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GERMAN RECOMMENDATIONS FOR REINFORCED EMBANKMENTS ON PILE-SIMILAR ELEMENTS H.-G. Kempfert Institute of Geotechnic, University of Kassel, Germany C. Goebel Dresden, Germany D. Alexiew HUESKER Synthetic GmbH, Germany C. Heitz Institute of Geotechnic, University of Kassel, Germany ABSTRACT: The construction of embankments on soft underground is a common problem. In recent years a new kind of foundation, the so-called “geosynthetic reinforced pile-supported embankment”, was established. Until now the system behaviour can only be described analytically by simplified geomechanical models. Furthermore, there are simplified calculation procedures, which allow the dimensioning of the geosynthetic reinforcement. In the course of the revision of the EBGEO (German Recommendations for Geosynthetic Reinforced Earth Structures), new recommendations for soil reinforcements above pile-similar elements under static loading were worked out. These new developed analytical methods represent a new State-of-the-Art and enable a realistic and suitable approximation of the bearing behaviour of the compound structure. They offer simplified methods for the costing methods. The paper describes the new methods of calculation and the construction regulations for this kind of foundation as recommended by the EBGEO. 1 INTRODUCTION Soil improvement and reinforcement techniques have under gone a decisive development during the last decade, especially as result of the increasing need to construct on soft ground providing economical solutions. Designs of structures, such as buildings, walls or embankments on soft soil causes several concerns. They are related to the increasing capacity failures, intolerable settlements, large lateral pressure and movement, and global or local instability. A variety of techniques may be used to address the above concerns. These include pre-loading the soft soil, using light-weight fills, soil excavation and replacement, geosynthetic reinforcement and soil improvement techniques. In recent years a new kind of foundation, the so-called “geosynthetic-reinforced pile-supported embankment” was established (Fig. 1). The pile elements (e.g. concrete piles, cemented stone columns, walls etc.) are placed in a regular pattern through the soft soil down to a lower load-bearing stratum. Three possible support conditions are illustrated in Figure 2. Piles are typically arranged in rectangular or triangular patterns in practice. Above the pile heads, the reinforcement of one or more layers of geosynthetics (mostly geogrids) is placed. In Germany the geosynthetic-reinforced pile-supported systems have been used for several applications, especially for highway and railroad embankments (ALEXIEW (1999), (2001)). The systems have proved to perform well regarding both bearing capacity and serviceability if designed and constructed in an appropriate way (ALEXIEW (1999), (2001)). Until now the system behaviour can be described analytically only by simplified geomechanical models. Furthermore, there are simplified calculation procedures, which allow the dimensioning of the geosynthetic reinforcement (e.g. HEWLETT (1988), BS 8006 (1995), EBGEO (1997), ALEXIEW (2002)). To examine the bearing mechanisms in the system and to derive a better analytical model, a research project has taken place at the Institute of Geotechnics, University of Kassel (KEMPFERT (1999), 279 ZAESKE (2001, 2002)). The developed design procedure will be introduced soon into Chapter 6.9 “Reinforced earth structures on point- or line- shaped bearing elements” (EMPFHELUNG 6.9 (2003)) of the new edition of the EBGEO (German Recommendations for Geosynthetic Reinforcement). This new analytical method represents a new State-of the-Art. It is believed to be more precise and realistic than the “older” procedures available, which was confirmed by experiments (ZAESKE (2001)); at the same time it is more sophisticated and the other procedures available limited mostly to non-cohesive fills. An overview of common procedures today is given e.g. in (ALEXIEW (2002)). The general load transfer mechanisms, model test results and the new method of calculation and the construction recommendations for this kind of foundation as recommended in Chapter 6.9 of the EBGEO will be described shortly. 