کاهش فحلیت کوتاه مدت بوسیله به هم پیوسته کردن لایه توسعه یافته در اطراف یک تجزیه و تحلیل حساسیت ژئوگرید

This paper presents a numerical investigation of the mitigation of the rutting process developed in the early stages of the utilization of a flexible pavement structure. The analysis is supported by the results of experimental research available in the technical literature. The mitigation of rutting achieved by application of a geogrid is tackled in the framework of sensitivity theory. The fact that the installation of a geogrid results in a decrease of permanent deformations is associated with the interlocking action that develops around a geogrid. It creates the formation of a new, stiffer layer of composite material. The experimental results on the rutting process provide information in terms of accumulated permanent deformations caused by repetitive load of constant magnitude. The constitutive model adopted for analysis is a type of rigid, perfectly plastic material. It is described by a modified Hooke's model that incorporates a modulus of permanent deformation. The functional of permanent displacement is formulated with respect to an unreinforced pavement system with the aid of a suitable adjoint system. The changes of permanent displacements caused by the insertion of a geogrid at the midst of the base layer are described as changes (first variation) of modulus of permanent deformation of the composite layer developed around the known location of the geogrid. Sensitivity theory allows for an extension of the constitutive equation due to the postulate that material characteristics are also considered as variables. The simplifications of the constitutive relationships expressed in variational form result from the fact that variations of permanent displacement are imposed on primary structure in the presence of constant load. The determined final form of the sensitivity equation of permanent displacement due to the changes of modulus of permanent deformation of the composite layer forms the basis for the numerical investigations. They are performed by means of the finite element method (FEM) for each (N)-th load repetition. The results in terms of permanent modulus of deformation of the composite layer surrounding the geogrid for some discrete values of its thickness demonstrate a considerable increase in stiffness of the newly developed layer as compared with an unreinforced pavement.

A geogrid provides a useful and cost-effective way of preventing sudden failure, collapse and rutting when building roads, railways and infrastructures sensitive to continuous and discontinuous subsides [1], [2], [3], [4], [5], [6], [7] and [8]. Numerous published studies like Bender and Barenberg [9], Chan et al. [2], Hass et al. [10], Jewell [11], Koerner [12], Moghaddas-Nejad and Small [13] and Wong and Small [14] indicate that, a function of reinforcement that the geogrid provides to the pavement system, is a complex set of mechanisms. The geogrid, when placed in a granular base course made of crushed stones, increases its stiffness and modulus. The lateral confinement is intended to resist the tendency for the base course to “walk out” from beneath as the result of repetitive vehicle load. The potential benefits resulting from the application of geogrid inclusions into base course include a decrease in the short term permanent deformations, increase in tensile strength, reduction of fatigue cracking, increase in durability of the pavement structure, and lowering the life cost of the pavement structure. The mechanism of stress transfer from the soil to the geogrid insertion depends primarily on the geometric properties of the inclusions. In particular, for geogrid, it depends on the more efficient interlocking principle. When stressed, the inclusion must be capable of sustaining the load without rupture and without generating unacceptably large deformations during the design lifetime of the pavement structure. Rutting is defined as the process of development of permanent deformations along the wheel paths. This type of unrecoverable deformation can unfold in the early stages of the application of the repetitive loads (short term rutting) or in the final stage of service life of the pavement structure. The former is attributed to the progressive stiffening process of the base layer. The latter is connected with two different mechanisms that define failure criteria in damage analysis [15]. Consequently, the first failure criterion defined with respect to fatigue cracking combines the admissible number of load applications with tensile strains developed at the bottom of the top asphalt layer as the result of the fatigue of the material having a given resilient modulus. The second failure criterion with respect to permanent deformations connects the number of load repetitions (producing damage of the pavement) to the compressive strains developed on the top of subgrade. All these criteria aim at a limit of excessive permanent deformations that affect performance of the pavement and reflect on its serviceability. One of the possible remedies improving the performance of a pavement in terms of mitigating the development of permanent deformations can be achieved by the installation of a geogrid within the granular course. The reported research on the application of geogrids to pavement systems located on soft clays [2], [4], [7] and [16] confirms the complexity of the mechanism of interaction of a geogrid and the surrounding base material. The major contribution to the stiffening process of the base layer is associated with interlocking, which in fact allows a sort of composite material to generate. The experimental results published by Moghaddas-Nejad and Small [13] provide valuable information on the behaviour of the model investigated. They are incentives for analytical and numerical studies. In particular, the available data [13] on the development and mitigation of short term rutting motivated an effort on numerical modelling of stiffening process that evolved around geogrid insertion. The laboratory model of the pavement structure was located on granular subgrade soil and was subjected to repetitive loading of constant value. The numerical investigations are focused on identification of the material characteristics of a stiffened layer that resulted in mitigation of the rutting process. The theoretical concept is formulated in the framework of sensitivity theory. The deformations that generate rutting are considered permanent and unrecoverable. The design variable is taken as the modulus of permanent deformation Ep. The available experimental results allow Ep to be considered as a function of the load repetitions. The functional of permanent deformation of the investigated pavement is determined with involvement of the adjoint system which can be loaded at any point where the record of laboratory displacement is collected. The constitutive model associated with unreinforced as well as reinforced structures is considered as rigid, perfectly plastic. The fact that the location of the geogrid in the base layer caused a considerable decrease of rutting, substantiated the assumption of the development of a new layer around the geogrid with a different modulus of permanent deformation as compared to an unreinforced pavement. In terms of sensitivity theory, it is interpreted as the change of modulus of permanent deformation that produces the change of permanent displacement. The functional of permanent deformation is formulated in integral form in the scope of variational calculus. The first variation (change) of the functional is due to the first variation (change) of the modulus of permanent deformations. For each load repetition, the variation of the functional is equal to the work of a unit force on the change of permanent deformation (which is equal to the difference between the displacement of an unreinforced and reinforced pavement system). Since the laboratory record of permanent displacement for an unreinforced as well as reinforced pavement is known, the change of permanent modulus developed in the stiffening layer can be determined for each load application.

