Theoretical Model and Numerical Analysis on Unsaturated Expansive Soil Slope during Digging and Climate Change Courses (II)-Numerical Analysis

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1 The 12 th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6 October, 2008 Goa, India Theoretical Model and Numerical Analysis on Unsaturated Expansive Soil Slope during Digging and Climate Change Courses (II)-Numerical Analysis CHEN Zheng-han Logistic Engineering University,Chongqing,P R China;Key Lab. for the Exploitation of Southwest Resources & the Environment Disaster Control Engineering, Ministry of Education, Chongqing 1, P R China LU Zai-hua Navy University of Engineering,Wuhan,P R China GUO Jianfeng, FANG Xiang-wei, ZHOU Hai-qing Logistic Engineering University,Chongqing,P R China Keywords: unsaturated soil, expansive soil, slope, digging, raining, evaporating, damage, numerical analysis ABSTRACT: In order to investigate the sliding mechanism and process of expansive soil slope during digging and raining-evaporating courses, a FEM program named UESEPDC was designed based on the elasticity-plasticity-damage constitutive model and the elasticity-plasticity-damage consolidation model of unsaturated expansive soil proposed by the authors, and the numerical analysis on solid-liquid-gas tri-phases and multi-field couple problem was conducted for four stages: 1 Raining and evaporating before digging; 2 The moment at digging finishing; 3 Three days after digging finishing; 4 Multi- raining-evaporating cycles. The fields of stress, displacement, pore water pressure, pore air pressure, water content and suction in an expansive soil slope were obtained, and the pictures of crack damage evolution and plastic zone development in the same expansive soil slope for each analysis stage were shown. The research results clearly reveal the mechanism of expansive soil slope sliding progressively. 1 Introduction In the China s Western Development and South-North Water Transfer Project, expansive soil road bed and slope attract a great deal of attention. As a typical unsaturated soil with over-consolidation, swelling-shrinkage and fissure, expansive soil whose deformation and strength vary acutely with the weather change can bring heavy damage to engineering. It is indicated by the researches that expansive slope is stable in the early days after digging, and then the slope will lose its stabilization and slide in the condition of the weather changing repeatedly. In this course the soil mass of the slope actually suffers a series of complex change events: digging and unloading, evaporating and dry cracking, raining and infiltrating, expanding and deforming, fissure closing partly, evaporating again, fissure enlarging more, the properties of soil deteriorating, etc. In the course of rainfall infiltration, the solid, liquid and gas in the soil are moving, and the water content, degree of saturation, suction, stresses and strength at each point are varying too. So only through the tri-phase and multi-field couple analysis on expansive slope during climate changing,the dynamic simulation of the slope from stabilization to slide can be carried on, and the movement laws of each phase and each state parameter can be found out, then the sliding mechanism of the slope can be brought to light. Recent years the authors devoted to the researches of unsaturated soil and expansive soil. For example, the authors established successively the theories of unsaturated soil about consolidation, nonlinear constitutive relationship, generalized soil-water characteristic curve, nonlinear consolidation model and elasticity-plasticity consolidation model. The authors also investigated systematically the deformation, strength, constitutive relationship and numeric analysis of expansive soil; developed a CT-triaxial equipment with which the law of constructive damage evolvement of unsaturated expansive soil during the course of loading and drying-wetting cycles is investigated, and presented the elasticity-plasticity-damage constitutive law and the elasticity-plasticity-damage consolidation model of unsaturated expansive soil, which offered a basis of the tri-phase and multi-field couple analysis on unsaturated expansive soil slope. In this article, using the 618

