ABSTRACT The shear stress parameters of the soil-structure interfaces were analyzed by Finite Element modeling of direct shear test. The model is used to determine the stress deformation behavior of clay-concrete interfaces, and to observe influence of area reduction to shear stress at the clay concrete interface. The results of the FE study showed that there is about seven percent stress increment due to the area change during the direct shear test and area correction can not be ignored for soil structure interface analysis. Finite Element, Soil Structure Interaction, Direct Shear, Area Reduction INTRODUCTION Soil-Structure Interaction (SSI) analyses have been studied last 30 years for analyzing, designing, and monitoring geotechnical structures. Clough and Duncan (1971), Ebeling et al. (1993), Ebeling and Mosher (1996), and Ebeling, Peters, and Mosher (1997), Ebeling, Pace, and Morrison (1997) are some examples of state-of-the-art studies available for SSI analyses. Most often, interface tests were performed to determine the soil-to-structure friction angle for design of geotechnical structures, such as retaining walls, buried culverts, piles, etc., and, in some cases, for the determination of parameters for constitutive modeling of interface response. Early systematic efforts to obtain data on the behavior of soil-to-structure interfaces were carried out by Potyondy (1961), and Peterson et al. (1976). Their tests were performed using a slightly modified Direct Shear Box (DSB) in which a concrete specimen occupied one of the halves of the shear box. In most cases, the soil sample was prepared against a concrete specimen situated at the bottom. The tests were typically performed by first increasing the normal pressure to a desired value, then shearing the interface under constant normal stress to a maximum displacement of about 12.5 mm. In SSI analyses, the soil-structure interface is represented by interface elements. Several kinds of interface elements have been developed to model the behavior of the interface under certain loading conditions. In most of the interface models, the interface yield stress is determined by the Mohr-Coulomb criterion (Goodman, Taylor, and Brekke 1968; Clough and Duncan 1971; Zaman, Desai, and Drumm 1984; Desai, Muqtadir, and Scheele 1986; and Wong, Kulhawy, and Ingraffea 1989). In this study Mohr Coulomb model is applied to direct shear type soil-concrete interface by considering the influences of area reduction on the SSI analysis. Finite Element Study of Soil Structure Interface Problem Haydar Arslan University of Colorado-Boulder Department of Civil Engineering Boulder, CO Sayfa 1 / 10 ejge paper 2005-0533 01.09.2005 http://www.ejge.com/2005/Ppr0533/Ppr0533.htm
Transcript
ABSTRACT
The shear stress parameters of the soil-structure interfaces were analyzed by Finite Element modeling of direct shear test. The model is used to determine the stress deformation behavior of clay-concrete interfaces, and to observe influence of area reduction to shear stress at the clay concrete interface. The results of the FE study showed that there is about seven percent stress increment due to the area change during the direct shear test and area correction can not be ignored for soil structure interface analysis.
Finite Element, Soil Structure Interaction, Direct Shear, Area Reduction
INTRODUCTION
Soil-Structure Interaction (SSI) analyses have been studied last 30 years for analyzing, designing, and monitoring geotechnical structures. Clough and Duncan (1971), Ebeling et al. (1993), Ebeling and Mosher (1996), and Ebeling, Peters, and Mosher (1997), Ebeling, Pace, and Morrison (1997) are some examples of state-of-the-art studies available for SSI analyses.
Most often, interface tests were performed to determine the soil-to-structure friction angle for design of geotechnical structures, such as retaining walls, buried culverts, piles, etc., and, in some cases, for the determination of parameters for constitutive modeling of interface response. Early systematic efforts to obtain data on the behavior of soil-to-structure interfaces were carried out by Potyondy (1961), and Peterson et al. (1976). Their tests were performed using a slightly modified Direct Shear Box (DSB) in which a concrete specimen occupied one of the halves of the shear box. In most cases, the soil sample was prepared against a concrete specimen situated at the bottom. The tests were typically performed by first increasing the normal pressure to a desired value, then shearing the interface under constant normal stress to a maximum displacement of about 12.5 mm.