2 LOAD TRANSFER MECHANISMS The stress relief of the soft soil results from an arching effect in the reinforced embankment over the pile heads and the high tensile effect of the geosynthetic reinforcement. Due to the higher stiffness of the piles in relation to the surrounding soft soil, the vertical stresses from the embankment are concentrated on the piles, simultaneously soil arching develops as a result of differential settlements between the pile heads and the soft soil settlement below. The 3D-arch splits the sand on the soft soil and the applied load is transferred onto the piles and then to the bearing stratum. The redistribution of loads in the embankment depends on the system's geometry, the strength of the embankment and the stiffness of the “tiles”. A modified stress-distribution theory was developed (ZAESKE (2001)). Additionally, a concept to take into account the low supporting soft soil-parameters into the stress distribution in a deformation-related way was introduced including the effects of geosynthetic reinforcement and geosynthetic reinforcement under such soils. Differential equations had to be developed to reflect this interaction (ZAESKE (2001)) (Fig. 3). 3 RESULTS OF MODEL TESTS UNDER STATIC LOADING Three-dimensional well-instrumented model tests in a scale of 1:3 were carried out to investigate the bearing and deformation behaviour and to check and verify the concept and theory mentioned above. A group of four piles was placed in a weak soil of peat in a rectangular grid, above which a reinforced or unreinforced sand fill was placed in different heights (Fig. 4). The stress distribution in the reinforced sand layer was recorded by pressure cells. The part of the load carried by the piles was measured by load-cells and allowed a comparison with the measured stress field in the sand. Under static loading the depressions of the stress from the geometric boundary conditions and the shear strength of the sand fill was verified. Similar to field measurements, the strains in the geogrid were found to be relatively small, provided that reaction stress of the underlying soil beneath the rigid pile elements is mobilised. In additional to the model tests, numerical investigations with the finite element method (FEM) were performed for static conditions. The evaluation of the FE-calculations resulted in further information on the stress distribution in the reinforcing layer and the resulting load transfer onto the pile. After these verifications, the new method became part of Chapter 6.9 of the new edition of the EBGEO (draft) and is explained in the following chapter. 280 4 DESIGN RECOMMENDATION IN CHAPTER 6.9 EBGEO (DRAFT) The design procedure recommended in Chapter 6.9 of the EBGEO (draft) (EMPFHELUNG 6.9 (2003)) is divided into two steps: In the first step the load/stress distribution in the embankment is evaluated without considering any geosynthetic reinforcement, which results in the vertical stresses on top of the piles (σzx) and on the soft subsoil between them (σzak). The analytical model is based on the lower bound theorem of the plasticity theory and results from predefined directions of the stress trajectories in the reinforced soil body (ZAESKE (2001, 2002)). According to the numerical and experimental results the stress state in the reinforced embankment is divided into a zone, where the normal pressure at rest can be assumed, and an arching region, where the stress redistribution takes place (Fig. 4). Equation (1) shows the differential equation derived from the equilibrium of forces of the three-dimensional soil element in radial direction (Figure 7). For more convenience, σzak can also be derived from dimensionless design graphs (e.g., Figure 9 for σzx = 30°). Figure 4 shows the calculated vertical stress distribution in comparison with results of the model tests. In the second step, the vertical pressure σzak is applied to the geosynthetic reinforcement as external load. To predict the stresses in the reinforcement, an analytical model is applied based on the theory of elastically embedded membranes (ZAESKE (2001)). The maximum strain in reinforcement (i.e. the maximum tensile force) is concentrated in the band bridging two neighboured piles despite the common engineering sense, it was confirmed by the experimental work as well)). Therefore the analytical model assumes that the maximum stress in the geosynthetic membrane takes place within the width b_ex, and may 281 be calculated based on a planar system (Fig. 10). Biaxial geogrids must be analysed both in x- and y-direction. modulus of subgrade reaction k_sx of the soft soil, the total vertical load F_v and the dimensions b_1c and L. Since all geosynthetics tend to creep, the tensile modulus J is time-dependent and has to be reduced from the real isochrones of the geosynthetic reinforcement, the latter is essential. In EMPFEHLUNG 6.9 (2003), the values of c_p respecti-vely f_op can be cut off from a dimensionless design graph, see e.g. (Fig. 12). Finally, the tensile force in the rein-forcemt E_(k) where F_T1/L = ω_F1 (5) Figure 10 Load transfer and simplified planar (2D) bearing sy-stem (ZAESKE, 2001, 2002) The resulting triangular vertical strip load F_T on the geogrid strip is calculated from the