## 3 Analysis of the Measurement Results of Geosynthetic Reinforcement Deflection  
There are many publications describing laboratory-scaled and natural-scale tests of embankments on a soft soil improved with columns and with reinforced LTP. In the case of LTP reinforcement, the required parameters are the values of the reinforcement strains [10]. Few researchers have measured the geosynthetic settlement, from which the deflection curve can be determined. For the present paper, measurements from five tests available in the literature were used, both the laboratory-scaled test and the full-scale tests. Dutch scaled tests  
[PERSON] conducted a series of 12 laboratory-scaled tests [10]. Soft soil was modelled by a foam rubber cushion. On the top of the foam cushion and the piles, a 1.5 to 2 cm thick sand layer was applied. Then a GR (geotextile or geogrid) was attached. The embankment was represented by a 42 cm layer of sand or granular fill. The consolidation process of the soft soil was also modelled; the tap allowed drainage of the cushion during each test. In the case of tests K2 and T3 in [10], vertical displacements of the reinforcement were reported at two points. In order to determine the approximation of the deflection curve resulting from the measurements, additional assumptions were made: zero rotation angle at \(x=0\) (halfway between the columns) and zero displacements at the edge of the column (\(x=L/2\)). The approximation of the deflection function was determined by assuming the seventh-degree polynomial in the form of: \(w_{\text{exp}}(x)=a_{8}x^{7}+a_{7}x^{6}+a_{6}x^{5}+a_{5}x^{4}+a_{4}x^{3}+a_{3 }x^{2}+a_{2}x+a_{1}\). The coefficients of the assumed function were determined so that the function passed through the points resulting from the displacement measurements. Plots of selected approximations are shown in Figures 4 and 5. Since one specific deflection curve for a given case is analysed each time, adopting the polynomial as an approximation function is justified. The adoption of the seventh order polynomial made it possible to find a function that accurately approximates the experimental results (see Figures 4 and 5). According to [10], the material used as reinforcement in test T3 was completely biaxial for larger strains. The calculations were made for two given reinforcement stiffnesses, but due to the same nature of the error distribution, the results of deflection curve mapping error for the higher of the values presented in Table 1 are shown. In the case of test referred in the paper as C, the results were reported in [9]. After the test, the fill and GR were removed. The deformed shape of the thin sand layer below the GR was assumed to be the same as the deformed shape of the GR in the final phase of the test. The deformed surface was laser scanned. This allowed for the determination of the number of points on the GR displacement curve. The measured deformed shape was not completely symmetric. Therefore, the measurements for both parts were analysed as independent deflection curves (denoted as C_L and C_R, respectively), like in [9; 10]. As it cannot be clearly stated which results of the Dutch tests were presented in [9], on the basis of the information contained in [9; 10], the reinforcement stiffness given in Table 1 and the most probable load value \(q_{av}\) were adopted for the analyses. The ratio of the load \(q_{av}\) and the stiffness of the reinforcement \(J\) in this case was 0.125. In order to investigate the effect of the \(q_{av}/J\) ratio for cases with no soil support on the distribution of the deflection curve mapping error depending on the distribution of the equivalent load, a parametric analysis was performed for the C_L case. Therefore, the deflection functions for \(q_{av}/J=0.075,\ 0.100,\ 0.125,\ 0.150,\ 0.175\) were determined. In the case of test C, the seventh degree polynomial was also used to approximate the results.