In SSI analyses, the soil-structure interface is represented by interface elements. Several kinds of interface elements have been developed to model the behavior of the interface under certain loading conditions. In most of the interface models, the interface yield stress is determined by the Mohr-Coulomb criterion (Goodman, Taylor, and Brekke 1968; Clough and Duncan 1971; Zaman, Desai, and Drumm 1984; Desai, Muqtadir, and Scheele 1986; and Wong, Kulhawy, and Ingraffea 1989). In this study Mohr Coulomb model is applied to direct shear type soil-concrete interface by considering the influences of area reduction on the SSI analysis.
Finite Element Study of Soil Structure Interface Problem
Haydar Arslan University of Colorado-Boulder Department of Civil Engineering
A Plane strain model is used for structures with a uniform cross section and corresponding stress state and loading scheme over a certain length perpendicular to the cross section. Displacements perpendicular to the cross section are assumed to be zero.
Soil Elements
The 6-node triangle element is chosen for a 2D analysis (Figure 1). It provides a second order interpolation for displacements. The element stiffness matrix is evaluated by numerical integration using a total of three Gauss points (stress points).
Mohr-Coulomb model is used as a first approximation of soil behavior in general. The model involves five parameters, namely Young's modulus, E, Poisson's ratio, ν, the cohesion, c, the friction angle, φ, and the dilatancy angle, ψ.
Figure 1. Position of nodes and stress points in soil elements (Brinkgreve et al., 1998)
Interfaces
Interfaces are used to model the interaction between structures and the soil. Examples of geotechnical structures involving interfaces are presented in Figure 2. A typical application of interfaces would be to model the interaction between a sheet pile wall and the soil, which is intermediate between smooth and fully rough. In this application interfaces are placed at both sides of the wall. The roughness of the interaction is modelled by choosing a suitable value for the strength reduction factor in the interface. This factor relates the interface strength (wall friction and adhesion) to the soil strength (friction angle and cohesion).
Figure 2. Examples in which interfaces are used (Brinkgreve et al., 1998)
Interface Elements.
Interfaces are composed of interface elements. Figure 3 shows how interface elements are connected to soil elements. When using 6-node soil elements, the corresponding interface elements are defined by three pairs of nodes. In Figure 3 the interface elements are shown to have a finite thickness, but in the finite element formulation the coordinates of each node pair are identical, which means that the element has a zero thickness.
Figure 3. Distribution of nodes and stress points in interface elements and connection with soil
elements (Brinkgreve et al., 1998)
Interface Strength.
An elastic-plastic model is used to describe the behaviour of interfaces for the modelling of soil-structure interaction. The Coulomb criterion is used to distinguish between elastic behaviour, where small displacements can occur within the interface, and plastic interface behaviour (slip).
For the interface to remain elastic the shear stress τ is given by:
For plastic behaviour τ is given by:
where φi and ci are the friction angle and cohesion of the interface and σn and τ are the normal stress and shear stress acting in the interface. The strength properties of interfaces are linked to the strength properties of a soil layer. Each data set has an associated strength reduction factor for interfaces (Rinter). The interface properties are calculated from the soil properties in the associated data set and the strength reduction factor by applying the following rules:
Calculation of a Factor of Safety value was executed by reducing the strength parameters of the soil (Phi-c reduction). In the Phi-c reduction approach the strength parameters tan(φ and c of the soil are successively reduced until failure of the structure occurs.
The total multiplier ΣMsf is used to define the value of the soil strength parameters at a given stage in the analysis,
where the strength parameters with the subscript 'input' refer to the properties entered in the material sets and parameters with the subscript 'reduced' refer to the reduced values used in the analysis. ΣMsf is set to 1.0 at the start of a calculation to set all material strengths to their unreduced values. The strength parameters are successively reduced automatically until failure occurs. At this point the factor of safety is given by,
This approach resembles the method of calculation of safety factors conventionally adopted in slip-circle analyses. When using Phi-c reduction in combination with advanced soil models, these models will actually behave as a standard Mohr-Coulomb model, since stress-dependent stiffness behavior and hardening effects are excluded.
