IJACE Vol.2 No.1 Jan-June 2012 pp.25-38 © Research …serialsjournals.com/serialjournalmanager/pdf/1346739642.pdf · Numerical Analysis of Earth–Rockfill Dams ... stability problems,

IJACE Vol.2 No.1 Jan-June 2012 pp.25-38 © Research Science Press, New Delhi www.rspjournals.com

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Numerical Analysis of Earth–Rockfill Dams Behavior, During Construction and First Stage Impounding

(Case Study: MASJED-E-SOLEYMAN Dam)

S.M. Ali Zomorodian* & Hossein Chochi Water Engineering Department, Shiraz University, Shiraz, Iran

E-mail: [email protected] or [email protected]

Abstract: This paper presents, the analysis of instrumentation data during construction and first filling reservoir (first impounding) of MASJED-E-SOLEYMAN dam. This is a rockfill dam with a central clay core and a height of 178 meters. The measured internal deformations, pore water pressures and total vertical stresses have been compared with the analysis results. To perform the analysis, GEOSTUDIO 2004 V. 6.02 software has been used. The staged construction of the dam has been modeled in the form of 2D coupled consolidation. The Non-linear elastic model for the core material and Linear Elastic model for other zones have been incorporated into the models. Keywords: Pore Water Pressure, Instrument, MES Dam, Non-Linear Elastic Model, Linear Elastic Model, Coupled Consolidation

1. INTRODUCTION

The most common causes of failure of the embankment dams are: internal erosion of fine-grained soils, erosion under the foundation or abutment, stability problems, consequence of developing high pore pressures, hydraulic gradients, and overtopping of the dam or spillway. A less common cause of failure is the development of high pore water pressures and possible liquefactions either in the foundation or embankment during earthquakes.

Developed excess pore water pressure in the clay core of zoned rockfill dams during the construction period and first stage impounding, may lead to initiation or progression of hydraulic fracturing. The ability to predict the development and dissipation of excess pore water pressures is one of the main tools in assessing the performance of such structures [1].

Dunnicliff and Green (1988) have studied the behavior of Nonhova dam in China, Cam clay soil model and CON2D program have been used [2]. Tedd et al. (1997) have evaluated the settlements of Ramsden dam during construction and first impounding using instrumental data [3].

Rattue et al. (2000) have studied the behavior of Sainte Marguerite-3 dam in Canada. The height of this dam is 171 meters. The results show that pore water pressure in this dam is negligible [4].

Maleki and Alavifar (2005) have studied the behavior of Masjed-Soleyman dam in Iran. FLAC 4.0 software has been used to predict the pore pressure ratio parameters and arching ratio [1].

MES dam is one of the highest dams in Iran and the Middle East that is located in Masjed Soleyman city in the province of Khozestan. MES1 dam has been constructed on Karon River [5].

The maximum height of this dam at section (CH260) is 177 meters (Fig. 1). Its crest length is 490 meters, 1:0.25 core side slopes and a maximum width of 90 meters. Foundation materials are conglomerate and sandstone with high strength. In Fig. 2 the general layout of MES dam project has been shown.

1 Masjed-E-Soleyman

Numerical Analysis of Earth–Rockfill Dams Behavior, During Construction and First Stage …..

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Fig.1. The Highest Cross Sections and Zoning of MES Dam (CH260)

Fig.2. General Layout of MES Dam Project

2. MATERIAL AND METHODS

2.1 Monitoring Instrumentation: For controlling and a proper assessment of MES dam behavior during construction and first

impounding, widespread instrumentation has been done in longitudinal and transverse cross sections, foundation and abutments. These instruments have been used for controlling and measuring total vertical stresses, pore water pressures, settlements, horizontal displacements and etc. The following types of instruments have been used most often:

1- Surface Settlement & Deflection Points 2- Inclinometer 3- Hydrostatic Settlement Gauge 4- Earth Pressure Gauge 5- Pore Pressure Gauge 6- Vibrating Wire 7- Standpipe Piezometer 8- Casagrande Piezometer 9- Groundwater Observation Hole 10- Earthquake Accelerometer and 11- V-Notch Seepage Measuring Weir [6].


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The comparison of the monitored data with the predicted data obtained from the numerical analysis may give important information concerning the quality of accepted geotechnical parameters.

