Non-linear Analysis of Stress and Strain of Concrete-faced Rockfill Dam for Sequential Impoundment Process

The rockfill is modeled as nonlinear elastic material, whose stress-dependent tangent modulus is related to the confining pressure. The parameters of constitutive relationship of stress and strain are determined by tri-dimensional compression test in laboratory. The model applied in this study adopts the technique of element birth and death to simulate the sequential impoundment process of concrete-faced rockfill dam with time. Nonlinear finite element method is used to simulate the prototype behavior of various components of the dam in sequential nonlinear analysis and some representative results are presented.


INTRODUCTION
Rockfill has been used in the construction of dams for over 150 years [1].The concrete-faced rockfill dam (CFRD) was used with increasing frequency in recent years, in many parts of the world.As worldwide experience is accumulating on the long-term performance of CFRD, their popularity may well increase in coming years.Rockfill dams are increasingly used because of their inherent flexibility, capacity to absorb large seismic energy, and adaptability to various foundation conditions.The behavior of the rockfill materials is affected by such factors as mineralogical composition, particle grading, size and shape of particles, and stress conditions [2].Ozkuzukiran carried out two dimensional plane strain finite element analyses to assess the total stresses and displacements in the dam by using computer program PLAXIS.Predicted stresses and settlements were compared with those observed and overall the results were found to be in good agreement for the construction stage [3].A parametric study of transition (supporting) zone stiffness was performed using a numerical model calibrated using the centrifuge results.The numerical results indicated that face slab deformation is more influenced by transition zone stiffness than face slab stiffness, supporting the centrifuge results [4].Khalid carried out studies in order to understand the prototype behavior of this type of rockfill dam and to identify the various factors influencing the development of stresses and strains in the face slab and the rockfill embankment [5].Xing reported the physical, mechanical, and hydraulic properties of weak rockfill during placement and compaction in three dam projects in China.This study provided the opportunities for further understanding the behaviors of CFRDs with weak rocks [6].Centrifuge model tests were conducted for a rockfill dam model in order to investigate behavior of dam during first reservoir filling.The simulation results showed that the settlements calculated agreed roughly with those measured and the settlements due to wetting could also be estimated; the horizontal movements calculated were fairly larger than those measured [7].
In this paper, Section 2 briefs the constitutive model used for rockfill dam body.Duncan EB model is employed to describe the non-linearity of rockfill materials.Section 3 numerically simulates impoundment process of concrete-faced rockfill dam.The stress and deformation distributions are shown in the section.

CONSTITUTIVE MODEL AND PARAMETERS OF ROCKFILL MATERIALS
In order to provide a simple framework encompassing the most important characteristics of rockfill stress-strain behaviour using material parameters available from conventional laboratory tests, Duncan and Chang developed a hyperbolic model based on the hyperbolic equation proposed by Kondner [8].Because of its simplicity and wide applicability, Duncan and Chang's model is adopted herein to define the non-linear stress-strain behaviour of the rockfill materials.The stress-strain behavior of conditioned soil depends on a number of different factors including density, water content, structure, drainage conditions, strain conditions, duration of loading, stress history, confining pressure, and shear stress.The hyperbolic equation proposed by Kondner is expressed as follows [9] 1 3 where σ 1 and σ 3 are the major and minor principal stresses; ε is the axial strain; a and b are constants whose values may be determined experimentally.By expressing the parameters a and b in terms of the initial tangent modulus value and the compressive strength, Eq. 1 can be rewritten as follows ) where R f is the failure ratio, which always has a value less than unity, the value of R f has been found to be between 0.75 and 1.00.(σ 1 -σ 3 ) f is the compressive strength.
Experimental studies by Janbu have shown that the relationship between initial tangent modulus and confining pressure may be expressed as where E i is the initial tangent modulus; p a is the atmospheric pressure expressed in the same pressure units as E i ; k is a modulus number; n is the exponent determining the rate of variation of E i with σ 3 .If it is assumed that failure will occur with no change in the value of σ 3 , the relationship between compressive strength and confining pressure may be expressed conveniently in terms of the Mohr-Coulomb failure criterion as where c and ϕ are the Mohr-Coulomb strength parameters.Eqs. 3, 4, combination with Eq. 2, provide a means of relating stress to strain and confining pressure by means of the five parameters K, n, c , ϕ and R f .