The paper offers a possible option for numerical assessment of experimental results that aim at the evaluation of the effect of a geogrid's insertion to mitigate short term rutting processes. The beneficial effect of a geogrid in mitigation of rutting is attributed to the combined effects of interlocking and stiffening that are developed around a geogrid. The laboratory based rutting process is investigated in the framework of sensitivity theory. It is shown that a sensitivity approach is well suited for this class of problems. The permanent deformations associated with each (N)-th load repetition is described by a rigid, perfectly plastic material. The constitutive law employed for the purpose of numerical analysis is the modified Hookean model with a modulus of permanent deformation that assures nonrecoverability of deformations. Consequently, this fact requires continuous updating of geometry of the system after each load repetition. The initial moduli of permanent deformation in each layer of the unreinforced system are functions of the number of load applications N. It is shown that analysis of a reinforced structure can be conducted in the framework of sensitivity theory with respect to an unreinforced pavement, which is consistent with the basic assumption of sensitivity theory. The required potential of permanent deformation is formed within the scope of variational calculus. It represents the internal unrecoverable energy which is determined by means of a primary and an adjoint structure. The first variation of the functional of permanent deformations is defined by means of first variations of permanent strains imposed on the primary structure and the changes of modulus of permanent deformation in that part of base layer where the insertion of the geogrid occurred. The constraints in terms of the imposed variations of permanent strains generated some simplifications in constitutive laws extended for the purpose of sensitivity analysis. The final form of sensitivity equation reveals that: 1. proper interpretation of all terms contributing to sensitivity of permanent displacement indicates the optimal location of geogrid, 2. optimal location of a geogrid produces the best interlocking, highest stiffness and maximum value of modulus of permanent deformation Ep of the composite layer, 3. the problem is analyzed with the assumption that changes in modulus of permanent deformation δEp of the composite layer developed around the geogrid is constant (with respect to spatial variables) for the (N)-th load repetition, 4. to assure realistic results for changes of δEp and corresponding thickness of composite layer, the experimental evidence on the upper bound value of Ep should be incorporated in the analysis. The results obtained from numerical analysis demonstrate a substantial increase in modulus of permanent deformation Ep in a newly developed composite layer.