2.2 Modeling Stages:

The numerical analysis has been performed by using Geostudio 2004 Software. This software is based on finite element method which can model the stage construction and consolidation. In this research the maximum and critical section of MES dam has been selected and modeled.

2.3 Selection of material model:

In MES dam, the non-linear elastic model for core material and the linear elastic model for other zones have been used for the analysis. Geotechnical and hydraulic properties of materials for the modeling process have been imported in SIGMA/W and SEEP/W models of Geostudio Pack respectively. The finite element formulation for a given time increment in the SIGMA/W is [7, 8]:

Where: [B] = strain-displacement matrix, [C] = constitutive matrix, {a} = column vector of nodal incremental x- and y-displacements, <N > = row vector of interpolating functions, A = area along the boundary of an element, v = volume of an element, b = unit body force intensity, p = incremental surface pressure, and {Fn} = concentrated nodal incremental loads.

This equation is applied over all elements. It should be noted that SIGMA/W is formulated for incremental analysis. For each time step, incremental displacements are calculated for the incremental applied load. These incremental values are then added to the values from the previous time step. The accumulated values are reported in the output files. Using this incremental approach, the unit body force is only applied when an element is included for the first time during an analysis. For a two-dimensional plane strain analysis, SIGMA/W considers all elements to be of unit thickness. For constant element thickness, the previous equation can be written as:

SIGMA/W solves this finite element equation for each time step to obtain incremental displacements and calculates the resultant incremental stresses and strains. It then sums all these increments since the first time step and reports the summed values in the output files.

SIGMA/W uses Gauss-Legendre numerical integration (also termed quadrature) to form the element characteristic (or stiffness) matrix [K]. The variables are first evaluated at specific points within an element. These points are called integration points or Gauss points. These values are then summed for all the Gauss points within an element.

SEEP/W is formulated on the basis that the flow of water through both saturated and unsaturated soil follows Darcy's Law which states that:


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q=ki Where: q = specific discharge, k = hydraulic conductivity, and i = gradient of total hydraulic head.

Darcy's Law was originally derived for saturated soil, but later research has shown that it can also

be applied to the flow of water through unsaturated soil (see Richards, 1931 and Childs & Collins-George, 1950). The only difference is that under the condition of unsaturated flow, the hydraulic conductivity is no longer constant, and varies with changes in water content and indirectly varies with changes in pore-water pressure. Darcy's Law is often written as:

v=ki Where: v = the Darcian velocity.

Note that the actual average velocity at which water moves through the soil is the linear velocity, which is equal to Darcian velocity divided by the porosity of the soil. In unsaturated soil, it is equal to Darcian velocity divided by the volumetric water content of the soil. SEEP/W computes and presents only the Darcian velocity.

The general governing differential equation for two-dimensional seepage can be expressed as:

Where: H = total head, kx = hydraulic conductivity in the x-direction, ky = hydraulic conductivity in the y-direction, Q = applied boundary flux, θ = volumetric water content, and t = time.

This equation states that the difference between the flow (flux) entering and leaving an elemental volume at a point in time is equal to the change in storage of the soil systems. More fundamentally, it states that the sum of the rates of change of flows in the x- and y-directions plus the external applied flux is equal to the rate of change of the volumetric water content with respect to time.

Applying the Galerkin method of weighed residual to the governing differential equation, the finite element for two-dimensional seepage equation can be derived as:

Where:

[B] = the gradient matrix, [C] = the element hydraulic conductivity matrix, {H} = the vector of nodal heads, < N > = the vector of interpolating function, q = the unit flux across the edge of an element, τ = the thickness of an element,


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t = time, λ = storage term for a transient seepage equals to mwγw A = a designation for summation over the area of an element, and L = a designation for summation over the edge of an element.

2.4 Accuracy assessment of non-linear elastic constitutive model Parameters: Triaxial tests have been performed for accuracy assessment of numerical analysis of MES dam

modeling, also for accurate evaluation of input parameters of non-linear elastic model. Then model parameters have been selected, as stress-strain analysis results and laboratory results to present its accuracy.

At first in this process, geotechnical parameters of samples are imported in SIGMA/W model and Hydraulic Parameters of samples are imported in SEEP/W model. According to the type of triaxial tests these softwares are used in coupled and uncoupled manners. The sample is modeled in an axisymmetric condition which at first the confining pressure and then the deviatoric pressure is applied to the model. Then strain values are read during axial loading and deviatoric pressure versus axial strain curves is drawn. In the next step, these curves are compared with triaxial laboratory test results [7,8].