2 elasticity-plasticity-damage consolidation model of unsaturated expansive soil established in Reference [18], the problems of unsaturated expansive soil slope during digging and raining-evaporating cycles, such as evolution of fissure damage, stresses, deformation and development of plastic zone, are analyzed, and the failure mechanism of expansive slope and sliding gradually is discussed, then the theoretic basis for designing, constructing and early forecasting the losing stabilization and sliding of an expansive slope can be provided and available. 2 Scheme and Method for Numerical Analysis Based on the elasticity-plasticity-damage consolidation model of unsaturated expansive soil established in Reference [18], applying the Galerkin weighted residual method and the concept of finite element, a 2-D finite element expression of the control equations can be obtained and a FEM program named UESEPDC which is composed by 33 subprograms is designed. The details of the program can be seen in Reference [19]. Using this program, a numeric simulation of an unsaturated expansive soil slope during digging and raining-evaporating cycle courses was carried on. And the analysis was conducted for four stages: 1 Rain and evaporation acting on the expansive soil site before digging (one raining-evaporating cycle); 2 The moment at digging finishing; 3 Stress adjustment after digging finishing (for three days); 4 Multi- raining-evaporating cycles action on the site (four times cycles). The discrete of the expansive soil site was performed with quad elements. Fig. 1 and Fig. 2 show the finite element meshes of the slope before and after digging. The section computed is 25 meters high and 48 meters wide. The height of the dug slope is 10 meters and the gradient is 1:2. There are 280 elements and 313 nodes in the model. The spatial discrete and time discrete are included in consolidation computation. The shape functions of the pore water pressure and the pore air pressure are same as the displacement s. Assuming t as time from consolidation beginning to any moment later, Δ t as time step, the finite element equation at t + Δt is formulated as: MELES NNODE MELES t+δt t+δt t+δt [ Kij ] e { X i} e = { Ri} e ( i = 1,2LL NNODE) (1) e= 1 j= 1 e= 1 Where MELES is the number of total elements of the structure, NNODE is the number of all nodes in an element. Here, 4 nodes isoparametric element is applied, i.e. NNODE=4. Because a node possesses four freedoms (horizontal displacement, vertical displacement, pore air pressure, pore water pressure), the size of element t+δt stiffness matrix is 16 16, and the size of every sub-matrix [ K ij ] e contained 16 elements is 4 4. It must be noticed that t and Δ t is contained in global stiffness matrix and load vector. Therefore, if the displacement and pore pressures at the moment t are known, the values at the moment t + Δt can be calculated by modify global stiffness matrix and load vector. Figure 1. Finite Element Meshes Before Digging 619

3 Figure 2. Finite Element Meshes After Digging The Constant Stiffness Initial Stress Method is applied in elasticity-plasticity-damage computation. In every time step the elastic-plastic damage is calculated as follows: 1 Regard both of undamaged and complete damaged parts as elastic bodies first in every load step, and calculate the strains increment and elastic stresses increment in two parts of the soil mass by the global elastic damage stiffness matrix; 2 Derive the total stresses of complete damaged part, undamaged part and elements at current iteration from adding the stresses increment to the stresses at previous iteration 3Regard the stresses increment as plastic stresses increment and recalculate the total stresses of elements if the stresses of complete damaged part exceed the value determined by yielding condition. 4Calculate the elastic equivalent nodal forces and plastic nodal forces on yielded elements by the basic variables of each nodes of the elements, and the equivalent nodal forces needed re-assignment are the difference between them. The entire structure s equivalent additional loads are determined by adding the nodal equivalent forces at same node for all elements. 5 Repeat the computations above until converging on all elements. 6 Calculate the hardening coefficient and damage increment based on volumetric strains increment, apply next load increment until loading finished. 3 Parameters According to Reference [19], the relative parameters are given as follow: 3.1 Complete Damaged Part The parameters associated with LY yield surface: k, λ (0), r, β, p c, M,κ and G, is given in Table 1. k (0) Table 1 Parameters Associated With LY Yield Surface λ r β p c The parameters related to shear yield surface SY: a and M 2, respectively equal 0.2 and 1.1. The parameters corresponding to the change of suction: k s, t i, M κ G [kpa] [kpa] td and n, respectively equal 0.008,, Undamaged Part There are 10 parameters for undamaged part, i.e. c, ϕ, c, ϕ, b ϕ, t d, n, 0 k, m, m 1, μ and R f. Where, b ϕ can be determined by triaxial drained shear test, and respectively equal 22.7kPa, 17.30, 10.60; the value of t d and n is same as the complete damaged part; μ and assigned to 0.3 and 0.6; 0 k, m and m 1 respectively equal 203.5, 0.1 and R f are constants and respectively 3.3 Damage Evolution The parameters of damage evolvement: A and Z, derived from the data of CT test, respectively equal 3.9 and

