# Resilient Modulus Characterization of Compacted Cohesive Subgrade Soil
## 1 Introduction  
The structures which are subjected to dynamic and repeated loads are mostly industrial foundations, railroads, and pavement. Such structures are based on occasionally highly plastic soils, where their origin is connected with a glacier. Such cohesive soils can be found in central and northeastern parts of Europe. Bituminous pavements are based on rigid and granular layers, to provide the optimal distribution of traffic loads [1]. Nevertheless, soft cohesive subgrade soils, even under low loading conditions and after improvement, still develop some deformations [2]. The uneven settlement or putting which can be observed as a premature exceeding of the serviceability limit state is caused by such deformation in the subgrade and, therefore, in the sub-base layer. The deformation of soils under dynamic and cyclic loading conditions is important to study [2; 3; 4; 5]. In the case of a pavement construction on an embankment based on soft soil, the permanent deformation characteristics caused by traffic become an important factor, which impacts the design life and maintenance of pavement [6; 7]. The long-term cyclic loading and short-term dynamic loading characterizes the traffic excitations. The typical strains in the base and sub-base vary from 0.01% to 1%. The strain change range in subgrade soil layers vary from 0.003% to 0.6% [8; 9]. The long-term loadings, defined as a \"quasi-static loading\", cause long-term settlements and creep processes to occur due to the dissipation of loading energy as a plastic strain. The dynamic loadings caused by traffic may occur in the form of short-term deformation of layers, characterized by the small permanent strain and the behavior of layer, which may be seen as reversible [1; 10; 11; 12]. The evolution of modulus value during cyclic lading shows different characteristics under certain strain range. Therefore, the popper adjustment of the moduli value is important. The design method of pavement layer thickness is based on the mechanistic pavement analysis, which uses the multilayer linear elastic model and a cyclic triaxial test. The laboratory tests conducted on the pavement layer material leads to the definition of the actual soil mechanical behavior under cyclic loading by simulating the in situ conditions [13; 14; 15; 16; 17]. The calculations of characteristic values for the pavement design purposes, in the mechanistic method, concerns the estimation of the Young's modulus E and Poisson ratio \(\upsilon\). The resilient modulus \(M_{r}\), defined as the unloading modulus of the hysteresis loop after many cycles of repeating loads, is a stiffness measurement of pavement layers. The \(M_{r}\) value is connected with the non-linear elasticity model [18; 19; 20; 21]. The plastic displacement which is another important part of pavement design and is calculated mostly on the basis of empirical models, based on the results of cyclic triaxial tests, which present the plastic strain function of a number of cycles [22]. The response of soil to repeated loading is stress dependent, therefore, the resilient modulus value is also stress-dependent. The low pressure conditions during dynamic tests results in small strain and elastic response of the soil, provided that the strain amplitude does not exceed \(10^{-4}\%\). One of the best methods of obtaining this kind of loading and separating the stress-strain elastic relation is propagating in the soil small amplitude stress waves [23; 24]. The linear stress-strain behavior below the strain level being equal to 0.001% was observed for uncemented granular soils [25; 26]. The small-strain characteristic modulus is called the \"maximum Young's modulus\" \(E_{max}\) or the \"maximum shear modulus\" \(G_{max}\). The \(G_{max}\) value corresponds to the linear elastic region of strain, where no plastic strains occur. If the shear force is high enough, the G value starts to deviate from \(G_{max}\)[27].