Three types of materials, M1, M2 and M3 have been used for construction of MES dam’s core. These materials have presented partly same results as in statical analysis. Materials properties have been presented in Table (1) [5].

Table 1 Approximate Materials Properties of MES Dam in Triaxial Tests Estimated dry density

(kN/m3) based on Walker-Halts equation

Material percentage above

4.76 mm

Combination percentage of GC and CL

in core materials

Materials sample for MES dam core in soil mechanics laboratory

17.96420GC40%-CL60%M1 18.26828GC60%-CL40%M2 18.58237GC80%-CL20%M3

An important section in each analysis is the presentation and definition of model parameters. In

fact, except the meshing state, definition of boundary conditions and abutments situation each have a special and effective role in the results of the analysis. Finding correct and proper model parameters and defining these parameters for the software is the most basic part in numerical modeling.

In this research, modeling of triaxial tests in consolidated drained (CD) and consolidated undrained (CU) conditions have been carried out for three types of core materials under 300, 600 and 900 kPa (confining pressures).

2.5 Determination of the number of fill layers for stage construction modeling:

Goodman (1963) and Clough and Woodward (1973) apply stage construction in finite element analysis. In fact, a minimum number of fill layers is required for obtaining acceptable displacement results. So it is important to determine the required fill layers for the analysis.

Number of layers are determined using the method presented by zomorodian, et al. (2006) [9].

2.6 Meshing of maximum section (CH260): Total number of considered elements and nodes in analysis of CH260 section and foundation of

MES dam (2 layers) were 7223 elements and 5536 nodes. In modeling of MES dam unstructured meshing has been used for covering total corners of dam zones. In this model the thickness of each fill layers was 9 meters. In Fig. 3 the meshing of MES dam zones and foundations are shown.


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Fig.3. Meshing of MES Dam (CH260)

2.7 Definition of material properties:

In this section, since effective stress analysis was used, geotechnical parameters of materials have been imported in SIGMA/W model and hydraulic parameters of materials have been imported in SEEP/W model and coupled consolidation has been done for modeling consolidation during construction.

Table (2) shows material properties of MES dam and Table (3) shows strength and deformation parameters of MES dam body are shown.

Table 2 Material parameters of MES dam body

Material Zones Drainage Condition

γsat γwet Ky W.C mv kN/m3 kN/m3 m/sec % -

1 Core Undraied 20.3 19.9 1E-10 19 0.000002 3A Upstream Shell Drained 23 21.6 - - 0.0001 3B Downstream Shell Drained 23 21.6 - - 0.0001 3C Downstream Shell Drained 23 21.6 - - 0.0001 2A Downstream Filter Drained 22.2 19.6 - - 0.0001 2B Downstream Transition Drained 22.2 19.6 - - 0.0001 2C Upstream Transition Drained 22.75 20.6 - - 0.0001

Table 3 Constitutive model parameters of MES dam body and foundation

Material Zones Constitutive model

E K ν n C φ Rf Emin

MPa (load) - Exp kPa Deg - kPa

1 Core Non-linear elastic - 110 0.34 0.76 200 33.5 0.95 101.3

33A Upstream

Shell Linear elastic 94 - 0.3 - 0 45 - -

3B Downstream Shell

Linear elastic 95 - 0.3 - 0 37 - -

3C Downstream Shell

Linear elastic 94 - 0.3 - 0 45 - -

2A Downstream Filter

Linear elastic 72 - 0.3 - 0 35 - -

2B Downstream Transition

Linear elastic 72 - 0.3 - 0 40 - -

2C Upstream Transition

Linear elastic 126 - 0.3 - 0 40 - -

Found.1 Conglomerate Linear elastic 3870 - 0.3 - 700 30 - -

Found.2 Siltstone Linear elastic 6670 - 0.3 - 2000 45 - -


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RESULTS Figs. 4, 5 and 6 show the results of MES dam’s core materials determined by non-linear elastic

model. In these figures measured and calculated the deviatoric stresses versus axial strain curves obtained from triaxial consolidated drained test and model are compared.

