as shown in Fig. 3. The actual size of the photos in Figs. 1, 2 and 3 is 29.5 cm × 19.7 cm. It can be seen that in the binaryzation images the white area (white pixel) represents the aggregate soil, and the black area (black pixel) represents the cracks. The following quantitative parameters were determined and calculated by the program to quantitatively analyze the morphological parameters of the cracks. (1) The crack porosity δc is the ratio of the surface area of the cracks to the total soil surface area. The program calculates the area by counting the number of the white or black pixels with the “bwarea” function of Matlab. (2) The crack width r indicates the opening degree of the cracks. In this investigation, the crack width was determined by calculating the shortest path from a randomly chosen point on one boundary to the opposite crack boundary.

J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44

37

(a) w = 32%

(b) w = 30.5%

(c) w = 30.16%

(d) w = 29.58%

(e) w = 28.22%

(f) w = 6.11%

Fig. 1

Crack development during a drying process

(a) w = 6.11%

(b) w = 8.2%

(c) w = 10%

(d) w = 16%

(e) w = 20%

(f) w = 32%

Fig. 2

Crack development during a wetting process

Fig. 3

Binaryzation image of the cracks

38

J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44

(3) The crack fractal dimension D is an indicator of the total distribution characteristics. In this study, box-counting dimension method was used to estimate the crack fractal dimension. It was calculated by using a grid consisting of the square elements with sides of dimension ε to cover the binaryzation image. The number of the elements that have black pixel (crack part), N (ε), changes with ε. The relationship between N (ε) and ε is lg N (ε) = A − D lg ε,

(1)

where A is a constant. Hence, D values can be derived from the slop of lg N (ε) versus lg ε plots.

fractal theories and the Washburn Equation to calculate D from MIP[14-15] : ln

dv = ln A = ln k + (2 − D) ln rp , drp

(4)

where v is the volume of the mercury intruded at a given pressure, rp is the pore radius, and k is a constant. dv Hence, D values can be derived from the slop of ln drp versus ln rp plots. The calculated result of the fractal dimension is shown in Fig. 4, where R2 is the square of correlation coefficient, and D is 2.78 according to Eq. (4). In this 2D study, D is 1.78.

2 Hydraulic Properties for the Cracked Soil

2

Test data Fitting

(2) (3)

where Se is the effective saturation degree, ϕ is the volumetric water content of the unsaturated soil at suction ps , ϕs is the volumetric water content when the soil is fully saturated, pse is the air-entry value, kr is the relative permeability coefficient of the unsaturated soil, ks is the saturated permeability coefficient, and kw is the permeability coefficient at suction ps . For a twodimensional (2D) space, D − 3 in Eq. (2) and 3D − 11 in Eq. (3) should be displaced by D − 2 and 3D − 8, respectively[11] . The fractal dimension for the soil has been measured in the laboratory by mercury intrusion porosimetry (MIP). The following expression is deduced from the

−2 −4 y = 4.963 42 − 0.784 42x R2 = 0.993 11 −6 2 4 6 8 10 lnrp

Fig. 4

12

Curve of ln A-ln rp for the intact soil without cracks

The saturated volumetric water content measurement ϕs for the soil sample in this study is 45%. The drying water retention curve of a soil can be obtained through the SWCC test with a pressure plate extractor. Fitting Eq. (2) to the measured drying SWCC can give the drying SWCC over the entire suction range. Figure 5 shows the fitted SWCCs. Pham et al.[16] proposed a scaling method to estimate the hysteretic SWCCs. According to the result, the wetting and drying curves can be interchanged by changing the distance between the two curves. The calculation result of a statistical analysis involving 34 kinds of soils shows that the distance between the two boundary curves is about 20% log-cycle. In this study, this scaling method is used to predict the wetting water retention curve for the crack network, as shown in Fig. 5. 50 40 ϕ/%

