## 1 Introduction  
For many years, embankments on soft soils improved with columns with transmission layer reinforcement have been the subject of worldwide research. This is an extremely complex problem due to a number of system interactions and occurring phenomena (e.g., the arching effect). The mechanism of load distribution and behaviour of such structure is still not fully understood, and models used for designing calculations differ significantly. The research results on embankments supported by a ground improved with columns are commonly presented in current literature, indicating the need for further analysis. The research concerns both cases, i.e., without LTP reinforcement and with reinforcement. [PERSON] and [PERSON] [1,2] described in detail a series of centrifuge tests of unreinforced piled embankments; these studies were aimed at a better understanding of the arching concept. The results of measurements of model experiments on embankments without LTP reinforcement were also presented, e.g., by [PERSON] and [PERSON] [3,4] and [PERSON] and [PERSON] [5]. A series of model tests of embankments with a reinforced LTP were also performed. The results of scaled field experiments are given in [6], and the results of scaled laboratory experiments are presented e.g., in [7,8]. Measurements from selected tests presented in [9,10] were used in the current paper. Full scale tests were carried out both on trial plots [7; 11; 12; 13] and in the final structure [14; 15]. In most cases, researchers measured the geosynthetic strains. Only in a few tests the displacement of the geosynthetic was also measured. Data reported by [PERSON] and [PERSON] [13] were particularly useful for application in the present paper. In the case of these studies, geosynthetic/soil settlements and the pressure exerted by the embankment between columns were measured over time. The experimental results presented in [16] showed that the membrane effect in a reinforcement combined with soil arching provides values of efficiency regarding load transfer to the piles close to 100% for all of the twenty-eight centrifuge tests performed. The analysis of road embankments on a ground improved with columns is carried out in two steps. In the first step, the load from the embankment and traffic is divided into the part carried directly by the columns (denoted as part A) and the rest (B + C) carried by the LTP reinforcement and the soft soil between the columns. This separation occurs as a result of arch mobilisation in the soil (the so-called 'arching' effect). Depending on local conditions, the geosynthetic may or may not be supported on weak soil (in the latter case C = 0). Whether soft soil is involved in the load distribution depends on its properties. In the case of BS [17], it is assumed that the soft soil does not contribute to the load transfer (C = 0). On the other hand, in the case of CUR [18] and EBGEO [19], the parameter characterizing soft soil for design purposes is subgrade reaction k [kh/m\({}^{3}\)]. Subgrade reaction k of the stratum can be estimated from the constrained modulus of the stratum E [kh/m\({}^{2}\)] and its thickness. In exceptional situations, such as loss of soil support, \(k=0\) is assumed for calculations [18; 19]. In the analytical methods, in order to determine the forces and strains of the reinforcement, the spatial system is reduced to the 1D problem of the membrane loaded with the equivalent load modelling the remaining part of the load (B + C). The arching effect and its description have been the subject of numerous reports (for example [20; 21; 22; 23; 24; 25; 26], [PERSON] and [PERSON] [27], [PERSON] [28] and [PERSON] [29] showed that various analytical calculation models for arching in piled embankments give different results in specific cases. [PERSON] et al. [30] with series of 3-D numerical analysis showed, that embankment on soft soil improved with columns with reinforced LTP performed better under uniform surface loading than under localized surface loading in terms of its deformation and load transfer.