4 3.4 Water Quantity Change The parameters of water quantity change: β s and β p, respectively equal / kpa and 4 % [6] 3.5 Permeability Coefficients The permeability coefficients of water and air, K w and K a, vary throughout the course of rainfall, evaporation and consolidation. Whereas they are regard as constants there to simplify computation, and respectively assigned to cm/s and cm/s. 4 Initial and Boundary Condition 4.1 Soil Indicator of Initial state And Initial Stress Condition Assuming the initial state in entire expansive soil site is uniform, and the initial values of suction, damage, specific volume, water content and air pressure respectively equal 50.0 kpa, 0.25, 1.75, 22.5% and 0 kpa. Generally the over-consolidation of expansive soil is stronger, and the horizontal stresses of the soil mass in shallow strata are larger than the vertical stresses. Considering that the soil in deep strata do not possesses the property of over-consolidation, the initial ground stresses in expansive soil with over-consolidation are formulated as: 60.0 (0 z 3.0 m) σ z = γ z (3.0m < z < + ) 2.5γ z (0 z 4.0 m) σ x = 0.5γ z + 7 z (4.0m < z < 23.0m) (2) 0.8γ z (23.0m < z) * The hardening parameter of elasticity-plasticity-damage model, p 0, which is the initial yield net average stress in saturated state, can be calculated from the initial yield net average stresses in each element. The hardening p parameter, ε s, is equal to 0.5% for all elements. 4.2 Boundary Condition The boundary condition of a boundary value problem of expansive soil can be divided into four categories: 1 Force: the loads applied on boundary nodes; 2 Displacement: the given values of displacements on boundary nodes; 3 Pore water pressure and pore air pressure: the water pressures and air pressures on boundary nodes are known; 4 Flow Discharge: the moisture permeating and evaporating at the boundary nodes are assigned. The forces and displacement boundaries are generally dealt by the method of elastic-plastic mechanics, i.e., the horizontal displacements of the boundary nodes on lift and right sides of computation section are restricted and both of the horizontal and vertical displacements on the bottom of the section are restricted. The top of the section, shown in Fig,1 and Fig. 2, is permeable to air and water, and the air pressures on the top of the section is zero because of connecting the atmosphere; the left and right sides of the section is impermeable to air and water, where the air pressures and water pressures vary freely in all stage. The nodal water pressures on the top boundary also vary freely in the stage of raining-evaporating and at the moment of digging finished; in the stage of stresses adjustment after digging, the nodal water pressures and air pressures on the top boundary are both assumed as zero. 4.3 Rainfall Infiltration and Evaporation Condition The flow of raining and evaporating is very complicated in the condition of real weather. So here it is simplified as: the raining continuing for three days, and then evaporating lasts for three days too. This is one drying-wetting cycle. The moisture seepage rate is 8 mm/day during raining course, same as the evaporation rate during evaporating course. The accumulated seepage discharge and the accumulated evaporation discharge for three days both are 24 mm. The flow loads are applied on the nodes of the top boundary. The inverse nodal forces induced by digging are calculated by the program, and are applied on the nodes on the left two segments of the top boundary in Fig

