Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2022.32.0025 Acta Polytechnica CTU Proceedings 32:25–31, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague REMEDIATION OF A RAILWAY EMBANKMENT USING GEOCELLS AND DEEP SOIL MIXING - A NUMERICAL ANALYSIS Jan Štefaňáka,∗, Josef Vašinab a Brno University of Technology, Faculty of Civil Engineering, Institute of Geotechnics, Veveří 331/95, Brno, Czech Republic b WALTEC GDS, s.r.o., Masarykova 1355, Blansko, Czech Republic ∗ corresponding author: stefanak.j@fce.vutbr.cz Abstract. Progressive settlement of the embankment under the railway track near Žďár nad Sázavou, the Czech Republic, has been observed for many years. Immediate improvement was needed to secure the safety of the traffic and to increase the travel speed of the track. The reconstruction work consisted of deep soil mixing. Also, a load spreading geocell reinforced mattress was designed. The evaluation of the proposed solution by means of numerical modelling and associated laboratory testing is described in the paper. Keywords: Geocell, deep soil mixing, remediation, numerical modelling. 1. Introduction The purpose of the remediation work is the reconstruc- tion of both an embankment and the railway track near the railway station Žďár nad Sázavou, Czech republic. The railway of interest is a national rail- way included in the European Transport Network TEN-T. The height of the embankment is cca 5.5m. The unsatisfactory condition of about 320 metres of the embankment was identified during the prelim- inary walk-over survey. Horizontal deformation of the crowns of the embankment body was observed. Tilting of the traction line columns were observed in some places also, as can be seen in Figure 1. The owners of the regional railway infrastructure proved the necessity of repeated tamping of the track ballast under railway tracks due to the disintegration of the geometrical position of the track rails [1]. Hence, the main purpose of both remediation and increasing the width of the embankment is to increase stability and to ensure the safety of railway transport. A conse- quent effect is an increase of the railway traffic speed. The measures designed to achieve the stated goals are described in detail later in the paper. The area concerned is built of metamorphic rocks of the Moravian branch of the Moldanubian in terms of geological structure. Metamorphic rocks in the sub- soil of the railway embankment are heavily weathered and to a considerable depth. The rock eluvium has the character of clay and dusty sand. The eluvium is covered with a layer of fill and or Quaternary clay of variable thickness. Clayey eluvium and clay are insulators from hydrogeological point of view. The clayey sandy and sandy eluvium is only slightly wa- terlogged. The slope of the groundwater level and the direction of groundwater flow is to the N, NNE and NE, towards the Sázava river. Climatic conditions in the area of interest are characterized by freezing depth hpr =1.1m. 1.1. Results of the geotechnical survey of the embankment Evidence of instability, visible to the eye, was found in both the railway tracks and the embankment. Tilt- ing of traction line columns and deformation of the embankment crown were observed during the prelimi- nary investigation and walk-over survey. Based on the results of the preliminary investigation, the strategy for a detailed survey of the embankment body was established. The survey was conducted in three typi- cal cross-sectional profiles. Combinations of trial pits, core boreholes, and dynamic penetration tests were performed in each profile. The results of penetration tests were evaluated according to [2]. The probes were evenly distributed at the base of the embank- ment body, at the top (in the axis of the two parallel rail tracks) and in the crowns on both sides of the embankment. Based on the results of dynamic prob- ing, the relative density of soil into the depth of 3.3m was recognized as loose to medium-dense. The soil sample was classified according to EN ISO 14688-2 as siSa. The percentages of the individual soil fractions were 4% of fine grains, 21% of sand and 62% of sand and 13% gravel. An admixture of slag by-products was found in the samples also. The material ranges from poorly permeable to permeable. Probes at the foot of the embankment body and in the axis of the embankment crown could not be performed due to an abundant presence of cable routes. 