The structural response in a rigid pavement allows to know how the system reacts to the different solicitations to which it is subjected during its work regime, therefore, its determination is the basis of the design methods. In these pavements two failure criteria are considered, which are taken into account by the design methods; the fatigue failure of the concrete slab and the erosion failure of the foundation. The analysis of these failures is based on obtaining the structural response in terms of tensions and displacements, and checking, using empirical models, if the admissible values at critical points of the slab are satisfied. The models describe the behavior of the system as consequence of the action of repeated loads during the design period.
Plaxis 3d Foundation 2.2 Cracked
In the analysis and design of these pavements, the assumptions made, offer certain limitations in their application. As a consequence, since the beginning of the year 1970, the MEF, which has become a widely used tool for the analysis of rigid pavements, shows some differences between the studies developed by different authors, related to the way of modeling the slab, the interface with the foundation and load transfer mechanisms (dowels). Such differences can be reflected in the most recent works of the authors (Bayrak & Hınıslıoğlu, 2016; Cobarrubias, 2012; López & Tejeda, 2015; Roy, Reddy, & Ramachandra, 2013).
The slabs composed of concrete, are connected in the transversal joints by means of load transfer pins, and are supported on a foundation floor (subgrade), represented in the model as an infinite semi-space.
The constitutive model used for the slab-foundation-dowels system was selected taking into account the nature of the phenomenon. The speed of application of the loads and their magnitude, added to the high stiffness of the slab, cause that the stresses originated, remain below the elastic limits of the materials, thus discarding the phenomenon of plasticization, therefore, considered the modeling of the pavement system as a linear, elastic and isotropic medium, characterized by the proportionality between stresses and unitary deformations, where the constants of proportionality are Young's Modulus and Poisson's ratio (E, ν).
An infinite semi-space through a rectangular domain geometry for the concrete slabs foundation have been represented. Boundary conditions were applied to define the peripheric and bottom constraints. All horizontal movements (x-direction and y-direction) were constrained. The vertical displacements in both sides are not restricted, allowing the tensions and displacements on this direction to propagate until the end of the continuum, without generating errors in the numerical model. At the edge of the concrete slab corresponding to the slab center, conditions of symmetry on X axis were placed on the slab and the foundation (XSIMM U1 = U2 = U3 = 0) defining only the study section (Figure 6).
For the selection of the appropriate mesh density a factorial design was made, as show Figure 7, combining the horizontal node span (b) and vertical node span (h); the aspect ratio of the element was respected. The study was only carried out in the center of the slab (including the concrete shoulders), in the rest of the slabs and soil foundation was maintained a constant mesh (100x100x100 mm concrete slabs and shoulders, 200x200x200 mm soil foundation). The spacing between nodes was varied from 100 mm to 20 mm in the vertical and horizontal directions. The control variable measured in each combination was the tensile stress at the point located below the load footprint applied at the edge of the concrete slab, where stresses are greatest.
The model studied presents the same characteristics of the slab as in the model developed by the University of Maine, but they differ in the way of characterizing the foundation. In order to test the solutions, achieving the equivalence between both results, the subgrade reaction module (k) required in the Maine model was transformed into an elastic module, through the correlation model obtained through the software (StreetPave, 2014).
It is concluded that the most recommended density for the available hardware is the resolution 40x40x20 mm in the slab and 200x200x200 mm in the foundation, with an approximate calculation time of 3 hours and 11 minutes.
It was tried to find with this analysis, the depth of soil foundation that represents the domain as the infinite semi-space in order to reduce the time of calculation. If the domain is very small, the joints placed in the contour introduce reaction forces that increase the soil response, reducing the stress by confinement effect. Different depths foundation was analyzed, verifying the displacement produced in each one, in a control node close to the contour. The most unfavorable condition of the model was taken (slab thickness 150 mm and foundation modulus 20MPa, without concrete shoulder). The results of the study are shown in Figure 11.
It is observed that when the depth in the soil foundation is bigger, it is closer to the condition of infinite space, however, the number of finite elements increases, therefore, the calculation time increases too. A depth was chosen, in which the calculation time was not high and the displacement was close to zero. The obtained depth is 1.50 m, this represents a calculation time of 33 minutes for the concrete slab without shoulders case. With a shoulder, time grew approximately 2.5 times (one hour and 23 minutes).
The graph shows that using the ABAQUS numerical model, lower stresses are obtained, than in the other two models, all the graphs present a decreasing tendency as the thickness of the slab increases. The Westergaards model presents the most conservative results due to the considerations made by the author. The ABAQUS and EverFE models, despite sharing the same numerical tool (FEM), have differences but not so significant compared to the Westergaards model. These differences are due to the fact that they do not share the same physical phenomenon, since the resistance in the foundation soil is not given by the same parameter, in one case the modulus of elasticity (E) is used and in the other the reaction module is used (k), the difference was reduced by using a mathematical relationship between the two parameters. The stresses differences between the model studied and that of EverFE are not higher than 10%, and therefore, the model proposed for the investigation could be accepted.
From the graph it is observed that, as the thickness of the slab increases, the variations of the stresses decrease, evidenced by the reduction in the curvature, which shows the stiffness contribution of the slab with the action of the load, supported every time in better foundation resistance. It is also observed that from 350 MPa, the soil tends to have less stress influence, corroborating what was expressed by authors and institutions (Cajka, Burkovic, Buchta, & Fojtik, 2014; PCA, 1984; Yoder & Witczak, 1975), who point out that improvements of the support layer do not have a structural purpose, these layers are placed to reduce the effect of erosion and the rise of fine materials to the surface (pumping). However, the improvement of the properties of the foundation, contributes slightly to improve the behavior of the system, which is a factor to be taken into account in the obtaining of the work stresses, especially when the slab is thin.
In the empirical-mechanistic design for concrete pavements, the system formed by the slab and the foundation is modeled, with dimensions and resistant characteristics adopted in the design, to provoke the response of the structure, in tensions and deformations, to loads imposed on specific critical areas, so that the thickness of the slab can be obtained capable of withstanding repeated solicitations until the failure occurs. The response of the system is obtained with the help of the computational model built using finite elements, placing the loads at the critical points.
The computational modeling then allows obtaining the tensions originated at the critical points, in different conditions and materials of the foundation and the slab, obtained from applying reference loads, quantities that must correspond to the design regulations. These tensions are reduced to values that can be obtained at a distance of 60cm from the edge, for which the factors offered by the PCA (Portland Cement Association) are used, and whose research has shown that only 6% of trucks pass to this distance.
The heterogeneous and random nature of the parameters involved in the tensions produced by the loads have led to the establishment of procedures that allow these tensions to be determined from a model conceived in specific working conditions. Once the computational model has been calibrated and validated, its importance lies in the fact that it can be used to generalize any specific condition of solicitations, both loads and traffic, modifying the variables involved, specific to a given territory, such as the conditions of the foundation and of the subbase, as well as the characteristics of the concrete and climatic conditions.
With the proposed model, the stress calculated was lower than the solutions obtained by the Westergaard and EverFE software models. The main differences in the tensions are due to the use of a continuous model in the foundation and improvements in the formulation of the finite element method, however, the proposal follows the same tendency in the tensions, for each one of the factors in the models analyzed, which shows a correct modeling of the phenomenon. 2ff7e9595c
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