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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 1, ISSUE 5, JUNE 2012

ISSN 2277-8616

Study On Dam Slope Stability Under The Condition of Rainfall Prof. Sun Keming, PhD Student: Moj Raj Bagale Abstract: Analyze the static simulation of the dam by using the strength reduction principle, get the stress, strain and displacement distribution rule and the corresponding safety factor in the water level change and rainfall infiltration are two working conditions of the reservoir’s retaining dam body respectively, get the displacement of the slip plane when the unstable failure happens on the dam, the influence of the reservoir’s water level on the dam’s safety factor, and the influence of the rainfall infiltration on the dam’s stability; Based on fluid-solid interaction mechanics theory, a coupled mathematical model for describing the slope stability of dam under the condition of rainfall was developed. The model is used to evaluate the safety of the slope. The model simulates the effect of the slope gradient ratio and the slope angle on the slope stability under the different conditions of rainfall in the return periods. Results show that slope safety factor in the different rainfall Conditions decreases with the increase in rainfall of time. Credible provided for designing and appraising stability of the dam, based on the assessment of the effect of slope gradient ratio on the slope stability in the different rainfall conditions of the return periods. Key words: slope stability; coupled mathematical model; numerical simulation, static simulation; fluid-solid interaction ;rainfall infiltration ;slope stability;

1 Introduction The dam slope instability often occurred, which has caused the problem of dam leakage and endanger the environment seriously. One important aspect to the slope stability research is rainfall infiltration effect towards the slope stability. Water increase the soil moisture content, further larger soil force density and finally causes the shear stress of the slip plane increased under the rainfall condition. Meanwhile, rainfall can change mechanical properties of slope soil, which decrease the soil cohesion, further matrix suction and finally shear strength. The two adverse factors of slope soil deadweight increase and strength decrease influence the slope stability simultaneously under the condition of rainfall, which could produce slope landslide as the factors reached a level. Therefore, the study on rainfall infiltration and landslide has the important meaning .The effect of rain condition (rainfall intensity and duration), initial condition and permeability anisotropy of soil on the temporal status infiltration field and slope stability are investigated.

2.1 Fluid-solid Coupling equations of unsaturated soil water flow 1) Stress equilibrium equations (without body force) From the Terzaghi effective stress theory, equation (1) can be ij, j

pf

ij

o

'

1

1 pf ) H

G(

i, j

2

Among it, G=E (1-v)/(1+v)(1-2v), H= E/1-2v Where E is elastic modulus, v is Poisson ratio, is volumetric strain. The solid particles flow along with water when there is seepage action in porous medium; it means that fluid have certain seepage velocity, so do the solid particles, where V is fluid velocity relative to solid particles velocity.

1 .q f .S f

V Where

3

Sf

is porosity;

KK rf ( )

q f is

Darcy

( pf

p f g)

4

f

Where k is absolute permeability tensor of porous medium; f

is fluid density

Liquid K rf follows:

relative permeability, the equation is as

y

r

' 2

K rf r

_______________________ Professor: Sun Keming, PhD Student: Moj Raj Bagale,

y y y2

y dy 5

s

'

y dy

s

C ln e

Department of Engineering and Mechanics: Liaoning Technical University, Fuxin , Liaoning Province, China.

is saturation;

velocity, the equation is as follows;

qf

2 Mathematical Models;

'

2) Constitutive model under the unsaturated media condition

/a

n

m

6

Among them n, m are constants; s is moisture content under saturation condition Liquid equilibrium equation;

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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 1, ISSUE 5, JUNE 2012

.

f

.S f

f .Vr

t

0 7

Solid equilibrium equation;

1

.

s

1

t

. s .Vs

0

8

Fluid-solid Coupling equations under unsaturated condition can be given by simultaneous equations including equation (1), (2),(3),(4)and (7).

K. K . . p f

A

pf t

1

1 Sf

f

0

t 9

A

f

1

Sf

.