NUMERICAL SIMULATION OF IMPOUNDMENT PROCESS OF CONCRETE-FACED ROCKFILL DAM
Pushihe pumped storage power station is located in Kuandian county, Liaoning province, China.Pushihe dam is 78.5 m high from river bed.The side slopes are 1:1.4 both in the upstream and downstream faces.The crest extends 714 m.Fig. 1 shows construction sequence of Pushihe Dam.
Fig. 1 Construction sequence of Pushihe CFRD The model applied in this study adopts the technique of element birth and death to simulate the impoundment process of concrete-faced rockfill dam with time.Model parameters of nonlinear constitutive relationship of rocfill are listed in Table 1.Computational procedure follows the construction sequence as shown in Fig. 1.Fig. 2 and 3 illustrate the computed vertical and horizontal displacements.Fig. 4 shows shear stress distribution in Section 276, Fig. 5 and 6 show distribution of the first principal stress and the third principal stress in Section 276.As shown in Fig. 2 and 3, in the upstream and downstream parts, the computed maximum horizontal displacement is -155mm (directional upstream) and 112mm (directional downstream), respectively.The maximum vertical displacement is 372mm, which is located in the middle of dam height and is about 0.50% of dam height.The horizontal displacement of dam is zero at the central line of dam section and increases towards both upstream and downstream faces.The maximum computed horizontal displacement doesn't occur at the dam faces, which is not same as the calculated results from reference [4].The maximum computed horizontal displacement at the upstream face of dam can reach 0.13m.The horizontal displacement at the upstream face of dam induced from sequential impoundment process must be considered in order to make upstream face of dam to a designed straight line after rockfill construction and ensure concrete slab to contact rockfill during casting concrete slab phase and service period.
As shown in Fig. 4, the shear stress is zero at the central line of dam and increases towards the upstream and downstream faces, until the maximum value of both negative and positive shear is reached at points midway between central line and upstream or downstream face.The maximum shear stress is 0.23 MPa.The third principal stress increase with the increase of deposition depth.The maximum occurs at the contacting face of dam body with rock foundation, on the central line of dam section.The maximum value of compression stress is 1.39 MPa.The stress state of dam body is governed by compression stress.The tensile stress zone occurs only at superficial layer of dam body.The depth of tensile stress zone is less than 5m.The maximum tensile stress of dam body is only 3kPa.If the contour line of upstream surface is constructed according to design contour line, the shape of contour line of upstream surface will become a curve shape, when the rockfill of CFRD is filled up.The maximum error can reach 155mm, which will make casting concrete-faced slab be very difficult.The adjustment of impounding contour line is performed during the rockfill construction period according to calculated horizontal deformation.The width of dam under and above neutral point must decrease or increase, respectively.The application of numerical simulation to Pushihe CFRD indicates the effectiveness and necessity.

CONCLUSION
1) By using element birth and death technique, sequential impoundment process of a concrete-face rockfill dam is numerically analyzed.Duncan EB model is employed to describe the non-linearity of rockfill materials.The parameters of constitutive relationship of stress and strain are determined by tri-dimensional compression test in laboratory.
2) Numerical simulation shows that the maximum computed horizontal displacement is 0.155m.The location of maximum computed horizontal displacement is 0.27 times of dam height.The maximum computed vertical displacement is 0.372m and 0.50% of dam height and occurs at 0.45 times of dam height, on the central line of dam section.
3) The maximum computed horizontal displacement at the upstream face of dam can reach 0.13m.The horizontal displacement at the upstream face of dam induced from sequential impoundment process must be considered in order to make upstream face of dam to a designed straight line after rockfill construction and ensure concrete slab to contact rockfill during casting concrete slab phase and service period.
4) The third principal stress (compression stress) increases with the increasing of deposition depth.The maximum occurs at the contacting face of dam body with rock foundation, on the central line of dam section.The maximum value of compression stress is 1.39 MPa.The stress state of dam body is governed by compression stress.The tensile stress zone occurs only at superficial layer of dam body.The depth of tensile stress zone is less than 5m.The maximum tensile stress of dam body is only 3kPa.The maximum shear stress is 0.23 MPa. 5) Based on numerical simulation of sequential impoundment process, the Pushihe CFRD is constructed.The practical application validates the accuracy and effectiveness of sequential impoundment simulation with nonlinear finite element method.

Table 1
Model parameters of nonlinear constitutive relationship of rocfill