Msf; ΣMsf multipliers are associated with the Phi-c reduction option for the computation of safety factors. The total multiplier ΣMsf is defined as the quotient of the original strength parameters and the reduced strength parameters and controls the reduction of the tan(φ) and c at a given stage in the analysis. In contrast to most other total multipliers, ΣMsf is set to 1.0 at the start of a calculation to set all material strengths to their unreduced values. ΣMsf is used to specify the increment of the strength reduction of the first calculation step.
The Total displacements are the total vectorial displacements |u| at all nodes at the end of the current calculation step, displayed in a plot of the undeformed geometry. The Total increments are the vectorial displacement increments |Δu| at all nodes as calculated for the current calculation step, displayed on a plot of the undeformed geometry.
Methodology
The effect of area correction on the concrete body and clay interface has been evaluated by modeling two separate direct shear tests and those have been compared in the project. The first model represents the real direct shear test with the dimensions of 6×6 cm. There is no area change at the second model, and two different boxes are used at the bottom and top of the shear box. The dimensions of the bottom box are 10×10 cm and the dimensions of the top box are 6×6 cm. The load and soil properties of the two models are the same. In order to observe the interface behavior, a direct shear model is set up using a commercially available finite element program Plaxis.
The Direct Shear Model
Since soil is a multiphase material, special procedures are required for the simulation of non-linear and time dependant behavior. To overcome these difficulties, simplified models that behave like the real model are used for the numerical analysis. In this study, direct shear model is used as a simplified model of the concrete-soil interface model.
The material properties used in this study are derived from Özer Çinicioglu’s thesis (Çinicioglu, 2001). Permeability of the clay is used as 1 mm/day. The interface permeability is taken as neutral, because the interface should not influence the flow in the surrounding soil. This means that the interface is neither works as a drain nor an impermeable material.
The material model selected for the clay material is Mohr-Coulomb model and the material type is undrained. The Mohr-Coulomb model is a model of perfect plasticity. Plasticity is associated with the development of irreversible strains. Table 1 gives the properties of the materials used in this study.
Table 1. The properties of the materials used in this study
The direct shear box model in the first phase of this study consists of two clusters, as it is seen in Figures 4 and 5.
Figure 4. The direct shear box model for the first phase of the first model
Figure 5. The direct shear box model for the first phase of the second model
The interfaces are created between two clusters to maintain full interaction between the structure and the soil. A positive interface in the concrete cluster and a negative interface in the clay cluster are created.
The generation of the mesh is based on a robust triangulation procedure. The generated mesh is shown in Figure 6 and Figure 7. Although interface elements have a zero thickness, the interfaces are drawn with a certain thickness in order to show the connection between soil elements and interfaces.
Figure 6. The generated mesh for the first direct shear box model.
Figure 7. The generated mesh for the first direct shear box model.
The phreatic line is chosen under the clay liner to eliminate the effect of water on the soil-concrete interface (Figure 8 and Figure 9). The calculation consists of two phases. The first one is for loading, and the second one is for the execution of shearing. In the first phase of the calculation, SMdisp is selected as zero to have zero displacement. The reason is to initiate the loading of the direct shear box. SMload and SMweight are selected as one in both phases to have permenant application of the traction loads and the weight forces. In the second phase SMdisp is increased to one in order to shear the clay surface with the movement of the concrete block.
Figure 8. The phreatic line of the direct shear model
Figure 9. The phreatic line of the direct shear model
RESULTS AND DISCUSSIONS
After running the direct shear box model, the generated mesh modified due to the interaction between the clusters representing the concrete block and the clay. The deformed mesh for the two models are shown in Figure 10 and Figure 11. The frictional behavior of the clay can be observed above the interface. Total deformation in the soil body for the both model is shown in Figure 12.
Figure 10. The deformed mesh after the direct shear test
Figure 11. The deformed mesh after the direct shear test
Figure 12. Total displacements inside the soil body at both models
Shear stresses inside clay body are shown in the Figure 13 and Figure 14. The figures show that shear stress increases by getting closer to the interface. It is in agreement with the deformed mesh of the model.