Fig. 4. Results of M1 Materials, Modeling and Laboratory in CD And CU Triaxial Tests.

Fig. 5. Results of M2 Materials, Modeling and Laboratory in CD Triaxial Tests


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Fig. 6. Results of M3 Materials, Modeling and Laboratory Results in CD Triaxial Tests

These triaxial tests are based on stress control conditions. In this research, triaxial tests with strain

control have been modeled in CD and CU tests for M1, M2 and M3 materials only in confining pressure of 600 kPa. Fig. 4 shows results for M1 materials which a proper match between model results and laboratory results is seen. Since, results of the model for M1 materials are closed to measured in both stress and strain control analysis than other materials, therefore non-linear elastic parameters of M1 material has been selected as main material in modeling of MES dam core.

The effective stress analysis apply in undrained situation. So, effective parameters of core and consolidated drained triaxial tests (CD) results have been used in modeling process.

Measured and calculated (modeled) pore water pressure and total vertical stress during construction and first impounding are presented in Tables 4 and 5 respectively.

Table 4 Comparison Between Measured and Modeled Parameters of MES Dam During Construction

Numerical results Instrumentation results Position

Instrument Total stress (kPa)

Pore pressure

ratio

Pore pressure

(kPa)

Total stress (kPa)

Pore pressure

ratio

Pore pressure

(kPa)

Position toward

centerline Installation

level Installation

section

2319.70 0.69 2083.70 2304.79 0.70 2115.62 Center 230 260 PPE212 & EP2103

2160.70 0.75 2095.60 2096.70 0.75 2096.70 30 m-Downstream 230 260 PPE213 &

EP2104

1492.80 0.54 1216.70 1463.90 0.63 1407.14 Center 270 260 PPE222 & EP2202

1477.90 0.57 1191.60 1433.21 0.67 1412.01 19.5 m- Downstream 270 260 PPE223 &

EP2203

780.07 0.21 459.28 750.32 0.22 492.08 11.5 m- Downstream 310 260 PPE232 &

EP2304


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Table 5 Comparison Between Measured and Modeled Parameters of MES Dam at First Impounding Numerical results Instrumentation results Position

Instrument Total stress (kPa)

Pore pressure ratio

Pore pressure (kPa)

Total stress (kPa)

Pore pressure ratio

Pore pressure (kPa)

Position toward

centerline Installatio

n level installation section

2422.67 0.71 2115.54 2351.78 0.72 2177.54 Center 230 260 PPE212 & EP2103

2306.18 0.70 2127.06 2246.42 0.73 2217.91 30 m-Downstream 230 260 PPE213 &

EP2104

1609.12 0.56 1246.23 1569.27 0.67 1498.77 Center 270 260 PPE222 & EP2202

The maximum settlements measured in MES dam core in different stages at the end of the

construction compared with calculated settlements (Table 6). Fig. 8 shows pore water pressure contours in the core at the end of construction in CH260 section. Table 6 Comparison Between Measured and Modeled Settlements of MES Dam at End of Construction

Measured settlement-mModeled settlement-mInclinometersInstallation level Date 0.4825 0.34047 SM-2318 373 20-NOV-2000

0.0755 0.12513 SM-2319 381 20-NOV-2000

Fig.8. Pore Pressure (Kpa) Contours in MES Dam Core at End of Construction

Figs.9, 10 and 11 shows comparisons between calculated (modeled) pore water pressure, pore pressure ratio (Ru) and total vertical stress (TVS) with measured pore water pressure, pore pressure ratio and total vertical stress during construction and first impounding in PPE212, PPE213 and PPE222 and EP2103, EP2104 and EP2202 pressure gauges, respectively.


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Fig.9. Comparison Between Calculated (Modeled) Pwp, Ru and TVS With Measured Pwp, Ru and TVS

During Construction and First Impounding in PPE212 and EP2103


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Fig. 10. Comparison Between Calculated (Modeled) PWP, Ru and TVS with Measured PWP,

Ru and TVS During Construction and First Impounding in PPE213 and EP2104


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Fig. 11. Comparison between calculated (modeled) PWP, Ru and TVS with measured PWP,

Ru and TVS during construction and first impounding in PPE222 and EP2202

The total vertical stresses during construction and specially at the end of the construction are similar. These results show that the elasticity modules of materials coincide with exact measurement.