ϕ pD−3 s = D−3 , ϕs pse kw p3D−11 s = 3D−11 , kr = ks pse Se =

lnA

0

In this section, the hydraulic properties for the cracked soil are predicted based on the capillary law and fractal model. The crack medium and the soil matrix co-exist in the cracked soil. The crack medium interacts with the soil matrix by exchanging water because of the pressure head differences. Under the equilibrium conditions, the suction in the crack medium and soil matrix can be assumed to be identical for both saturated and unsaturated conditions[10] . The hydraulic properties for the two mediums can be regarded as independent existence. 2.1 SWCC and Permeability Function for the Soil All hydraulic properties are closely related to the pore-size distribution of a porous medium. Studies have shown that the spatial distribution of the crack and pore structure is self-similar at certain scales[11-13] . Xu and Dong[11] established a theoretical basis for predicting the hydraulic properties of the unsaturated soil from the fractal model:

30 20 10

Drying process Wetting process

0 10−2 10−1 100 Fig. 5

101 102 103 104 105 ps/kPa

SWCCs for the soil

J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44

39

space, Eqs. (7) and (8) can be re-written as

2.2

SWCC and Permeability Function for the Crack Equations (2) and (3) are applicable to all porous media that behave in accordance with the capillary law. Based on the capillary theory and Sierpinski space hypothesis[17-18] , Eqs. (2) and (3) are valid for the water retention characteristics of the cracks. If the crack medium is not fully saturated, the water in the crack will be held under the surface tension. It is assumed that the pore air is connected to the atmosphere, the height of the water column under the surface tension is hc =

2σ cos α , γw r

kwc

2σ cos α , r

(6)

where pw is the pore water pressure. Eq. (6) into Eqs. (2) and (3) yields

Substituting

3−D 2σ cos α , ps rmax  11−3D 2σ cos α = ksc , ps rmax

r3−D ϕc = ϕsc 3−D = ϕsc rmax kwc = ksc

r11−3D 11−3D rmax

(9)

(10)

where f1 (w), f2 (w) and f3 (w) are the curve relationships between the morphological parameters D, rmax , δc and the water content, respectively, and they are derived from the curves shown in Fig. 6. Based on the experimental results in Subsection 1.2, the relationships between the crack porosity, the crack fractal dimension and the maximum crack width with the water content can be developed and shown in Fig. 6. The morphological parameters fi (w), i ∈ Z can be derived from the experimental results. In this study, the cracks are assumed to be nondeformable in a very short period during the dryingwetting process, and the SWCCs at various soil water contents can be combined for the cracked soil considering the crack volume changes. Figure 7 illustrates the three-dimensional (3D) diagram with a proposed procedure to obtain the SWCCs and permeability functions considering the crack volume changes. The procedure is described as follows. (1) The SWCCs and permeability functions for the crack medium can be predicted based on the fractal model (Eqs. (9) and (10)). (2) The SWCCs (or the permeability functions) for the cracks corresponding to the morphological parameters shown in Fig. 6 at the specified state can be obtained at a certain state corresponding to certain soil water content. Figure 8 shows the SWCCs at different states in the ps -ϕc plane. The soil water content at crack porosity δc,i is wi .

(5)

where hc is the height of the water column, γw is the unit water weight, α is the contact angle, and σ is the surface tension. When the pore air pressure pa is not zero, an isolated water phase can exist in the crack medium and the following equation can be obtained: p s = pa − pw =

 2−D r2−D 0.072 8 = ϕ = sc 2−D ps rmax rmax 2−f1 (w)  0.072 8 , f3 (w) ps f2 (w)  8−3D r8−3D 0.072 8 = ksc 8−3D = ksc = ps rmax rmax 8−3f1 (w)  0.072 8 , ksc ps f2 (w)

ϕc = ϕsc



(7) (8)

where rmax is the maximum crack width, ϕc is the volumetric water content of the cracks at suction ps , ϕsc is the volumetric water content of the cracks when the cracks are fully saturated (it is in fact the crack porosity δc and equals the ratio of the crack area to the total area of the soil mass containing these cracks), ksc is the saturated crack permeability coefficient, and kwc is the crack permeability coefficient at suction ps . Given σ = 72.8 kN/m at 20 ◦ C and α = 60◦ , for a 2D 1.6

7

6 5

rmax/mm

D

δc/%

1.4

3

1.2

4 2

1 0

10

20 w/%

30

40

1.0 0

10

20 w/%

Drying process, Fig. 6

30

40

0

10

Wetting process

Changes of the morphological parameters with the water content

20 w/%

30

40

40

J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44

δc

(ps,3, ϕc,3)

