Effect of Assumed Boundary Conditions in Numerical Model of Road Pavement-Mining Subsoil System on Criterial Values Used in Design Using Mechanistic Methods

Underground mining brings benefits in the form of the extracted mineral. The negative effects of mining exploration are deformations of the rock mass, which also cause deformations on the ground surface. There are continuous deformations, discontinuous deformations and mining-induced tremors. Recommendations regarding the protection of the structure of cubature building against the negative effect of mining operations are discussed in detail, for example, in the recommendation published by the Building Research Institute (ITB) in Warsaw. In the case of road structures, the situation is different. Firstly, there are no general rules that would provide clear guidelines for the procedure for designing road pavement in mining areas, similarly to cubature buildings. Secondly, in the computer programs used for the individual design of road pavement, it is not possible to assign additional actions, including mining impact. Therefore, in order to analyze the behavior of the pavement-mining subsoil system, an advanced numerical analyze should be carried out. In this case, the subsoil thickness, the boundary conditions and the constitutive relationships of the materials of the road pavement layers and subsoil should be determined. This paper presents an attempt to select kinematic boundary conditions for the FEM model of the road pavement-mining subsoil system, analogically to the model of the building-mining subsoil system. The paper is aimed at assessment of the influence of kinematic boundary conditions selection on the criterial values that are taken into account during the design process of road pavement using mechanistic methods. For this purpose, three cases were considered: (i) horizontal mining strain (εdesign ), (ii) curvature of surface (Kdesign ), (iii) combined impact of these actions. In these cases, each time vehicle wheel load was assumed. Based on the analyzes, the computational horizontal strain of the mining area εcomp is decisive when assessing the criterial values taken into account in the design process of road pavement structures.


Introduction
There are significant benefits from mining in the form of minerals, e.g. coal. However, in addition to the benefits, negative effects are also observed, see Figure 1.
A surface subsidence curve is formed due the impact of continuous displacement [4], [5]. It is described by a number of different indicators, e.g.: subsidence (w), terrain inclination (T), horizontal ground strain (ε), horizontal displacement (u), ground curvature (K) or radius of curvature (R=1/K), see Figure 2. -minimum compressive radius of curvature [1] All mining impact (continuous or discontinuous deformations in mining area, changing water levels and mining-induced tremors) the appearance of damage in all types of building structure subject to these impacts [1]. In the case of road pavement, this may cause a problem in their use or even  [3]), see gray area in Figure 1. The subsidence causes changes in the longitudinal profile [7] (see Figure 3) and the cross-section of the road and influences the creation of additional load in the pavement layers and subsoil . These damages may cause counter-falls and thus stagnation of water on the pavement surface, which endangers traffic safety (e.g. through aquaplaning) [8]. Except subsidence, effect of horizontal (compressive or loosening) strain on the pavement layers materials and subsoil is very important. While horizontal (compressive or loosening) strain may change parameters of pavement layers materials and subsoil [3], [9]- [11]. The compressive strain causes the uplift of terrain, including pavement or stones [12] (Figure 4) and deformation of the associated infrastructure and equipment of road elements [13], [14] ( Figure 5). The loosening strain may reduce soil stiffness [15] and layers made from aggregate not stabilized with hydraulic binders [8] and cause transverse cracks of pavement structure [7] (Figure 6).
Discontinuous deformation fractures the subsoil area. Their effects on the pavement and road subsoil were presented by Kotyrba and Kowalski [16], Grygierek 2018 [8], Adelsohn i in. 2020 [17], Grygierek and the others [18] - [21], Ju and Xu [22].    The rules for taking into account mining impacts when designing cubature structures or assessing their technical condition are presented in the Instructions of the Building Research Institute [23], [24], [25] as well as in the monograph [1]. In the case of road structures, the situation is different. Firstly, there are no general rules that would provide clear guidelines for the procedure for designing road pavement in mining areas, similarly to cubature buildings. Secondly, in the computer programs used for the individual design of road pavement, it is not possible to assign additional actions, including mining impact. Therefore, in order to analyze the behavior of the pavement-mining subsoil system, an advanced numerical analyze should be carried out. In this case, the subsoil thickness, the boundary conditions and the constitutive relationships of the materials of the road pavement layers and subsoil should be determined. This paper presents an attempt to select kinematic boundary conditions for the FEM model of the road pavement-mining subsoil system, analogically to the model of the buildingmining subsoil system. The paper is aimed at assessment of the influence of kinematic boundary conditions selection on the criterial values that are taken into account during the design process of road pavement using mechanistic methods. For this purpose, three cases were considered: -(i) horizontal mining strain (εdesign), -(ii) curvature of surface (Kdesign), -(iii) combined impact of these actions. In these cases, each time vehicle wheel load was assumed.
Based on the analyzes, the computational horizontal strain of the mining area εcomp is decisive when assessing the criterial values taken into account in the design process of road pavement structures.