1.2. Proposed remediation work The following sequence of remediation measures was proposed, based on results of the conducted surveys: 25 https://doi.org/10.14311/APP.2022.32.0025 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en Jan Štefaňák, Josef Vašina Acta Polytechnica CTU Proceedings Figure 1. Condition of the railway before recon- struction: tilting of the traction line columns (top) and Temporary measures against disintegration of the track rail geometrical position(bottom). (1.) Removal of the top part of the embankment along its entire length to a depth of approximately 1.6m below the current sub-ballast layer. (2.) Construction of the Deep Soil Mixing (DSM) columns evenly distributed in the embankment. The purpose of DSM columns is to increase the stiffness of the embankment and to help transfer the traffic load from the rail through the embankment body to the subgrade formed by competent weathered gneiss rock. (3.) Building of a gabion wall situated at the foot of the embankment body. The height of the wall varies between 1.0m and 3.0m, according to the actual height of the embankment in specific sections. The purpose of the gabion walls is to improve a currently too steep geometry of embankment slopes and to eliminate the vertical deformation of the embankment due to the traffic loading. (4.) Construction of the geocell mattress filled with crushed stone. The mattress is constructed above the hi-strength single-axial geogrid and geomem- brane that cover the heads of DSM pillars. 2. Numerical analysis A relatively high number of technologies and struc- tural elements is combined in the above described remediation measures. Hence, it was decided to use the Finite Element Method (FEM) as a tool for assess- ing the effect of designed measures on the stability and deformation of the embankment. The Plaxis 2D pack- age was used for simulation of the development of the stress-strain state in the embankment, with respect to the sequence of the remediation work phases. 15- node finite elements were used for modelling the soil, which approximates the deformation by quartic poly- nomials. "Plastic" and "safety" types of calculations were performed. The input values of the properties of the soil materials forming the embankment and the subgrade were determined on the basis of the re- sults of conducted laboratory tests and in-situ tests. Approaches for transforming each component of the remediation measures into a plane strain numerical model are described in the following paragraphs. 2.1. Modelling of deep soil improvement The installation of Deep Soil Mixing (DSM) pillars with a diameter of 0.6 meters with axial distance 1.2 metres in the longitudinal direction is one of the key components of the proposed remediation measures. The process of column mixing is captured in Figure 6. Adequate data from the literature [3] were used to determine the strength and deformation proper- ties of the final product of the DSM technique, the soil–cement composite. The line of columns is repre- sented by the virtual wall in the 2D numerical model. The equivalent modulus of elasticity of the wall was calculated as the weighted average of the modulus of elasticity of the column Ecol=2000MPa [3] and of the modulus of the soil between the pillars in the longitudinal direction Esoil=6MPa. The principle of calculation of the equivalent modulus of elasticity 26 vol. 32/2022 Remediation of a railway embankment – a numerical analysis of the wall summarised in [4] is described by equa- tions (1)–(3) and schematically illustrated in Figure 2. Symbol Acol represents the cross-sectional area of the DSM column and the Ar the area of the virtual wall. rcol = Acol Ar = Acol Acol +Asoil (1) rsoil = 1− rcol (2) Eeq = (rcolEcol) + (rsoilEsoil) (3) The uniaxial compressive strength of the DSM col- umn composite material was estimated according to [3] as σc=3.5MPa. The methods proposed by [5] were used then for the transformation of the uniaxial compressive strength on the strength parameters of Mohr-Coulomb failure criterion ϕ and c. The input value of angle of internal friction is ϕ = 35 °. The value of cohesion was determined as c = 187 kPa using equation (4). c = √ σc 100 (4) Contact between the outer surface of the virtual wall and the surrounding soil was modelled by a contact element with the value of parameter Rinter =0.75. 2.2. Modelling of the Geocell Mattress The geocell filled with crushed stone was modelled as a layer with equivalent strength and stiffness param- eters. The input values of the strength and stiffness parameter of equivalent material were determined ac- cording to [6],[7], and [8], considering the beaviour of crushed stone to be governed by the Duncan–Chang non–linear constitutive model [9]. Increasing of the values of the strength and deformation parameters of the filling material is considered due to the 3D stress state in the individual cell pocket [10]. The devel- opment of the apparent cohesion cr depends on the increased lateral stress ∆σ3 arising in the soil inside the cell due to the membrane stress induced by the wall of the cell. The relationship between the apparent cohesion cr and the lateral stress ∆σ3 is illustrated in Figure 3. The smallest circle illustrates the failure stress state of the unreinforced filling material. The lateral stress σ3 increases to the value σ3 + ∆σ3 due to the confine- ment of the filling material by the cell wall. The value of major principal stress σ1 increases also from the value σ1u. This stress state is illustrated by the circle named "with confinement" in Figure 3. However, the same stress state can also be described by the largest circle, which is determined by the lateral stress σ3 and the apparent cohesion cr. The relationship between cr and σ3 can be derived using Mohr–Coulomb failure theory. The