5 5 Result and Analysis The computation was conducted for four stages: 1 Raining and evaporating before digging; 2 The moment at digging finished; 3 Three days after digging finishing; 4 Multi- raining-evaporating cycles. Fig. 3~ Fig. 6 show the computing results at the moment of digging finished, Fig7~ fig.9 show the computing results at 72h after digging finished, and Fig. 10~ Fig.20 show the results at 72h after rainfall or evaporation. For convenient the time associated with each figure is not explained later. 5.1 The Result before Digging In this stage there is only one raining-evaporating cycle as mentioned above, and the accumulated seepage discharge is assumed to be equal to the accumulated evaporation discharge. The computing results indicated that the water content and suction of the soil go back to the initial values at last. For example, the initial value of suction is 50 kpa, after raining the suction of shallow strata declines to 36 kpa, then recovers 50 kpa after evaporating. Because the suction fluctuation is smaller (only 14 kpa) and the stresses of soil mass change very small, so they will not be discussed more in this article. The initial value of damage is 0.25, the value of surficial damage become after raining and evaporating. However, the amount of ground heave induced by raining is about 8 mm, approximately equal to the depth of ground settlement induced by evaporating, about 7.5 mm. The site is like taking breath. And this accords with the fact observed in expansive soil slope. 5.2 The Result at The Moment Of Digging Finished The shear stresses field, damage field and plastic zone at the moment of digging finished are shown in Fig.3, Fig. 4 and Fig. 5. The shear stresses induced by digging increase obviously. The shear stress is larger at the foot of slope than at the other places of the slope, up to kpa. The farther the distance is from the foot of slope, the smaller the shear stresses of the earth mass is. The damage evolution induced by digging is remarkable. The damage increments at the slope border and the slope foot are largest (the damage value at the foot of slope is up to ). This fits in with the distribution of shear stresses. And after digging the soil mass at the foot of slope yields first due to stress concentration, this accords with existing knowledge. The distribution of horizontal displacement increments is illustrated in Fig. 6. All of the horizontal displacements are negative. This means that the earth mass moves toward the free face. And the horizontal displacements at the middle of the slope are larger than other places, the most largest value is up to 8-9 cm. The changes of moisture and suction are small, and no longer described here Figure 3 Shear Stress At Moment Of Digging Finish(kPa) 622

6 Figure 4 Damage Value At Moment Digging Finished Figure 5 Plastic Zone At The Moment Digging Finished Figure 6 Horizontal Displacement At The Moment Gigging Finished(m) 623

7 Figure 7 Shear Stress Distribution After Stress Adjustment(Unit:kPa) Figure 8 Damage Field Distribution After Stress Adjustment Figure 9 Horizontal Displacement increments After Stress Adjustment (Unit: m) 5.3 The Results at 72h after Digging Finished Through stresses adjustment for three days after digging finished, the shear stresses of slope increase further (Fig. 7), and the shear stress at the foot of slope is up to kpa. The damage of soil structure becomes heavily, the damage value at the foot of slope increases to (Fig. 8). And the horizontal displacements increase to 9-10 cm (Fig. 9). But the plastic zone expands slightly, so the figure is omitted. 624

8 5.4 The Results for Slope Undergoing Several Raining-Evaporating Cycle The Results for Slope Undergoing First Raining The developments of water content, suction, horizontal stress, damage and plastic zone for slope undergoing the first raining are illustrated in Fig. 10~Fig. 14. After rainwater seep into soil mass, the water content in shallow strata increases obviously (Fig. 10), and the suction decreases (Fig. 10). But both of them do not vary in deep strata. The horizontal stresses of the strata on the slope top, slope surface and upper of slope base increase with soil mass expanding, and the horizontal stress increment on the foot of slope is largest (Fig. 12). The horizontal stresses in lower strata vary insignificantly. Raining induces the mechanical properties of soil deteriorate, thus all of the damage values of shallow strata on the top, surface and foot of the slope increases (Fig. 13). With the suction declining, the shear strength decreases and the anti-deformability fade out, then more elements yield. The plastic zone expands towards inner of the slope (Fig. 14), so that the diseases of slope such as landslide etc. will be induced. These is in accordance with the phenomena that expansive soil slope slide most in the rainy season. Because of raining the soil mass in shallow strata expand upward, and the ground rises obviously (Fig. 15). To a great extent, no shear stresses increase due to raining (figure omitted), and the vertical stresses on the top and the base of the slope do not vary too (figure omitted). However, the vertical stresses in the shallow strata increase some few. The main reason inducing to the vertical stresses increments in the shallow strata is that the soil mass on the top can expand freely while the soil mass in shallow strata beneath the slope surface expands few because it is restricted in vertical direction by the top-right soil mass of the slope Figure 10 The Water content Of Dug Slope After First Raining (%) Figure 11 The Suction Of Dug Slope After First Raining(kPa) 625