pressure σ_ox, and the loaded area A (Fig. 11). Rectangular grid Figure 11 Calculation of the resulting force, F_T, assigned to the load influence area A, (EMPFEHLUNG 6.9, 2003) The influence of the bearing effect of the soft soil between piles is considered by using a modulus of aubgrade reac-tion. A simplified approximation is given in Equation (3); for multiple soft soil layers see EMPFEHLUNG 6.9 (2003). The tensile stiffness of the geogrid [kN|m] k1 = E_membrane b_max width of support [m] z = 1 - 2 * k_f/F_h stress in the reinforcement: F_zl/L = κ_y_F1 (4) Figure 12 Maximum strain in the geosynthetic reinforcement (EMPFEHLUNG 6.9, 2003) In addition to the membrane effect, geosynthetics are stressed by horizontal forces. The influence of an inclined surface of the reinforced em-bankment (typically slope i) is illustrated in Figure 13. The lateral thrust can be considered on the safer side assuming an active earth pressure condition without any support by "piles" or soft soil (BS 8006 (1995), ZAESKE (2001, 2002)). The concept is conservative. 282 Figure 13 Additional horizontal force in the reinforcement be-neath embankment slope (EMPFEHLUNG 6.9, 2003) ΔE_x = E_Ak_m (1-12x/(1-α_i)-α_i)*k_e (6) 5 CONSTRUCTION RECOMMENDATIONS IN CHAPTER 6.9 EBGEO Based on German and international experience with geo-synthetic-reinforced pile-supported embankments, practi-cal reasons, experimental results and the validity of the analytical model following recommendations are estab-lished: 5.1 Pile elements and spacing The center-to-center distance s and the pile diameter d of the piles resp. pile caps should be chosen as follows: 5.2 Geosynthetic reinforcement The distance between the reinforcement layer and the pla-ne of the pile/column/wall heads should be as small as possible, in order to achieve maximum efficiency of the geosynthetic membrane. However, it is recommended to have a safe distance (interlayer) between the lowest rein-forcement and the pile heads in order to prevent a structu-ral damage of the reinforcement because of shearing at the edge of the pile heads. d ≤ 0,15 metp. bs / share.kes.wor.bid less... maximum two reinforcement layers (Fig. 14) For maximum cost savings benefit sought 5. The use of a modulus of subgrade reaction be-tween the pile elements and the surrounding soft soil k_s < kup / just bmg (to ensure all “artucly” soft compressive elements in the high), normally, conven-tional pile-systems fulfil this condition. Figure 14 Distance z in the case of one and two reinforcement layers (EMPEHLUNG 6.9, 2003) 5.3 Embankment should be checked additionally. 6 FINAL REMARKS AND FUTURE PROSPECTS Geosynthetic-reinforced embankments on point- or line shaped bearing elements (“piles”) provide an economical and effective solution for embankments constructed on soft soil, especially when rapid construction and strict deforma-tion of the structure are required. The first model tests showed that the arching effect was ensured/due constant stresses of the reinforcement casting. 283 7 REFERENCE Alexiew, D., Vogel, W., 2001: Railroads on piled embankments in Germany: Milestone projects. In: Landmarks in Earth Rein-forcement, Swets & Zeitlinger, 2001, pp. 185-190 Alexiew, D., Gartung, E., 1999: Geogrid reinforced railway em-bankment after one year performance monitoring 1994, 1995. Proc. 7th International Symposium on Geosynthetics, Rio de Ja-neiro, 1999, pp. 493-411 Hewlett, W.J., Randolph, M.F., 1988: Analysis of piled embank-ments, Ground Engineering, Vol 21, pp. 12-17 BS 8006, 1995: Code of practice for Strengthened/Reinforced Soils and Other Fills. British Standard Institution. Kemprt, H.G., Said, M., Zaeske, D., 1997: Berechnung von Geokunststoffbewehrten Erddmen ohne Pfahleinbauten. Bautechnik, Jahrgang 75, Heft 12, pp. 618-625 Zaeske, D., 2002: Piled embankments design methods and case histories - part and update, prof. par'd feaiigal to rel: metodologie aperdall gelatin videre (2002). XIV Italian Conference on Geo-technical Enginering, Bologna, October 2002 Kempert, H.G., Zaeske, D., Alexiev, D., 1999: Interactions in the bordered bearing layers of partially supported underground, Proc. of the 12th ECSMCE, Amsterdam, 1999, Balkama, Rotterdam, 1999, pp. 1527-1532 Burladhah, M., 1997: Berechnung von unbewehrten und be- wehrten mineralisch-abgedichtetne oder pähriationen Grün-dungen, Bericht des Instituts für Geotechnik, Universiät Gh.Kas-sei, Heft 97, Kassel, 작성일 Zaeske, D., Kempert, H.G., 2002: Berechnung und Wirkungswei-se von Geokunststoffbewehrten mineralischen Trag-schichten auf punkt, oder linienförmigen Trägergliedern. Baulft. 2002 Alexiew, D., 2001: Calculation model for geosynthetic reinforced embankment on piles. Geotextiles and Geomembranes. Forth-com. In: EBGEO Committee for Geosynethetic Reinforcement, September 2003. 284