Figure 13. Shear stress of the clay when area reduction is not considered
Figure 14. Shear stress of the clay body when area reduction is considered
CONCLUSIONS
In this study, the clay-concrete interface shear behavior is investigated by using finite element package program, Plaxis. Direct shear box is modeled to represent the shearing and to determine the role of interface material. The direct shear box model provides to analyze the shear stress parameters for the interface elements, and the stress deformation behavior of the soil during the shearing. The results of the models are in accordance with Metehan’s (1996) experimental direct shear test results. The FE study showed that stress rotation starts after the 1% strain under shear loading shearing. Stress rotation continues up to 4% strain, however stress rotation is not observed after the 4% strain level. The area change during the direct shear test affects the shear stress of the soil-concrete interface. The shear stress of the real direct shear test model is 78.45kN/m2, and the shear stress of the second model that ignores the area change is 83.66kN/m2. The results show that there is about seven percent stress increment due to the area change during the direct shear test.
REFERENCES
1. Bathurst, R. J., D. J. Benjamin and R. M. Jarret (1988) “Laboratory study of geogrid reinforced soil walls” Proc. of Sym. of Geosynthetics for soil improvement, Geotechnical Division, pp. 178-192, USA.
2. Brinkgreve, R.B.J., et al. (1998) Plaxis Finite Element Code for Soil and Rock Analyses, Delft University of Technology,The Netherlands.
3. İnicioglu, Ö. (2001) Modelling and Evaluation of the Behavior of Concrete-Lime Modified Clay Interface, MS Thesis, Bogaziçi University, Turkey
4. Desai, C. S., A. Muqtadir, and F. Scheele (1986) Interaction analyses of anchor-soil systems Journal of Geotechnical Engineering, ASCE, 112(5), 537-553.
5. Duncan, J. M., and G. W. Clough (1971) Finite element analyses of Port Allen Lock, Journal of the Soil Mechanics and Foundations Division, ASCE, 97(SM8), 1053-1067.
6. Ebeling, R. M., R. L. Mosher, K. Abraham, and J. F. Peters (1993) “Soilstructure interaction study of Red River Lock and Dam No. 1 subjected to sediment loading,” Technical Report ITL-93-3, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.
7. Ebeling, R. M., J. F. Peters, and R. L. Mosher (1997) The role of non-linear deformation analyses in the design of a reinforced soil berm at Red River UFrame Lock No. 1, International Journal for Numerical and Analytical Methods in Geomechanics 21, 753-787.
8. Ebeling, R. M., and R. L. Mosher (1996) Red River U-Frame Lock No. 1 backfill-structure-foundation interaction, ASCE Journal of Geotechnical Engineering 122(3), 216-225.
9. Ebeling, R. M., M. E. Pace, and E. E. Morrison (1997) “Evaluating the stability of existing massive concrete gravity structures founded on rock,” Technical Report REMR-CS-54, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.
10. Goodman, R. E., R. L. Taylor, and T. L. Brekke (1968) A model for the mechanics of jointed rock, Journal of the Soil Mechanics and Foundations Division, ASCE, 94(SM3), 637-659.
11. Metehan, C. T., Shear Strength Improvement at the Interface of Lime-Treated Soil and Conctrete Structures, M.S. Thesis, Bogaziçi University, 1994.
12. Peterson, M. S., F. H. Kulhawy, L. R. Nucci, and B. A. Wasil (1976) “Stress deformation behavior of soil-concrete interfaces,” Contract Report B-49 to Niagara Mohawk Power Corporation, Syracuse, NY.
13. Potyondy, J. G. (1961) Skin friction between various soils and construction materials, Géotechnique 11(4), 339-353.
14. Wong, P. C., F. H. Kulhawy, and A. R. Ingraffea (1989) “Numerical modeling of interface behavior for drilled shaft foundations under generalized loading.” Foundation engineering: current principles and practice, ASCE Geotechnical Special Publication 22, 565-579.
15. Zaman, M. M., C. S. Desai, and E. C. Drumm (1984) Interface model for dynamic soil-structure interaction, ASCE Journal of Geotechnical Engineering 110(9), 1257-1273.
