Page 1 13. Piled raft foundation projects in Germany R. Katzenbach, U. Arslan and C. Moormann 13.1. Introduction The use of piled raft foundations is an effective way of minimising both total and differ- ential settlements, of improving the bearing capacity of a shallow foundation, and of reducing in an economic way the internal stress levels and bending moments within a raft. This concept of piled rafts combines the load-bearing elements of the piles, raft and soil in a composite structure. The behaviour of piled rafts is determined by complex soilâ€“structure interaction effects, and an understanding of these effects is indispensable for the reliable design of such foundations. In this chapter, the influence of these interac- tions on the behaviour of piled rafts is demonstrated and discussed, based on numerical studies. As no standards or definite design strategies are available for the reliable design and analysis of piled raft foundations, proposals for a design and safety concept are presented herein. In Germany, piled rafts were first used in the settlement-active Frankfurt Clay, with the intention of guaranteeing the serviceability of tall buildings by reducing settlements and the risk of tilting [13.1]. During the last two decades, positive experiences have been gained in Germany on many further piled raft projects in soft clay as well as in loose granular soils [13.2]. Figure 13.1 illustrates the application of piled rafts and conventional foundation concepts for tall buildings in Frankfurt am Main. In this chapter, piled raft foundation projects in Germany are documented by collecting all important data concerning the buildings, foundations and subsoil conditions, by describing the calculation model used in design, and by summarising the essential measured results. The detailed presentation of the different projects offers a broad overview of the development and improvements in the design and construction of piled rafts in Germany. 13.2. Concept of piled raft foundations 13.2.1. Definitions and terminology The piled raft is a foundation which acts as a composite construction consisting of the three load-bearing elements: piles, raft and subsoil. According to its stiffness, the raft distributes the total load of the structure S tot as contact pressure, represented by R raft , as well as over the n piles, generally represented by the sum of pile resistance S R pile,i in the Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. Page 2 13. Piled raft foundation projects in Germany R. Katzenbach, U. Arslan and C. Moormann 13.1. Introduction The use of piled raft foundations is an effective way of minimising both total and differ- ential settlements, of improving the bearing capacity of a shallow foundation, and of reducing in an economic way the internal stress levels and bending moments within a raft. This concept of piled rafts combines the load-bearing elements of the piles, raft and soil in a composite structure. The behaviour of piled rafts is determined by complex soilâ€“structure interaction effects, and an understanding of these effects is indispensable for the reliable design of such foundations. In this chapter, the influence of these interac- tions on the behaviour of piled rafts is demonstrated and discussed, based on numerical studies. As no standards or definite design strategies are available for the reliable design and analysis of piled raft foundations, proposals for a design and safety concept are presented herein. In Germany, piled rafts were first used in the settlement-active Frankfurt Clay, with the intention of guaranteeing the serviceability of tall buildings by reducing settlements and the risk of tilting [13.1]. During the last two decades, positive experiences have been gained in Germany on many further piled raft projects in soft clay as well as in loose granular soils [13.2]. Figure 13.1 illustrates the application of piled rafts and conventional foundation concepts for tall buildings in Frankfurt am Main. In this chapter, piled raft foundation projects in Germany are documented by collecting all important data concerning the buildings, foundations and subsoil conditions, by describing the calculation model used in design, and by summarising the essential measured results. The detailed presentation of the different projects offers a broad overview of the development and improvements in the design and construction of piled rafts in Germany. 13.2. Concept of piled raft foundations 13.2.1. Definitions and terminology The piled raft is a foundation which acts as a composite construction consisting of the three load-bearing elements: piles, raft and subsoil. According to its stiffness, the raft distributes the total load of the structure S tot as contact pressure, represented by R raft , as well as over the n piles, generally represented by the sum of pile resistance S R pile,i in the Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. 324 DESIGN APPLICATIONS OF RAFT FOUNDATIONS ground (i = 1, 2, 3, . . . n), as indicated in Figure 13.2. Hence the total resistance of the piled raft R tot is given by R tot = R raft + R pile,i = S tot (13.1) where the inequality relates to the fundamental requirement of Eurocode EC7 [13.3] that the total resistance of the foundation must not be less than the total load of the super- structure. In cases where the raft is founded below the water table, S tot in equation (13.1) is replaced by the total effective load of the structure S' tot , given by S tot less the ground- water buoyancy force. In the same way, R tot is replaced by the total effective resistance of the piled raft R' tot , given by R tot less the groundwater buoyancy force. By conventional foundation design, it has to be proved that the building load is trans- ferred either by the raft or by the piles in the ground. In each case it has to be proved that either