Fig. 12 shows a comparison between calculated (modeled) settlements and measured settlements in SM23 inclinometer. (2 situations: full reservoir and half-full reservoir until 13-May-2001)


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Fig. 12. Comparison Between Calculated (Modeled) Settlements and Measured Settlements in SM23

Inclinometer. (2 Situations: Full Reservoir and Half-Full Reservoir Until 13-May-2001)

Measured Pore water pressure values with an increase of fill level are higher than modeled pore water pressure values. The reason of this difference is the variation in saturation conditions on different levels as in lower level materials the degree of saturated is more than on upper levels materials. So, this difference on lower levels have a more significant result than upper levels.

Due to the height of the dam and the low conductivity of the materials of the core of the dam, pore pressure ratio is in an acceptable range during construction. And pore pressure values are more than the same values in other dams during and at end of the construction.

The reasons for the slight differences between the measured and analyzed pore pressures ratio can be due to different hand calculation assumptions for pore pressure ratio in the selected points ( the point that pore pressure ratio has been calculated).

Also, this slight difference can be due to the difference of H (level of fill or height of fill column above the point that pore pressure ratio has been calculated in model and field because of the differences between meshing situation and field position. CONCLUSIONS

Increasing in the pore water pressure near the foundation level in the core materials relatively well estimated during construction of embankment dam by using nonlinear elastic model. Calculated pore water pressure during construction and first impounding are close to those measured. At lower levels the results are more coincident than the upper levels and in the upper levels the measured values are more than the analyzed values.

Pore water pressure ratio increases as time elapses and as the height of the embankment increases, rate of variation decreases. Finally, the variation rate of pore pressure ratio tends to a constant value.

The selection of M1 material as the main material of the dams core and a non-linear elastic constitutive model for the core material and a linear elastic constitutive model for the other zones have correctly predicted the geotechnical behavior of MES dam.

The results of the analysis indicate that the presented method by Zomorodian et al. (2006) has correctly predicted the behavior of different parameters such as pore pressures, stresses and etc. and has modeled an acceptable staged construction.

Application and efficiency of this method and software in modeling of earth-rockfill dams and staged construction and first impounding of these dams is proper and acceptable.


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REFERENCES [1]. Maleki, M. and Alavifer, A. (2005). "Safety Evaluation of MASJED-E-SOLEYMAN, During Construction and First Stage Impounding." 73rd Annual Meeting of ICOLD, Tehran, Iran, No.101-S5. [2]. Dunnicliff, J. and Green, G. E. (1988). "Geotechnical Instrumentation for Monitoring Field Performance." John Wiley and Sons Publications. [3]. edd, P., Charles, J. A., Holton, I. R. and Roberstshow, A. C. (1997). "The effect of reservoir drawdown and long-term consolidation on the deformation of old embankment dams." Geotechnique 47, No. 1, pp.33-48. [4]. Rattue, D. A., Hammamji Y. and Tournier, J. P. (2000). "Performance of the Sainte Marguerite-3 dam during construction and reservoir filling." Proc. 20th Int. Con. Large dams. Vol. 3, pp. 899-915 [5]. Iran Water and Power Resources Development Co. (1996). GODAR-E-LANDER HEPP, Review on Additional Laboratory Test (Static Test Result). Ministry of Energy. [6]. Water and Power Resources Development Co. (2001)."Report on behavior of MASJED-E-SOLEYMAN, During Construction and First Stage Impounding". Ministry of Energy. [7]. GEOSTUDIO, Seepage Modeling with SEEP/W. Geostudio Manuals, Version, 6.02, 2004 [8]. GEOSTUDIO, Stress and Deformation Modeling with SIGMA/W. Geostudio Manuals, Version, 6.02, 2004. [9]. Zomorodian, S.M. ali,, Sahebzadeh, K. and Torabi Haghighi, A. (2006). “Effect of Number of Layers on Incremental Construction Analysis of Earth and Rock Fill Dams” Dams and Reservoirs, Societies and Environment in the 21st Century, Taylor and Francis grops ple, London

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IJACE Vol.2 No.1 Jan-June 2012 pp.25-38 © Research …serialsjournals.com/serialjournalmanager/pdf/1346739642.pdf · Numerical Analysis of Earth–Rockfill Dams ... stability problems,