major principal stress σ1 is stress that the soil is able to sustain before failure, and can be described by equation (5). σ1 = 1 + sinϕ 1− sinϕσ3 + 2cr √ 1 + sinϕ 1− sinϕ = Kpσ3 + 2cr √ Kp (5) Where Kp is the passive earth pressure coefficient of the filling material. If the confining pressure σ3 + ∆σ3 is applied to such material, then the σ1 is given by the equation (6) σ1 = Kp(σ3 + ∆σ3) (6) However, the value of σ1 stays unchanged. The increment in the apparent cohesion cr due to the increase of the confining pressure can be expressed from the comparison of equations (5) and (6), which results in formula (7). cr = ∆σ3 2 √ Kp (7) Increase in the confining pressure ∆σ3 on the soil due to the presence of geocell is given by equation (8), which originates in the membrane theory proposed by [12]. ∆σ3 = 2M d0 [ 1− √ 1− ξa 1− ξa ] (8) Where M is the secant modulus of the geocell ma- terial at axial strain ξa, which is obtained from the tensile load–strain response of the geocell material at 2% axial strain, and d0 is the equivalent diameter of the geocell pocket. The stiffness of the composite ma- terial depends on the stiffness of the filling material and on the secant modulus of the geocell material. The nonlinear relationship between these two parame- ters and between the parameter Kr can be expressed by the equation (9). Kr = Ke + 200M0.16 (9) In the above Ke is the modulus number, which is a dimensionless parameter that represents Young’s modulus of the filling material [9]. The elastic modulus of the Duncan–Chang model in loading conditions Ei is given by equation (10), where n is a modulus exponent and Pt is the atmospheric pressure which is used to normalise the stress inputs. Ei = KrPa ( σ3 Pa )n (10) 27 Jan Štefaňák, Josef Vašina Acta Polytechnica CTU Proceedings DSM column wall width soil between columns (walls) DSM column wall Figure 2. The principle of replacing DSM pillars in a plain strain model by a virtual wall. Adapted from [4]. σ1σ3 Δσ3 cr σ1,u φ φ unreinforced reinforced composite with confinement unreinforced σ τ Figure 3. Mohr circles for unreinforced, reinforced and composite (geocell filled with crushed stone) ma- terial (Adapted after [11]) The values M =450MPa, d0 =0.24m, Ke=725, n=0.43 and Kp=3 were used in this presented anal- ysis. The contact between the equivalent geocell layer and the surrounding soil was modelled by a contact element with the value of parameter Rinter =1.0 ac- cording to the results of experiments published in [13]. The gabion walls constructed on both sides of the embankment were also included in the model. The gabion baskets were modelled by the "geogrid" type of finite elements. The mechanical parameters of the welded gabion basket net made of steel wire of diame- ter= 3.0mm and wire spacing of 75 mm were deter- mined according to [14]. The value of axial stiffness of the net was EA=19.0E3 kN/m. The contact between the basket net and the filling material and the wall backfill material was modelled by a contact element with the parameter Rinter =0.75 . The geogrid ele- ment with stiffness EA=12.9E3 kN/m was used also for modelling the hi–strength geogrid placed above the heads of the DSM columns. The 60.0m×36.0m model with 48 172 finite elements was used for anal- ysis. The detailed cutout of the FE model with all proposed remediation measures is shown in the Figure 4. The Elastic–perfectly plastic Mohr Coulomb (MC) constitutive model was used to describe the behavior of soil and composite materials. Input values of the MC model are summarised in Table1. 3. Laboratory testing of DSM composite material Some of the design assumptions stated above were evaluated by execution of laboratory tests. Prepro- duction laboratory tests were conducted due to the uncertainities in the chemical reactions in the cement- soil mixture, because the slag by-products was added into the embankment during its construction. Mix- tures for these tests were prepared according to the recommended procedures described in detail in [15], [16]. Three variants of the mixture were prepared from the soil taken from the embankment during in- vestigation and from a cement suspension. Cement content in suspension varied between 250 kgm−3 to 350 kgm−3. Water to cement ratio was varied between w/c=0.85 to 1.3. The uniaxial compressive strength of the composite material produced by the DSM tech- nology was measured. The compressive strength was determined by placing cylindrical specimens of known dimensions in a test press and loading them at a rate of 1% of the sample height per minute until failure. The reduction of the resulting strength due to the ratio of the length of the speciment to its height was performed according to [15] to normalise the results of tests performed on samples with a different geome- try. The laboratory testing programme follows with an evaluation of the uniaxial compressive strength of the samples taken in-situ. These control tests were performed on the samples prepared from the mixture taken on site directly from the fresh column and cured in laboratory conditions. The second type of samples for control test were prepared