2 G1

f

1

f

f s

Sf

,

ISSN 2277-8616

the use of rigid body limit equilibrium method. Internal friction angle is 35°, cohesive force of size is 20Mpa. In this case, it is also divided into two situations are analyzed and compared, in order to get more accurate result and the conclusion. A case is in the natural conditions of the dam slope stability analysis; the other is for dam slope stability considering rainfall effect. The rainfall intensity is 0.2mm / h. (a) Under natural conditions for the slope stability analysis of the dam; The finite element calculation in reduction coefficient is 1.349 which is not convergence; this is in natural conditions of the dam safety coefficient. Combined with strain cloud of maximum principal figure 55, strain distribution figure56, and the maximum principal stress distribution analysis figure 59, see the feet of slope, the most vulnerable to yield skeleton of the dam and deformation and failure, because in the slope toe size change dramatically, will lead to stress concentration, so the most dangerous.

K f Sf

K

From them, f is fluid compressibility and skeleton compressibility 3] Slope safety factor equation

C

N tan W sin

C

W cos W sin

s

tan

is

solid

Fs Fig. 1. Diagram of penetrating velocity

10 Where

is minimum interface friction angle in multi-layer

covers system; is the slope angle, W is the total gravity of typical covering soil slices; N is the effective normal stress

2.2 Definite conditions The mechanism process of water movement of unsaturated earth fill dam under the condition of rainfall can be solved by equation (9), and the definite condition was given to solve the mathematical model. 1) Initial condition; P(x,y,t)| t 0 = p 0 11

x, y, t |t P(x,y,t)|

K

0

0

p1

1

.

p | n 1, 2

rainfall intensity; horizontal plane .

Fig. 2.Diagram of pore water pressure distribution

12 13

Rt R t cos

14 among them: R (t) is

is the angle of the dam slope and

[3].Consider the rainfall on stability influence analysis;

dam

slope

The natural conditions of the dam slope stability have a long and huge impact, the rainfall on dam slope stability for a detailed analysis. Because of this case of elastic-plastic model of iterative calculation is very complex, so take the elastic model, and not by strength reduction method, and

Fig.3 Diagram of saturation line

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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 1, ISSUE 5, JUNE 2012

ISSN 2277-8616

Fig.4 Diagram of saturation Fig.8 Diagram of plain strain

Fig.5. Diagram of displacement Fig.9 Max principal strain distribution

Fig.6. Levels displacement diagram Fig.10Min principal strain distribution

Fig.7 Vertical displacement diagram Fig.11 Diagram of mises stress distribution

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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 1, ISSUE 5, JUNE 2012

Fig.12 Max principal stress distribution

ISSN 2277-8616

Fig.16 Diagram of Pore water pressure distribution

Fig.13 Min principal stress distribution

Fig.17 Diagram of saturation line

(b) After the rain of slope stability analysis of the dam

Fig.14 Diagram of penetrating velocity Fig.18 Diagram of displacement

Fig.19 Levels displacement diagram

Fig.15Diagram of Pore water pressure distribution

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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 1, ISSUE 5, JUNE 2012

Fig.20 Vertical displacement diagram

ISSN 2277-8616

Fig.24 Max principal stress distribution

Fig.25 Min principal stress distribution Fig.21 Diagram of plain strain

Fig.22Max principal strain distribution

Fig.23 Diagram of mises stress distribution

In the reduction coefficient is 1.268, the iterative calculation is no longer convergence, therefore, under the effect of rainfall the slope safety coefficient of the dam is1.268. Considering the situation of the rainfall, need above the water of the boundary loading conditions of rainfall infiltration, is based on the form of the pore pressure load, different from before boundary conditions to add pore pressure, here to force load directly loading. From the figure 11 to figure 13 and figure 23 to figure 25 shows the all kinds of stress distribution, consider rainfall, due to increased the load, so the internal stress field of dam body changes. Corresponding figure 1 to figure 4 and figure 13 to figure 16 can see, rainfall makes the flow velocity of the water inside the dam has increased dramatically, the current water distribution area greatly increase; Internal degree of saturation distribution of the dam is quite changed; The pore pressure distribution has been changed obviously; Of course, infiltrating the position of the line also have outstanding change. This shows that rainfall makes dam seepage field of internal generate a large changes. So the conclusion is: the internal stress field of dam body changes on the seepage field has very big effect. From figure 18 to figure 20 can be seen, in the slope feet by the largest amount displacement, and explains the instability. Again from strain analysis, as shown in figure 21 and figure 22 , slope feet strain is also the biggest, this and the analysis of the above conclusion is consistent. But the example the displacement figure 4 and strain cloud figure 8 contrasts can be seen, the skeleton of the deformation of the dam location, size and distribution has change greatly, and visible rainfall for the stability of the dam body has very big