9 Figure 12 The Horizontal Stresses of Dug Slope After First Raining(m) Figure 13 The Damage Value of Dug Slope After First Raining Figure 14 The Plastic Zone of Dug Slope After First Raining 626

10 Figure 15 The Increments of Vertical Displacement of Dug Slope After First Raining(m) Results of Dug Slope After First Raining-Evaporating Cycle After evaporating the suction increases, the water content decreases, and the contours of equal suction approximately parallel the top boundary. The expansive soil mass generates desiccation deformation, both of the horizontal and vertical displacements are negative. These illustrate the slope shrinks in horizontal and sinks in vertical (Fig. 16), moreover the vertical displacement contours approximately also parallel with the top boundary. The horizontal stresses of shallow strata near lower boundary declines, and change few far away the top boundary. Because the shear strength and the capability of anti-distortion are enhanced and horizontal stresses reduce due to the earth mass shrinking, the number of elements yielded declines and the plastic zone becomes smaller (the figure omitted). The damage values of shallow strata under top of the slope increase some few. (Fig.17), which is obviously induced by the crack extends after desiccation of the earth mass. The horizontal displacements of the soil mass distribute as that after raining, but the direction is inverse. In Ref. [20] an observation was carried on to watch the deformation of an expansive soil affected by weather in Xunxian, Hubei province, and the deformation characteristics of expansive soil slope can be summarized as follow: 1 The curves of expanding-shrinking and rising-declining of the slope, cycled one time a year, were synchronous with the curve of water content change, but lagged the later. 2 When the water content increase, the earth mass expand, and the vertical deformations rise up, the horizontal deformation extends toward outer of the slope. On the other hand, when the water content decrease, the earth mass shrinks, and the vertical deformations go down, the vertical deformations shrink toward the inner of slope. 3 Generally the deformations at the slope border are larger than those in the middle of slope, and the deformations in the middle of slope are larger than those at the foot of slope. 4 The amount of deformation decreases along with the depth increasing. Except for the third point, the numerical analysis results mentioned above in this article agree well with the observation. Figure 16 The Displacement Vector graph of Dug Slope After First Evaporating 627

11 Figure 17 The Damage Values of Dug Slope After First Evaporating The Results of Dug Slope in Subsequent Raining-Evaporating Cycles It is assume that four raining-evaporating cycles applied on the dug slope. The computing results show that the water content field, suction field, stresses field, displacement field, damage field and plastic zone development during the second, the third and the forth dry-wet cycle vary as those during the first cycle, i.e.: Raining Stage: the horizontal stresses of the soil mass on the top, surface and foot of the slope increase due to the soil mass expanding, and the horizontal stress increments on the foot of the slope is greatest, but the horizontal stresses in the lower strata have no changes to a great extent. On the top and base of the slope, the vertical stresses vary few, but increase to some extent in the shallow strata beneath the surface of the slope. The shear stresses distribution has almost no changes. The plastic zone extends toward inner slope. And all of the damage values on the border, surface and foot of the slope increase. In the earth mass of shallow strata, the water pressure increases, the air pressure keeps steady, the suction decreases obviously, the water content augments, but in the deep strata all have no changes. Raining induces the soil mass in shallow strata expanding upward, and the ground rises obviously. But the horizontal displacements are smaller. The earth mass on the border, top and surface of the slope move towards left, the right-hand earth mass of the foot of the slope moves towards right. Evaporating stage: After evaporating the drying shrinkage deformations are presented in the expansive soil. The horizontal stresses in the shallow strata beneath the top boundary decrease, but are almost unchanged far away from the top boundary. The vertical stresses vary little in the earth mass. And the shear stresses in right side of the earth mass decrease slightly. The plastic zone reduces. The damage values of the shallow strata beneath the top increase some few. After evaporating the surface of slope settles, and the displacement contours parallel the top boundary line by and large. The water pressure increment in the soil mass of shallow strata beneath the top boundary is negative, the pore water pressure declines, the suction increases, the water content decreases, and the contours of suction tend to parallel the top boundary line Figure 18 The Shear Stresses Distribution After The Forth Raining Unit:kPa) 628