ϕc,3 δc,3

ϕc

ps,3 Drying path (ps,2, ϕc,2)

ϕc,2 δc,2

ps,2

(ps,1, ϕc,1)

ϕc,1 δc,1

ps,1 ps

O

SWCCs for the crack medium during the crack development process

2 0 10−2

10−1

100 101 ps/kPa (a) w = 6.11%

102

5 4 3 2 1 0 10−2

10−1

100 101 ps/kPa (b) w = 18.72%

102

5 4 3 2 1 0 10−2

3

1.5

0.6

2

1.0

0.4

1 0 10−2

10−1

100 101 ps/kPa (d) w = 28.22% Fig. 8

102

ϕc/%

ϕc/%

ϕc/%

4

ϕc/%

ϕc/%

6

ϕc/%

Fig. 7

0.5 0 10−2

10−1

102

10−1

102

100 101 ps/kPa (c) w = 25.32%

0.2

10−1

100 101 102 ps/kPa (e) w = 29.58% Drying process, Wetting process

0 10−2

100 101 ps/kPa (f) w = 30.16%

SWCCs for the crack network at various water contents

7

(3) The crack development path is obtained according to the relationship between the crock porocity and the soil water content, as shown in Fig. 6(a). The path is shown in Fig. 9. (4) The crack development path and the SWCCs (or the permeability functions) for the cracks are combined at the specified state in the 3D coordinate like Fig. 7. The SWCCs (or the permeability functions) intersect with the crack development path at suctions ps,i . Then, a pair of (ps,i , ϕi ) (or (ps,i , ki )) can be found on the corresponding SWCC (or permeability function).

ϕc/%

5 3 1 0 10−1

Fig. 9

Drying path Wetting path 100

101

102 103 104 105 ps/kPa Crack development path during the drying-wetting process with the suction change

J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44

41

(5) The pairs of (ps,i , ϕi ) (or (ps,i , ki )) in each SWCC (or permeability function) are connected to create the SWCC (or permeability function) for the crack medium considering the development process of the cracks.

3 The Crack-Pore Dual Media Model According to the study result of National Research Council[19] , there are three major conceptual seepage models in the cracked unsaturated medium. Besides the equivalent porous medium model, the discrete medium model and the dual media model have been used to simulate the seepage in the cracked medium. Among these three groups, the dual media model is the most suitable for studying the changes in a crack seepage field with time[20] . In this paper, a crack-pore dual media model is presented to simulate both water flows in the porous soil mass and cracks. In this model, the porous medium is represented by a 2D quadrilateral meshed element and the crack medium is represented by a one-dimensional (1D) linear meshed element. These two meshes are embedded and the overlapped elements share the same nodes with the same hydraulic head. When the geometry, hydraulic properties, initial condition and boundary condition for the soil and cracks are given, the flow can be simulated. The saturated-unsaturated seepage in a porous medium obeys the Darcy’s Law. The saturated flow through a crack is described by the Hagen-Poiseuille equation[19,21] . The water flux qs between two parallel plates with the opening width of r is qs = −ksc

dH , dl

(11)

where H is the hydraulic head height, and l is the distance. The saturated crack permeability coefficient is defined as ksc =

ρg r2 , μ 12

(12)

where ρ is the fluid density, g is the gravitational acceleration, and μ is the dynamic viscosity of the fluid. Equation (11) shows that the saturated flow in the crack also obeys the Darcy’s Law. It is assumed that the unsaturated flow in the crack also obeys the Darcy’s Law. The flow in the cracked porous medium can be solved by the Richards’ equation. When the compressibility of the water phase is neglected, 2D governing equation with hydraulic head can be expressed as     ∂ ∂H ∂H ∂H ∂ kx + ky + Q = mw γw , (13) ∂x ∂x ∂y ∂y ∂t where mw = ∂ϕ/∂pw is the slope of SWCC; Q is the seepage quantity of the node; kx and ky are the saturated hydraulic conductivities in the x and y directions, respectively. The terms mw , kx and ky are the nonlinear functions in the unsaturated zone. During the process of numerical solution, mw is interpolated from the SWCC, and kx and ky are interpolated from the hydraulic conductivity function in each element. In addition, in the saturated zone, kx and ky are the saturated hydraulic conductivities.