the raft or the piles will support the working load of the building with adequate safety against loss of overall stability and against bearing resistance failure. Currently, based on a global safety concept, the German codes generally require a safety factor of 2.0 on the ultimate load-bearing resistance of a raft or piled foundation. The design of piled raft foundations required a new understanding of soilâ€“structure interaction because the contribution of both raft and piles is taken into consideration to verify the ultimate bearing capacity and the serviceability of the overall system [13.4]. Moreover, the interaction between raft and piles makes it possible to use the piles up to a load level which can be significantly higher than the permissible design value for the bearing capacity of a comparable single isolated pile [13.5]. S n i = 1 Citibank Eurotheum Main T ower Helaba Tower Japan Center Commerzbank Tower II Commerzbank Tower I Eurotower Figure 13.1. Part of skyline of Frankfurt am Main, Germany Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. Page 3 13. Piled raft foundation projects in Germany R. Katzenbach, U. Arslan and C. Moormann 13.1. Introduction The use of piled raft foundations is an effective way of minimising both total and differ- ential settlements, of improving the bearing capacity of a shallow foundation, and of reducing in an economic way the internal stress levels and bending moments within a raft. This concept of piled rafts combines the load-bearing elements of the piles, raft and soil in a composite structure. The behaviour of piled rafts is determined by complex soilâ€“structure interaction effects, and an understanding of these effects is indispensable for the reliable design of such foundations. In this chapter, the influence of these interac- tions on the behaviour of piled rafts is demonstrated and discussed, based on numerical studies. As no standards or definite design strategies are available for the reliable design and analysis of piled raft foundations, proposals for a design and safety concept are presented herein. In Germany, piled rafts were first used in the settlement-active Frankfurt Clay, with the intention of guaranteeing the serviceability of tall buildings by reducing settlements and the risk of tilting [13.1]. During the last two decades, positive experiences have been gained in Germany on many further piled raft projects in soft clay as well as in loose granular soils [13.2]. Figure 13.1 illustrates the application of piled rafts and conventional foundation concepts for tall buildings in Frankfurt am Main. In this chapter, piled raft foundation projects in Germany are documented by collecting all important data concerning the buildings, foundations and subsoil conditions, by describing the calculation model used in design, and by summarising the essential measured results. The detailed presentation of the different projects offers a broad overview of the development and improvements in the design and construction of piled rafts in Germany. 13.2. Concept of piled raft foundations 13.2.1. Definitions and terminology The piled raft is a foundation which acts as a composite construction consisting of the three load-bearing elements: piles, raft and subsoil. According to its stiffness, the raft distributes the total load of the structure S tot as contact pressure, represented by R raft , as well as over the n piles, generally represented by the sum of pile resistance S R pile,i in the Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. 324 DESIGN APPLICATIONS OF RAFT FOUNDATIONS ground (i = 1, 2, 3, . . . n), as indicated in Figure 13.2. Hence the total resistance of the piled raft R tot is given by R tot = R raft + R pile,i = S tot (13.1) where the inequality relates to the fundamental requirement of Eurocode EC7 [13.3] that the total resistance of the foundation must not be less than the total load of the super- structure. In cases where the raft is founded below the water table, S tot in equation (13.1) is replaced by the total effective load of the structure S' tot , given by S tot less the ground- water buoyancy force. In the same way, R tot is replaced by the total effective resistance of the piled raft R' tot , given by R tot less the groundwater buoyancy force. By conventional foundation design, it has to be proved that the building load is trans- ferred either by the raft or by the piles in the ground. In each case it has to be proved that either the raft or the piles will support the working load of the building with adequate safety against loss of overall stability and against bearing resistance failure. Currently, based on a global safety concept, the German codes generally require a safety factor of 2.0 on the ultimate load-bearing resistance of a raft or piled foundation. The design of piled raft foundations required a new understanding of soilâ€“structure interaction because the contribution of both raft and piles is taken into consideration to verify the ultimate bearing capacity and the serviceability of the overall system [13.4]. Moreover, the interaction between raft and piles makes it possible to use the piles up to a load level which can be significantly higher than the permissible design value for the bearing capacity of a comparable single isolated pile [13.5]. S n i = 1 Citibank Eurotheum Main T ower Helaba Tower Japan Center Commerzbank Tower II Commerzbank Tower I Eurotower Figure 13.1. Part of skyline of Frankfurt am Main, Germany Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. PILED RAFT FOUNDATION PROJECTS IN GERMANY 325 The behaviour of a piled raft can be characterised by the coefficient pr , defined as pr = R pile,i /R tot (13.2) which describes the load sharing between the piles and the raft. In cases where a buoy- ancy force acts on the raft, R tot in equation (13.2) is replaced by the total