12 Figure 19 The Damage Field After The Forth Raining Figure 20 The Plastic Zone After The Forth Raining Here only the results after the forth raining are illustrated bellow and only the dry-wet cycles influences to the deformation and stability of slope are analyzed. In Fig.18~ Fig.20 the shear stresses, damage and plastic zone after the forth raining are shown. Compared them with the relative figures during the former raining-evaporating cycle, it is concluded that: the shear stresses of the whole slope vary few, only the shear stresses on the slope surface above of the slope toe increase slightly. The damage values present clear trend of evolvement. The damage value in the earth mass near the foot of slope increases to 0.8. The contour line equal to 0.45 gradually extends to approach the slope top, but the contour line equal to 0.4 at the deeper part of the slope almost stays in its original place. The raining and evaporating mainly affect the earth mass near the surface of the slope. With the action of several times dry-wet cycles due to ranging and evaporating, the strata near the surface of slope shrink and expand repeatedly and the degree of cranny damage increases gradually. Being different from the cranny damage in Fig. 4 and Fig. 8, which is induced by the unloading due to digging, the current cranny damage of the earth mass is mostly induced by the shrinking and expanding. After damage increasing, more elements of the soil mass yield with the deterioration of the mechanical properties of soil mass even when the shear stresses have no changes. The plastic zone of the slope gradually extends from the foot to the surface and top of the slope. The above results of numeric analysis illustrated: The digging induces the shear deformation and the shear cranny damage in the slope. During the raining-evaporating cycles subsequent, the cranny damage in the soil mass beneath the surface of the expansive earth mass due to shrinking and expanding increases gradually, and the mechanical properties of the earth mass deteriorates. So the plastic zone develops gradually along the shallow strata near the surface of the slope, the deformation increases and then the collapse and landslide take place. In Ref. [20] the failure mechanism of slope is analyzed as follow: The expansive landslide is gestated in dry season and happened in raining season. When drought, the earth mass is heavy desiccated, cracks extend to deeper strata, the mass is broken up further. When raining season coming, the atmospheric water pour into the cracks, the fissure planes are lubricated, and the shear strength of the earth mass decreased, the active earth pressure due to the moist earth mass increases, then sliding occurs. Moreover, the sliding soil blocks often drag down each other, which will result in successive slides, at last a large-scale breakdown is happened. The results of the numerical analysis to canny damage evolvement on expansive soil slope during the course of digging and raining-evaporating cycles in this article describe quantitatively the rules above-mentioned by and large. 629