Designing road pavement structures in mining areas
The guidelines used for designing road pavement structures [26] recommend that the design of structures in mining areas be applied individually. In this purpose, the numerical analyses can be used. Examples of these numerical analysis were presented by Fedorowicz and Fedorowicz [25], Grygierek et al. [8], [9], [18], [19], Kawalec et al. [21].
In the general approach, the task involving the building-subsoil system subjected to mining impact can be solved using the following methods [25]: A -conventionally using the methods of building structure mechanics, using substitute static diagrams and parametric description of the subsoil; B -using 2D or 3D FEM analysis and parametric description of the subsoil; C -using FEM analysis (2D or 3D) of the building-subsoil system. For contact-related problems concerning the pavement-subsoil system, so far two main trends used in the description of these systems have been applied, which are included in the classical approach  9). Unfortunately, the above-mentioned models hardly simplify the currently recognised description of subsoil behaviour [30]- [35]. It should be emphasised that considerable progress has been made in the constitutive modelling of the subsoil in the last fifty years [33], [36], [37], [39], [40]. This is probably related to the needs of large construction projects, the development of implementation capabilities of large endeavours, as well as the development of engineering and computational technology related to numerical modelling of the advances structures. Moreover, the analysis of the pavement structure as isotropic elastic layers lying on the half-space does not allow additional impacts, including the mining impacts.
The modelling inconsistencies with reality relate to the adoption of linear elasticity relationships to describe the behaviour of the pavement layers and subsoil, as well as to assume of the subsoil area cooperated with the pavement structure. These issues were the subject of the authors' earlier considerations.  The paper presents numerical analyses used to solve the task involving the pavement structuremining subsoil system, assuming approach C, i.e. FEM analyses for both subsystems. Such an approach seems appropriate to solve the problems presented earlier. When considering the possibility of a reliable assessment of the road pavement structure (without mining impacts) operation in the FEM model, the strong coupling of the pavement structure's response to the behaviour of subsoil should be included [32].

Numerical analyses
The numerical analysis of the pavement-mining subsoil system was performed using a 2D model (flat strain state). Due to symmetry, only one half of the model was analysed. The analysis was carried out using ZSoil.PC ver. 16.03. The analysed the structure of the road pavement with the layout and parameters are shown in Figure 10. A rectangular subsoil area with overall dimensions of 7.50 x 5.00 m was assumed. The dimensions of the subsoil area were assumed according to recommendations in Fedorowicz [36], Fedorowicz [37] and Kadela [32], [38]. The finite elements with dimensions in the highest-density area of 0.05 x 0.04 m (the ratio of the dimensions of the sides of finite elements in other grid subareas does not exceed 1:3) was assumed. Source: [12] For the purpose of the analyses, the following assumptions were adopted: -there is full interlayer bonding; -pavement load is 100 kN per axle, which results in vehicle wheel load (50 kN) uniformly transferred to the surface of the wheel-shaped trace (contact pressure q = 850 kPa); the value of the substitute distributed load q(2D) = 180 kPa was assumed according to Kadela [32] so that the resulting values of strains in the state (2D) are sufficiently close to the values determined in the axial symmetry state for the actual load q = 850 kPa.
-a elastic model (e) was used, as accepted in mechanical analyses; -there is no friction between the pavement structure and the surface of the subsoil; -mining impacts were determined in the form of vertical and horizontal displacements applied to the lower edge of the subsoil area and to the outer vertical edge of the same subsoil area ( Figure 11). The combined action of the vehicle wheel load and the impact of mining-related area deformation were assumed. Wheel load was introduced in two computational steps with an increment of 0.5; after the last step, mining impacts were introduced in ten stages with an increment of 0.1. The impact of mining deformation of the area, represented by kinematic input (vertical and horizontal displacements were introduced into the model nodes respectively), was analysed for values of horizontal ε and the curvature radius R=1/K corresponding to categories of mining areas 0 to IV. Characteristic and design values of the parameters (ε and R) as well as partial values of safety factors are included in Table 1. The computational analysis was performed for three cases as follows: I -impact of vehicle wheel load and εdesign impact, II -impact of vehicle wheel load and Rdesign impact, III -impact of a vehicle wheel and the joint impact of εdesign and Rdesign.  Figure 11. Loads and impacts adopted in the model analysis: a) εdesign impact; b) Rdesign impact.
Source: [12].   Figure 16 shows the effect of system rigidity on the obtained values. It can be observed that, along with the rigidity of the pavement structure, the criterion values taken into account in designing are lower for the same category of the mining area.

Conclusions
This paper presents an attempt to select kinematic boundary conditions for the FEM model of the pavement-mining subsoil system, referring to the method of taking into account mining impacts in the models of the building-mining subsoil system and their impact on the criterion values taken into account in designing road pavements. For this purpose, the impact of vehicle wheel loads and three cases were considered: separate impacts of horizontal mining strain (εdesign) and the area curvature radius (Rdesign) as well as the combined impact of these parameters. The following conclusions can be drawn on the basis of the results of the carried out numerical analyses: 1) For the road pavements structure exposed to mining impacts, the kinematic boundary conditions can be assumed; the procedure for determining displacements on the edges of the computational model of this system is the same as for the building-subsoil system [37]. 2) When assessing the criterion values and deflections taken into account in the assessment of the technical condition and designing pavement structures (for the cases analysed in this paper), horizontal deformation of the mining area εdesign is decisive, whereas the impact of the values of the Rdesign radius is negligible. 3) There is an effect of system rigidity on the analysed values, namely with the rigidity of the pavement structure the criterion values and deflections taken into account in design engineering are lower for the same category of the mining area.
In order to full assessment regarding the operation of road surfaces in mining areas, further analyses are required; it is also necessary to use advanced constitutive models to describe the behaviour of pavement layers materials and subsoil. This will be the subject of further research.