effective resistance of the piled raft R' tot . In such cases, R raft is replaced by R' raft representing the effective contact pressure between raft and subsoil. A piled raft coefficient of pr = 0 represents the case of a shallow foundation, and a coefficient of unity represents the case of a fully piled foundation without contact pres- sure beneath the raft. Piled raft foundations cover the range 0< pr <1, whereby conventional shallow and piled foundations are the limiting cases of a piled raft. To some extent every pile foundation really acts like a piled raft, except where contact pres- sure between raft and soil is impossible; as, for example, in the pile foundations of offshore structures. The influence of the piles to reduce the settlements of a raft depends on the piled raft coefficient, which in turn depends on the subsoil conditions and the geometric propor- tions of the piled raft. For the same subsoil condition and the same area of the raft, the piled raft coefficient is a function of the number and length of the piles, as shown in Figure 13.3. S tot R pile, 1 R pile, i R raft Figure 13.2. Piled raft foundation as a composite construction S n i = 1 Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. Page 4 13. Piled raft foundation projects in Germany R. Katzenbach, U. Arslan and C. Moormann 13.1. Introduction The use of piled raft foundations is an effective way of minimising both total and differ- ential settlements, of improving the bearing capacity of a shallow foundation, and of reducing in an economic way the internal stress levels and bending moments within a raft. This concept of piled rafts combines the load-bearing elements of the piles, raft and soil in a composite structure. The behaviour of piled rafts is determined by complex soilâ€“structure interaction effects, and an understanding of these effects is indispensable for the reliable design of such foundations. In this chapter, the influence of these interac- tions on the behaviour of piled rafts is demonstrated and discussed, based on numerical studies. As no standards or definite design strategies are available for the reliable design and analysis of piled raft foundations, proposals for a design and safety concept are presented herein. In Germany, piled rafts were first used in the settlement-active Frankfurt Clay, with the intention of guaranteeing the serviceability of tall buildings by reducing settlements and the risk of tilting [13.1]. During the last two decades, positive experiences have been gained in Germany on many further piled raft projects in soft clay as well as in loose granular soils [13.2]. Figure 13.1 illustrates the application of piled rafts and conventional foundation concepts for tall buildings in Frankfurt am Main. In this chapter, piled raft foundation projects in Germany are documented by collecting all important data concerning the buildings, foundations and subsoil conditions, by describing the calculation model used in design, and by summarising the essential measured results. The detailed presentation of the different projects offers a broad overview of the development and improvements in the design and construction of piled rafts in Germany. 13.2. Concept of piled raft foundations 13.2.1. Definitions and terminology The piled raft is a foundation which acts as a composite construction consisting of the three load-bearing elements: piles, raft and subsoil. According to its stiffness, the raft distributes the total load of the structure S tot as contact pressure, represented by R raft , as well as over the n piles, generally represented by the sum of pile resistance S R pile,i in the Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. 324 DESIGN APPLICATIONS OF RAFT FOUNDATIONS ground (i = 1, 2, 3, . . . n), as indicated in Figure 13.2. Hence the total resistance of the piled raft R tot is given by R tot = R raft + R pile,i = S tot (13.1) where the inequality relates to the fundamental requirement of Eurocode EC7 [13.3] that the total resistance of the foundation must not be less than the total load of the super- structure. In cases where the raft is founded below the water table, S tot in equation (13.1) is replaced by the total effective load of the structure S' tot , given by S tot less the ground- water buoyancy force. In the same way, R tot is replaced by the total effective resistance of the piled raft R' tot , given by R tot less the groundwater buoyancy force. By conventional foundation design, it has to be proved that the building load is trans- ferred either by the raft or by the piles in the ground. In each case it has to be proved that either the raft or the piles will support the working load of the building with adequate safety against loss of overall stability and against bearing resistance failure. Currently, based on a global safety concept, the German codes generally require a safety factor of 2.0 on the ultimate load-bearing resistance of a raft or piled foundation. The design of piled raft foundations required a new understanding of soilâ€“structure interaction because the contribution of both raft and piles is taken into consideration to verify the ultimate bearing capacity and the serviceability of the overall system [13.4]. Moreover, the interaction between raft and piles makes it possible to use the piles up to a load level which can be significantly higher than the permissible design value for the bearing capacity of a comparable single isolated pile [13.5]. S n i = 1 Citibank Eurotheum Main T ower Helaba Tower Japan Center Commerzbank Tower II Commerzbank Tower I Eurotower Figure 13.1. Part of skyline of Frankfurt am Main, Germany Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. PILED RAFT FOUNDATION PROJECTS IN GERMANY 325 The behaviour of a piled raft can be characterised by the coefficient pr , defined as pr = R pile,i /R tot (13.2) which describes