from the borehole cores taken from the colums which had already reached a certain strength. The uniaxial compressive strength was evaluated on the 7, 21 and 28 days old specimens. The mean value of a uniaxial compressive strength of 28 vol. 32/2022 Remediation of a railway embankment – a numerical analysis 5 2 3 11 7 8 1 9 10 6 4 DSM column Geocell mattress Gabion wall Hi-strength geogrid Figure 4. Cutout of the FEM model - detail of the embankment. (The numbers in circles refer to the material characteristics summarised in Table (1)). Material Unit weights Strength par. Deformation par. γunsat γsat c´ ϕ´ E´ ν´ [kN/m3] [kN/m3] [kPa] [◦] [MPa] [-] 1 Eluvium 18.5 20 4 30 11.89 0.3 2 Gabion infilling rock 17.9 19.6 100 35 20 0.2 3 Geocell mattress 17.5 19.0 33 30 80 0.3 4 Silty gravel 19.00 20.50 3 35 26 0.3 5 Ballast 20.00 22.00 1 40 135 0.25 6 Fills 17.00 18.00 4 30 8.9 0.3 7 Embankment - upper part 17.50 19.00 1 35 80 0.25 8 Embankment - lower part 17.50 19.00 2.8 30 3.13 0.28 9 Weathered rock in subgrade 28.00 28.00 5600 39.5 600 0.25 10 DSM columns 20 21 187 35 844 0.3 11 Backfill 17.50 19.00 4 32 10.4 0.3 Table 1. Input values of MC constitutive model parameters the composite was σc=13.8MPa. Hence, it can be said that the results of numerical analysis are on the safe side. 4. Results The calculated value of the factor of safety was F =1.09, when only the self-weight of the embank- ment was applied to the model of current state of the embankemnt without any proposed remediation measures. This result confirms the in-situ observed sit- uation - the permanent increase of deformations. The implementation of remediation measures increased the calculated factor of safety to the value F =1.57. The calculated total deformation of the embankment body will not exceed 13.4mm after the reconstruction. The calculated field of total deformations is presented in Figure 5. 5. Conclusions The paper describes the evaluation of the design of remediation action at defective railway embankment. The remediation measures consisted of Deep Soil Mix- ing columns covered by a geocell mattress. The effect of the proposed measures was verified by numerical analysis. The process of building the 2D numerical model is presented. Results of numerical analysis proved, that the proposed remediation measures leads to a redistribution of the stress field in the embank- ment body. The stress in the embankment body im- proved by DSM technique is concentrated in the DSM columns, because they have significantly higher stiff- ness than the surrounding soil. The largest portion of stress is transmitted by two pillars located closest to center of the embankment body. The laboratory tests are also described, erformed for the purpose of the design and evaluation of the DSM composite material. 29 Jan Štefaňák, Josef Vašina Acta Polytechnica CTU Proceedings Figure 5. Isolines of computed total deformations caused by a traffic loading of intensity 80 kN/m Figure 6. Construction of DSM columns at the Žďár nad Sázavou building site List of symbols hpr Freezing depth [m] Ecol Modulus of elasticity of DSM column [MPa] Esoil Modulus of elasticity of soil [MPa] Eeq Modulus of elasticity of virtual wall [MPa] Acol Cross-sectional area of DSM column [m2] Ar Cross-sectional area of virtual wall [m2] σc Uniaxial compressive strength [MPa] ϕ Angle of internal friction [◦] c Cohesion [kPa] cr Apparent cohesion [kPa] ∆σ3 Lateral stress increment [kPa] σ3 Minor principal stress [kPa] σ1 Major principal stress [kPa] σ1u Major principal stress in unreinforced material [kPa] M Secant modulus of the geocell material [MPa] d0 Equivalent diameter of the geocell pocket [m] Ei Elastic modulus in loading conditions [MPa] Pt Atmospheric pressure [kPa] Rinter Interface strength Kp Passive earth pressure coefficient ξa Axial strain Kr Modulus number of reinforced material Ke Modulus number of unreinforced material n Modulus exponent Acknowledgements This work was funded by the research project No. TA04031092 supported by the Technology Agency of the Czech Republic. 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Kwiecień. The analysis of the usefulness of welded meshes to embankment reinforcement. Studia Geotechnica et Mechanica 39(3):3–9, 2017-09-1. https://doi.org/10.1515/sgem-2017-0024. [15] B. C. M. Ellen, R. R. Berg, J. G. Collin, et al. Federal Highway Administration Design Manual. Office of Transportation Management Federal Highway Administration, 400 7th Street SW Washington, DC 20590, 2013. [16] M. Kitazume, M. Terashi. The Deep Mixing Method. CRC Press/Balkema, EH, Leiden,The Netherlands, 2013. 31 https://doi.org/10.1007/s10706-008-9176-5 https://doi.org/10.1139/cgj-2018-0866 https://doi.org/10.1016/S0266-1144(98)00034-X https://doi.org/10.1515/sgem-2017-0024 Acta Polytechnica CTU Proceedings 32:25–31, 2022 1 Introduction 1.1 Results of the geotechnical survey of the embankment 1.2 Proposed remediation work 2 Numerical analysis 2.1 Modelling of deep soil improvement 2.2 Modelling of the Geocell Mattress 3 Laboratory testing of DSM composite material 4 Results 5 Conclusions List of symbols Acknowledgements References