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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 1, ISSUE 5, JUNE 2012

effect. So, for slope problems of the research, natural condition is very important factors. Comprehensive analysis of the various examples above, we can draw the conclusion: the internal stress field of dam seepage field and the stability of the slope are on the dam has a great influence, and both influence each other, interaction, coupling relationship.

[5]Soil and Water Conservation Journal, 36.

ISSN 2277-8616

1995, 9(1):31-

[6] Kaehanov L M Time of the rapture process under creep conditions [J]. TVZ Akad Nank S S R Otd Tech. Nuak .l958,8 [7]Rabonov Y N. Creep rapture[C] Proc12,Ienter Congress

[4] Conclusion This paper researches the static and dynamic simulation analysis of the cracks. Analyze the static simulation of the dam by using the strength reduction principle, get the stress, strain and displacement distribution rule and the corresponding safety factor in the water level change and rainfall infiltration two working conditions of the reservoir’s retaining dam body, the rules are shown as follows: The rainfall has a great influence on the slope stability of the dam. The rainfall impact will cause the great change of the seepage field and the stress field, influences the stress and strain distribution of the dam, and changes the situation of the dam skeleton’s deformation, finally causes the instable failure of the dam. Based on underground water seepage theory, a fluid-solid coupled mathematical model for describing permeation process under unsaturated condition is established, which calculates the safety factor of the dam slope under the condition of rainfall in the paper. Then, the curves which describe the relationship between slope gradient ratio, slope angle and rainfall duration (24 hours) are given in the different return periods of rainfall. The results of numerical calculation show that safety factor decreases along with rainfall duration increasing in the different return periods of rainfall. When the slope is reduced, slope safety factors reduce slowly in the range of allowable value. Safety factors of slope decrease obviously as the slope is increased. Therefore, the theoretical basis is more credible provided for designing and appraising stability of the dam in the paper.

[8]Appl Mech Stanford, Springer, Berlin 1969. [9] Lemaitre J Application of damage concepts to predict creep-fatigue failure[C]. JEngMatTech, ASME, 1979, 101:202-209 [10] Leckie F A,Hayhurst D ruptureofstructure[C].Proc.R.Soc.A340,1974

R.Creep

[11] Hult J.Damage induced instability[C].Trans.3rdAMIRT, London, 1974.

tensile

[12] Kajcionovic D. Continuum damage theory of brittle materials [J].J. Appl. Mech. 1981 (48):809-824.

[5] Acknowledgment Firstly,I like to give thanks Chinese government of providing unique opportunity of three years scholarship for my doctoral degree and secondly, I like to give thanks to Liaoning technical university ,Fuxin, Lliaoning Province China for providing exciting environment for my research work.Lastly I like to thanks for dedicated and committed professor sun keming for his valuable and precious time for writing my paper. I could write this paper after his continuous guideline and many meetings with him.

[5]REFERENCES [1] Chen Yunmin, Wang Lizhong etc Study on Slope Stability of the Municipal Solid Waste [2] Fredlund, D.G.and H.Rahardjo. Unsaturated Soils [M].

Soil Mechanics for

[3]AmericanSocietyofCivilEngineers.1993:241-270. [4] Chen Minhua, Zhou Fujian, Huang Yanhe, Lu Chenlong, Lin Fuxing.Effects of Slope Length andGrade on Soil and Water Loss [J].

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Study-On-Dam-Slope-Stability-Under-The-Condition-of-Rainfall