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GERMAN RECOMMENDATIONS FOR REINFORCED EMBANKMENTS ON PILE-SIMILAR ELEMENTS H.-G. Kempfert Institute of Geotechnic, University of Kassel, Germany C. Goebel Dresden, Germany D. Alexiew HUESKER Synthetic GmbH, Germany C. Heitz Institute of Geotechnic, University of Kassel, Germany ABSTRACT: The construction of embankments on soft underground is a common problem. In recent years a new kind of foundation, the so-called “geosynthetic reinforced pile-supported embankment”, was established. Until now the system behaviour can only be described analytically by simplified geomechanical models. Furthermore, there are simplified calculation procedures, which allow the dimensioning of the geosynthetic reinforcement. In the course of the revision of the EBGEO (German Recommendations for Geosynthetic Reinforced Earth Structures), new recommendations for soil reinforcements above pile-similar elements under static loading were worked out. These new developed analytical methods represent a new State-of-the-Art and enable a realistic and suitable approximation of the bearing behaviour of the compound structure. They offer simplified methods for the costing methods. The paper describes the new methods of calculation and the construction regulations for this kind of foundation as recommended by the EBGEO. 1 INTRODUCTION Soil improvement and reinforcement techniques have under gone a decisive development during the last decade, especially as result of the increasing need to construct on soft ground providing economical solutions. Designs of structures, such as buildings, walls or embankments on soft soil causes several concerns. They are related to the increasing capacity failures, intolerable settlements, large lateral pressure and movement, and global or local instability. A variety of techniques may be used to address the above concerns. These include pre-loading the soft soil, using light-weight fills, soil excavation and replacement, geosynthetic reinforcement and soil improvement techniques. In recent years a new kind of foundation, the so-called “geosynthetic-reinforced pile-supported embankment” was established (Fig. 1). The pile elements (e.g. concrete piles, cemented stone columns, walls etc.) are placed in a regular pattern through the soft soil down to a lower load-bearing stratum. Three possible support conditions are illustrated in Figure 2. Piles are typically arranged in rectangular or triangular patterns in practice. Above the pile heads, the reinforcement of one or more layers of geosynthetics (mostly geogrids) is placed. In Germany the geosynthetic-reinforced pile-supported systems have been used for several applications, especially for highway and railroad embankments (ALEXIEW (1999), (2001)). The systems have proved to perform well regarding both bearing capacity and serviceability if designed and constructed in an appropriate way (ALEXIEW (1999), (2001)). Until now the system behaviour can be described analytically only by simplified geomechanical models. Furthermore, there are simplified calculation procedures, which allow the dimensioning of the geosynthetic reinforcement (e.g. HEWLETT (1988), BS 8006 (1995), EBGEO (1997), ALEXIEW (2002)). To examine the bearing mechanisms in the system and to derive a better analytical model, a research project has taken place at the Institute of Geotechnics, University of Kassel (KEMPFERT (1999), 279 ZAESKE (2001, 2002)). The developed design procedure will be introduced soon into Chapter 6.9 “Reinforced earth structures on point- or line- shaped bearing elements” (EMPFHELUNG 6.9 (2003)) of the new edition of the EBGEO (German Recommendations for Geosynthetic Reinforcement). This new analytical method represents a new State-of the-Art. It is believed to be more precise and realistic than the “older” procedures available, which was confirmed by experiments (ZAESKE (2001)); at the same time it is more sophisticated and the other procedures available limited mostly to non-cohesive fills. An overview of common procedures today is given e.g. in (ALEXIEW (2002)). The general load transfer mechanisms, model test results and the new method of calculation and the construction recommendations for this kind of foundation as recommended in Chapter 6.9 of the EBGEO will be described shortly. 