4 Use of the Crack-Pore Dual Media Model to Simulate Seepage 4.1 Geometry and Finite Element Mesh As shown in Fig. 10, a soil flowerpot with water ponding on the soil surface is used as an example. The horizontal length and the vertical depth of the computational model are 0.3 m. The region is divided into 20 sections with the length of 0.015 m in the horizontal and vertical directions, respectively. There locate 92 linear 1D crack elements of 0.002 m wide and 0.015 m long in the middle part. The width of the crack element changes with the water content, as shown in Fig. 6(c). The 1D crack elements are embedded into the 400 2D elements for the soil mass. The overlapped 1D and 2D elements have the same node number and different element number in the whole finite element mesh. Point III

0.3

A

B

0.3

Point II

Point I

A' B' (c) Grid map of rock and soil containing cracks Grid maps of the computational model of the soil containing cracks (m)

(a) 1D crack element Fig. 10

0.015 (b) 2D soil element

Point IV

42

Two vertical sections (A-A and B-B ) and four key points (I, II, III and IV) have been selected to illustrate the distribution of the pore-water pressure. Section AA is 0.015 m from the left boundary, and Section B-B is at the centre of the model. The crack network is symmetrical in this model, so Points I, II, III and IV are located in the upper, bottom, middle parts of the model, respectively. 4.2 Soil and Crack Properties For the cracked soil, the hydraulic properties are closely related to the pore-size distribution. For the crack part, the pore-size distribution refers to the distribution of the crack volume with respect to the crack aperture. The cracks are assumed not to vary with deepness in this study. Therefore, the pore-size distribution of the cracks can be obtained by the surface crack morphological parameters, such as crack porosity, crack fractal dimension and crack width. The saturated volumetric water content of the soil is 0.45. The SWCC of the soil mass is described by the fractal model, as shown in Fig. 5. For the soil mass, the saturated hydraulic conductivity is 0.5 µm/s and its hydraulic conductivity function is estimated by fractal model as Eq. (3). The crack volume is defined by the crack length multiplying opening. When the cracks in the soil are full of water, the saturated volumetric water content of the crack is 100%. For the crack, ν is the kinematic viscosity of water (defined as μ/ρ) and it is 0.896 mm2 /s at 25 ◦ C. Then, the saturated hydraulic conductivity of the crack is about 3.6 m/s. The hydraulic conductivity function of the crack medium is presented in Eq. (10). 4.3 Initial and Boundary Conditions for the Model Calculation The left and right boundaries are both impermeable. The top boundary has been divided into two stages. In the first stage, the water head has been set to 0.1 m for the first 5 min. Then in the next 180 min, the top water head has been set to zero. At the bottom of the model, there is a hole with 0.06 m diameter in the centre. All the other bottom boundaries are modeled to be impervious except for the hole. Like the boundary at the top, the boundary conditions for the hole have also been modeled in the two stages. In the first stage, the hole is set to a flux boundary and the pore pressure head is set to zero in the second stage. The initial water level is at the bottom of the pot, and the maximum negative pore pressure is −98 kPa. 4.4 Discussion The two stages for rainfall infiltration are simulated, and the pore water pressure results are presented. The pore water pressure contours at the end of the first stage in the soil are illustrated in Fig. 11(a). The cracks have significant impact on the infiltration through the soil. The permeability of the crack is much greater than the permeability of the soil mass, and the

J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44

water is totally absorbed into the crack and flows out of the hole at the bottom of the pot. The shape of the pore water pressure contours is similar to the shape of the cracks. The water quickly flows to the bottom from the crack channel before the soil around the cracks has enough time to absorb the water. Hence, the pore water pressure of the soil remains negative. The water is absorbed slowly and then rises due to the capillary forces with time. The pore water pressure then rises towards equilibrium. Figure 11(b) shows the pore water pressure contours in the cracked soil at the end of the second stage. −2.8 −2.2 −1.8 −1.4

0 −20 −40 −60 (a) After 5 min Fig. 11

−1.0 −0.6 −0.2 (b) After 185 min

Contours of the pore water pressure (kPa)