13 6 Summary Based on the elasticity-plasticity-damage consolidation model of unsaturated expansive soil, through a systemic soil-water-air tri-phases and multi-field couple analysis to an expansive slope during the course of digging and several raining-evaporating cycles, the law of stresses, moisture, displacement, strength, evolvement of canny damage and development of plastic zone in the slope mass and the mechanism of expansive slope losing stability are revealed in this article. And the position and scale of the shallow layer landslide of the expansive slope are also described quantitatively. These possess certain guidance value to the expansive soil slope engineering in the Middle Route of South-North Water Transfer Project and the expressway building projects of the Western China. 7 References Liu Te-hong The problems of expansive soil in engineering, Beijing (China). Institute of the Yangtze River Science Proc on the Canal Slope Stability and Forecast in Expansive Soil Region for the Middle Route Project of South-North Water Transfer, Wuhan (China) Bao Cheng-gang Behavior of unsaturated soil and stability of expansive soil slope. Chinese J of Geotechnical Engineering, 26(1), CHEN Zheng-han, XIE Ding-yi, LIU Zu-dian Consolidation theory of unsaturated soil based on the theory of mixture(), Applied Mathematics and Mechanics(English Ed), 14(2), 127~137. CHEN Zheng-han. 1993, Consolidation theory of unsaturated soil based on the theory of mixture(). Applied Mathematics and Mechanics(English Ed), 14(8), 687~698. ZHOU Hai-qing, Fredlund D G, et al A nonlinear model for unsaturated soil and its application, Chinese J of Geotechnical Engineering, 21(5), 603~608 HUANG Hai, CHEN Zheng-han, Li Gang Research for soil-water characteristics curve and yield locus of unsaturated soil on p-s plane, Rock and Soil Mechanics, 21(4), CHEN Zheng-han, HUANG Hai, LU Zai-hua A non-linear and elasto-plasticity consolidation models of unsaturated soil and applications, Applied Mathematics and Mechanics(English Ed), 22(1), 93~103. LU Zai-hua, CHEN Zheng-han, CAO Ji-dong A study on the strength and deformation characteristics and the constitutive model of natural expansive soils, Rock and Soil Mechanics, 22(3), 339~342. LU Zai-hua, WANG Quan-min,CHEN Zheng-han Test study and analysis on the constitutive relation of unsaturated soil, J. of Ground Space, 21(5), LU Zai-hua, CHEN Zheng-han, SUN Shu-guo Study on deformation and strength characteristic of expansive soil in Nanyang with triaxial tests, Chinese J of Rock Mechanics and Engineering, 21(5), CHEN Zheng-han Coupled nonlinear analysis for air flow and water flow as well as expansive soil deformation of canal slope[c]. In: Proc on the Canal Slope Stability and Forecast in Expansive Soil Region for the Middle Route Project of South-North Water Transfer. Wuhan(China), 68~78. SUN Shu-guo, CHEN Zheng-han, HUANG Hai An analysis method for stability of expansive soil slope considering rainfall-infiltration [C]. In: Proc. on the Canal Slope Stability and Forecast in Expansive Soil Region for the Middle Route Project of South-North Water Transfer. Wuhan(China), 63~67. CHEN Zheng-han, LU Zai-hua, PU Yi-bin The matching of computerized tomography with triaxial test apparatus for unsaturated soils, Chinese J of Geotechnical Engineering, 23(4), 387~392. LU Zai-hua, CHEN Zheng-han, PU Yi-bin Study on damage evolution of natural expansive soil with computerized tomography during triaxial shear test, Chinese J. of Water Conservancy, 6,106~112. LU Zai-hua, CHEN Zheng-han, PU Yi-bin A CT study on the crack evolution of expansive soil during drying and wetting cycles, Rock and Soil Mechanics, 23(4), 417~422. LU Zai-hua, CHEN Zheng-han, PU Yi-bin Quantitative analysis on damage evolution of natural expansive soils during shearing process, Chinese J. of Rock Mechanics and Engineering, 23(9), LU Zai-hua, CHEN Zheng-han, FANG Xiang-wei, ZHOU Hai-qing. Theoretical model and numerical analysis on unsaturated expansive soil slope during digging and climate change course ( I )-Elasto-plasticity-damage constitutive relationship and consolidation model. (to appear) LU Zai-hua Elasto-plasticity-damage constitutive model of unsaturated expansive soil and applications on multi-field coupling numerical analysis for Soil Slope. Logistical Engineering University, Chongqing (China). HOU Shi-tao On expansive soil slope, Chinese J. of Engineering Prospecting, 2,