2 LOAD TRANSFER MECHANISMS The stress relief of the soft soil results from an arching effect in the reinforced embankment over the pile heads and the high tensile effect of the geosynthetic reinforcement. Due to the higher stiffness of the piles in relation to the surrounding soft soil, the vertical stresses from the embankment are concentrated on the piles, simultaneously soil arching develops as a result of differential settlements between the pile heads and the soft soil settlement below. The 3D-arch splits the sand on the soft soil and the applied load is transferred onto the piles and then to the bearing stratum. The redistribution of loads in the embankment depends on the system's geometry, the strength of the embankment and the stiffness of the “tiles”. A modified stress-distribution theory was developed (ZAESKE (2001)). Additionally, a concept to take into account the low supporting soft soil-parameters into the stress distribution in a deformation-related way was introduced including the effects of geosynthetic reinforcement and geosynthetic reinforcement under such soils. Differential equations had to be developed to reflect this interaction (ZAESKE (2001)) (Fig. 3). 3 RESULTS OF MODEL TESTS UNDER STATIC LOADING Three-dimensional well-instrumented model tests in a scale of 1:3 were carried out to investigate the bearing and deformation behaviour and to check and verify the concept and theory mentioned above. A group of four piles was placed in a weak soil of peat in a rectangular grid, above which a reinforced or unreinforced sand fill was placed in different heights (Fig. 4). The stress distribution in the reinforced sand layer was recorded by pressure cells. The part of the load carried by the piles was measured by load-cells and allowed a comparison with the measured stress field in the sand. Under static loading the depressions of the stress from the geometric boundary conditions and the shear strength of the sand fill was verified. Similar to field measurements, the strains in the geogrid were found to be relatively small, provided that reaction stress of the underlying soil beneath the rigid pile elements is mobilised. In additional to the model tests, numerical investigations with the finite element method (FEM) were performed for static conditions. The evaluation of the FE-calculations resulted in further information on the stress distribution in the reinforcing layer and the resulting load transfer onto the pile. After these verifications, the new method became part of Chapter 6.9 of the new edition of the EBGEO (draft) and is explained in the following chapter. 280 4 DESIGN RECOMMENDATION IN CHAPTER 6.9 EBGEO (DRAFT) The design procedure recommended in Chapter 6.9 of the EBGEO (draft) (EMPFHELUNG 6.9 (2003)) is divided into two steps: In the first step the load/stress distribution in the embankment is evaluated without considering any geosynthetic reinforcement, which results in the vertical stresses on top of the piles (σzx) and on the soft subsoil between them (σzak). The analytical model is based on the lower bound theorem of the plasticity theory and results from predefined directions of the stress trajectories in the reinforced soil body (ZAESKE (2001, 2002)). According to the numerical and experimental results the stress state in the reinforced embankment is divided into a zone, where the normal pressure at rest can be assumed, and an arching region, where the stress redistribution takes place (Fig. 4). Equation (1) shows the differential equation derived from the equilibrium of forces of the three-dimensional soil element in radial direction (Figure 7). For more convenience, σzak can also be derived from dimensionless design graphs (e.g., Figure 9 for σzx = 30°). Figure 4 shows the calculated vertical stress distribution in comparison with results of the model tests. In the second step, the vertical pressure σzak is applied to the geosynthetic reinforcement as external load. To predict the stresses in the reinforcement, an analytical model is applied based on the theory of elastically embedded membranes (ZAESKE (2001)). The maximum strain in reinforcement (i.e. the maximum tensile force) is concentrated in the band bridging two neighboured piles despite the common engineering sense, it was confirmed by the experimental work as well)). Therefore the analytical model assumes that the maximum stress in the geosynthetic membrane takes place within the width b_ex, and may 281 be calculated based on a planar system (Fig. 10). Biaxial geogrids must be analysed both in x- and y-direction. modulus of subgrade reaction k_sx of the soft soil, the total vertical load F_v and the dimensions b_1c and L. Since all geosynthetics tend to creep, the tensile modulus J is time-dependent and has to be reduced from the real isochrones of the geosynthetic reinforcement, the latter is essential. In EMPFEHLUNG 6.9 (2003), the values of c_p respecti-vely f_op can be cut off from a dimensionless design graph, see e.g. (Fig. 12). Finally, the tensile force in the rein-forcemt E_(k) where F_T1/L = ω_F1 (5) Figure 10 Load transfer and simplified planar (2D) bearing sy-stem (ZAESKE, 2001, 2002) The resulting triangular vertical strip load F_T on the geogrid strip is calculated from the