The pore water pressure distributions with time at Section A-A are illustrated in Fig. 12(a). The pore water pressure at the top quickly rises from −80 to 0 kPa as the water starts to infiltrate. For the soil above 18 mm depth, the pore water pressure changes from 0 to −78.5 kPa with the increase of the height in 2 min. However, for the soil below 18 mm depth, there is little change in the pore water pressure because the wetting front has not reached there. After 5 min, the changes in the pore water pressure are mainly within the soil above 16.5 mm, as the wetting front continues to move downwards. In the second stage, since there is no hydraulic head at the top, the water moves deep into the soil through the cracks. For this part of the soil, the pore water pressure becomes negative. At the same time, the soil near the bottom absorbs water under the capillary forces. This characteristic results in a balance in pressure. Hence, at about 65 min, the pore water pressure distribution curve comes near to a straight line. With further infiltration, the pore water pressure begins to increase. After about 185 min, this pressure stabilizes at around zero. The pore water pressure distributions with time at Section B-B are illustrated in Fig. 12(b). The changes of the pore water pressure are similar to those of Section A-A . Because Section B-B is located at the centre of the model and affected by the crack on both sides of it, the variation of the wetting front is not so regular. Nevertheless, the general trend for the wetting front is downwards. After 3.5 min, the pore water pressure

J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44

0 min 2 min 5 min 12 min

0.35

43

25 min 65 min 125 min

0.35 0.25 H/m

H/m

0.25 0.15 0.05 −0.05 −90

0 min 0.1 min 0.5 min 2 min 5 min 8 min

25 min 105 min 185 min

0.15 0.05

−70

−50 −30 pw/kPa

−10

10

−0.05 −90

−70

(a) Section A-A'

−10

10

(b) Section B-B'

Variations of the pore water pressure with time along two vertical sections

reverses from negative to positive. The distribution map coincides with that at the end of 5 min, and the soil located in all nodes of Section B-B is saturated. Due to the subsequent drainage, the pore water pressure gradually decreases and becomes negative again. The final pressure decreases to zero at about 185 min because of the capillary forces. Figure 13 shows the pore water pressure at four key points. Point I is relatively far away from the cracks. Therefore, the pore water pressure at Point I is not seriously affected by the quick infiltration of the water in the cracks. The pressure at Point I is slightly negative. Point II is along the same section as Point I. Compared to Point I, it responds quicker to the change in the pore water pressure, because it is in the upper part of the soil and near to a crack on the left side. The pore water pressure at Point II increases from −78.5 to −3.43 kPa in 5 min. Point III is at the same elevation as Point II. Since Point III lies between two cracks on the left part of the soil, the pore water pressure increases from −78.5 to 0.441 kPa in the first 5 min. Point IV is at the same elevation as Point I with the cracks on the left and right sides, and the cracks are symmetrical. Hence, its response to the change in the pore water pressure is faster than that at Point I. After the first 5 min, the pore water pressure at Point IV increases from −78.5 to −2.21 kPa. However, the response at Point IV is slower than that at Point III because Point IV is at the lower part of the soil. Point I is always unsaturated in the ponding infiltration, drainage and capillarity process. Capillary action dominates in Point I. Points II, III and IV are affected by the crack network obviously. During the ponding infiltration process, the pore water pressure in these three points responds quickly to time. In the next drainage process, the moisture is lost and the pore water pressure decreases to about −10 kPa. In the bottom part of the model, the pore water pressure rises back and trends to zero because of the capillarity.

Ponding 10 infiltration process

Drainage and capillarity process

−10 pw/kPa

Fig. 12

−50 −30 pw/kPa

−30 −50

Point Point Point Point

−70 −90 100 Fig. 13

101

102

t/s

103

104

I II III IV 105

Variations of the pore water pressure with time in key points

5 Conclusion In this paper, an experimental study has been conducted to investigate the dynamical development of the cracks in the soil under the drying-wetting cycle. The relationships between the crack morphological parameters and the water content are presented by using the information from the experiment. The SWCCs and permeability functions for the cracks including the dynamical development process have been predicted according to the fractal model. By the predicted SWCC and the permeability function, a conjunctive crack-pore dual media model is presented to simulate the ponding infiltration in the cracked soil. The simulation results show that the pathways provided by the cracks significantly increase the hydraulic conductivity of the expansive soil. The bottom part of the cracks quickly becomes a saturated zone. As a consequence, the pressure head rises and the suction decreases in this zone. This is the cause of most of the expansive slope failures in the vicinity of cracks. The calculation result illustrates that the prediction of the SWCCs and permeability functions for

44

the cracked soil is reasonable.

References [1] XU Y, ZHANG L M. Breaching parameters of earth and rockfill dams [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2009, 135(12): 19571970. [2] TALBOT J R, DEAL C E. Rehabilitation of cracked embankment dams [C]//Proceedings of Geotechnical Practice in Dam Rehabilitation. North Carolina, USA: ASCE, 1993: 267-283. [3] YAO H L, ZHENG S H, CHEN S Y. Analysis of the slope stability of expansive soils considering cracks and infiltration of rainwater [J]. Chinese Journal of Geotechnical Engineering, 2001, 23(5): 606-609 (in Chinese). [4] LI J H. Field experimental study and numerical simulation of seepage in saturated/unsaturated cracked soil [D]. Hong Kong, China: Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, 2009. [5] ZHANG L M, FREDLUND D G. Characteristics of water retention curves for unsaturated fractured rocks [C]//Proceedings of the Second Asian Conference on Unsaturated Soils. Osaka, Japan: ASIA, 2003: 425428. [6] BURGER C A, SHACKELFORD C D. Soil-water characteristic curves and dual porosity of sanddiatomaceous earth mixtures [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2001, 127(9): 790-800. [7] MILLER C J, MI H, YESILLER N. Experimental analysis of desiccation crack propagation in clay liners [J]. Journal of the American Water Resources Association, 1998, 34(3): 677-686. [8] VOGEL H J, HOFMANN H, ROTH K. Studies of crack dynamics in clay soil: Experimental methods, results, and morphological quantification [J]. Geoderma, 2005, 125: 203-211. [9] TANG C S, SHI B, LIU C, et al. Influencing factors of geometrical structure of surface shrinkage cracks in clayey soils [J]. Engineering Geology, 2008, 101(3/4): 204-217.

J. Shanghai Jiao Tong Univ. (Sci.), 2017, 22(1): 35-44 [10] PETERS R R, KLAVETTER E A. A continuum model for water movement in an unsaturated fractured rock mass [J]. Water Resources Research, 1988, 24(3): 416-430. [11] XU Y F, DONG P. Fractal approach to hydraulic properties in porous media [J]. Chaos, Solitons and Fractals, 2004, 19(2): 327-337. [12] RIEU M, SPOSITO G. Fractal fragmentation, soil porosity, and soil water properties: Theory [J]. Soil Science Society of America Journal, 1991, 55 (5): 1231-1238. [13] GUARRACINO L. A fractal constitutive model for unsaturated flow in fractured hard rock [J]. Journal of Hydrology, 2006, 324(1/2/3/4): 154-162. ´ [14] LEON C A L Y. New perspectives in mercury porosimetry[J]. Advances in Colloid and Inteface Science, 1998, 76: 341-372. [15] SHENG Y G, XU Y, LI Z H, et al. Determination of fractal dimensions of silicon dioxide xerogel by means of gas-adsorption [J]. Acta Physica Sinica, 2005, 54(1): 221-227 (in Chinese). [16] PHAM H Q, FREDLUND D G, BARBOUR S L. A study of hysteresis models for soil-water characteristic curves [J]. Canadian Geotechnical Journal, 2005, 42(6): 1548-1568. [17] REITAM S, KUPER B H. Laboratory measurement of capillary pressure-saturation relationships in a rock fracture [J]. Water Resources Research, 1994, 30(4): 865-878. [18] REN Q, XU W Y. Fractal model for unsaturated seepage flow in fractured rock masses [J]. Rock and Soil Mechanics, 2008, 29(10): 2735-2740 (in Chinese). [19] National Research Council. Conceptual model of flow and transport in the fractured vadose zone [M]. Washington: National Academy Press, 2001. [20] ZHANG Y T. Rock hydraulics and engineering [M]. Beijing: China Water Power Press, 2005: 243-244 (in Chinese). [21] CURRIE I G. Fundamental mechanics of fluids [M]. New York: McGraw-Hill, 1993.