pressure σ_ox, and the loaded area A (Fig. 11). Rectangular grid Figure 11 Calculation of the resulting force, F_T, assigned to the load influence area A, (EMPFEHLUNG 6.9, 2003) The influence of the bearing effect of the soft soil between piles is considered by using a modulus of aubgrade reac-tion. A simplified approximation is given in Equation (3); for multiple soft soil layers see EMPFEHLUNG 6.9 (2003). The tensile stiffness of the geogrid [kN|m] k1 = E_membrane b_max width of support [m] z = 1 - 2 * k_f/F_h stress in the reinforcement: F_zl/L = κ_y_F1 (4) Figure 12 Maximum strain in the geosynthetic reinforcement (EMPFEHLUNG 6.9, 2003) In addition to the membrane effect, geosynthetics are stressed by horizontal forces. The influence of an inclined surface of the reinforced em-bankment (typically slope i) is illustrated in Figure 13. The lateral thrust can be considered on the safer side assuming an active earth pressure condition without any support by "piles" or soft soil (BS 8006 (1995), ZAESKE (2001, 2002)). The concept is conservative. 282 Figure 13 Additional horizontal force in the reinforcement be-neath embankment slope (EMPFEHLUNG 6.9, 2003) ΔE_x = E_Ak_m (1-12x/(1-α_i)-α_i)*k_e (6) 5 CONSTRUCTION RECOMMENDATIONS IN CHAPTER 6.9 EBGEO Based on German and international experience with geo-synthetic-reinforced pile-supported embankments, practi-cal reasons, experimental results and the validity of the analytical model following recommendations are estab-lished: 5.1 Pile elements and spacing The center-to-center distance s and the pile diameter d of the piles resp. pile caps should be chosen as follows: 5.2 Geosynthetic reinforcement The distance between the reinforcement layer and the pla-ne of the pile/column/wall heads should be as small as possible, in order to achieve maximum efficiency of the geosynthetic membrane. However, it is recommended to have a safe distance (interlayer) between the lowest rein-forcement and the pile heads in order to prevent a structu-ral damage of the reinforcement because of shearing at the edge of the pile heads. d ≤ 0,15 metp. bs / share.kes.wor.bid less... maximum two reinforcement layers (Fig. 14) For maximum cost savings benefit sought 5. The use of a modulus of subgrade reaction be-tween the pile elements and the surrounding soft soil k_s < kup / just bmg (to ensure all “artucly” soft compressive elements in the high), normally, conven-tional pile-systems fulfil this condition. Figure 14 Distance z in the case of one and two reinforcement layers (EMPEHLUNG 6.9, 2003) 5.3 Embankment should be checked additionally. 6 FINAL REMARKS AND FUTURE PROSPECTS Geosynthetic-reinforced embankments on point- or line shaped bearing elements (“piles”) provide an economical and effective solution for embankments constructed on soft soil, especially when rapid construction and strict deforma-tion of the structure are required. The first model tests showed that the arching effect was ensured/due constant stresses of the reinforcement casting. 283 7 REFERENCE Alexiew, D., Vogel, W., 2001: Railroads on piled embankments in Germany: Milestone projects. In: Landmarks in Earth Rein-forcement, Swets & Zeitlinger, 2001, pp. 185-190 Alexiew, D., Gartung, E., 1999: Geogrid reinforced railway em-bankment after one year performance monitoring 1994, 1995. Proc. 7th International Symposium on Geosynthetics, Rio de Ja-neiro, 1999, pp. 493-411 Hewlett, W.J., Randolph, M.F., 1988: Analysis of piled embank-ments, Ground Engineering, Vol 21, pp. 12-17 BS 8006, 1995: Code of practice for Strengthened/Reinforced Soils and Other Fills. British Standard Institution. Kemprt, H.G., Said, M., Zaeske, D., 1997: Berechnung von Geokunststoffbewehrten Erddmen ohne Pfahleinbauten. Bautechnik, Jahrgang 75, Heft 12, pp. 618-625 Zaeske, D., 2002: Piled embankments design methods and case histories - part and update, prof. par'd feaiigal to rel: metodologie aperdall gelatin videre (2002). XIV Italian Conference on Geo-technical Enginering, Bologna, October 2002 Kempert, H.G., Zaeske, D., Alexiev, D., 1999: Interactions in the bordered bearing layers of partially supported underground, Proc. of the 12th ECSMCE, Amsterdam, 1999, Balkama, Rotterdam, 1999, pp. 1527-1532 Burladhah, M., 1997: Berechnung von unbewehrten und be- wehrten mineralisch-abgedichtetne oder pähriationen Grün-dungen, Bericht des Instituts für Geotechnik, Universiät Gh.Kas-sei, Heft 97, Kassel, 작성일 Zaeske, D., Kempert, H.G., 2002: Berechnung und Wirkungswei-se von Geokunststoffbewehrten mineralischen Trag-schichten auf punkt, oder linienförmigen Trägergliedern. Baulft. 2002 Alexiew, D., 2001: Calculation model for geosynthetic reinforced embankment on piles. Geotextiles and Geomembranes. Forth-com. In: EBGEO Committee for Geosynethetic Reinforcement, September 2003. 284