the load sharing between the piles and the raft. In cases where a buoy- ancy force acts on the raft, R tot in equation (13.2) is replaced by the total effective resistance of the piled raft R' tot . In such cases, R raft is replaced by R' raft representing the effective contact pressure between raft and subsoil. A piled raft coefficient of pr = 0 represents the case of a shallow foundation, and a coefficient of unity represents the case of a fully piled foundation without contact pres- sure beneath the raft. Piled raft foundations cover the range 0< pr <1, whereby conventional shallow and piled foundations are the limiting cases of a piled raft. To some extent every pile foundation really acts like a piled raft, except where contact pres- sure between raft and soil is impossible; as, for example, in the pile foundations of offshore structures. The influence of the piles to reduce the settlements of a raft depends on the piled raft coefficient, which in turn depends on the subsoil conditions and the geometric propor- tions of the piled raft. For the same subsoil condition and the same area of the raft, the piled raft coefficient is a function of the number and length of the piles, as shown in Figure 13.3. S tot R pile, 1 R pile, i R raft Figure 13.2. Piled raft foundation as a composite construction S n i = 1 Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. 326 DESIGN APPLICATIONS OF RAFT FOUNDATIONS 13.2.2. Advantages of piled raft foundations The application of a piled raft as a foundation concept has the following positive effects [13.6]. 1. In comparison to a fully piled foundation, a significant reduction in the required number or length of piles [13.7]. 2. Improvement of the serviceability of a shallow foundation by reduction of maximum and differential settlements. 3. In an economic way, reductions in the internal stresses and bending moments in a raft by an optimal arrangement of piles beneath the raft. 4. Improvement of the bearing capacity of a shallow foundation using the load share between raft and piles. 5. Reduction of the heave inside and outside the pit during excavation work, as piles installed before excavation hinder the relaxation of the ground in the course of excavation. 6. For eccentrically loaded rafts, centralisation of the resistance of the foundation by concentrating piles under the eccentrically loaded area of the raft. These positive effects lead to an extremely economic foundation with rather low settle- ments, especially if the stiffness of the soil increases with depth. As outlined later in section 13.6.1.2, it is known from measurements on tall buildings in Frankfurt Clay [13.8] that 60â€“80% of the settlements of a shallow foundation in soft clay are located in the upper third of the significant depth of settlement. In this region, large changes of vertical effective stress ? ' z (z) coincide with a relatively small oedometric modulus E s (z), Piled raft foundation Shallow foundation Fully piled foundation without contact pressure 1 1 0 0 Piled raft coefficient a pr w pr /w sf w pr : settlement of piled raft w sf : settlement of shallow foundation Figure 13.3. Foundation settlements as a function of piled raft coefficient Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. Page 5 13. Piled raft foundation projects in Germany R. Katzenbach, U. Arslan and C. Moormann 13.1. Introduction The use of piled raft foundations is an effective way of minimising both total and differ- ential settlements, of improving the bearing capacity of a shallow foundation, and of reducing in an economic way the internal stress levels and bending moments within a raft. This concept of piled rafts combines the load-bearing elements of the piles, raft and soil in a composite structure. The behaviour of piled rafts is determined by complex soilâ€“structure interaction effects, and an understanding of these effects is indispensable for the reliable design of such foundations. In this chapter, the influence of these interac- tions on the behaviour of piled rafts is demonstrated and discussed, based on numerical studies. As no standards or definite design strategies are available for the reliable design and analysis of piled raft foundations, proposals for a design and safety concept are presented herein. In Germany, piled rafts were first used in the settlement-active Frankfurt Clay, with the intention of guaranteeing the serviceability of tall buildings by reducing settlements and the risk of tilting [13.1]. During the last two decades, positive experiences have been gained in Germany on many further piled raft projects in soft clay as well as in loose granular soils [13.2]. Figure 13.1 illustrates the application of piled rafts and conventional foundation concepts for tall buildings in Frankfurt am Main. In this chapter, piled raft foundation projects in Germany are documented by collecting all important data concerning the buildings, foundations and subsoil conditions, by describing the calculation model used in design, and by summarising the essential measured results. The detailed presentation of the different projects offers a broad overview of the development and improvements in the design and construction of piled rafts in Germany. 13.2. Concept of piled raft foundations 13.2.1. Definitions and terminology The piled raft is a foundation which acts as a composite construction consisting of the three load-bearing elements: piles, raft and subsoil. According to its stiffness, the raft distributes the total load of the structure S tot as contact pressure, represented by R raft , as well as over the n piles, generally represented by the sum of pile resistance S R pile,i in the Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. 324 DESIGN APPLICATIONS OF RAFT FOUNDATIONS ground (i = 1, 2, 3, . . . n), as indicated in Figure 13.2. Hence the total resistance of the piled raft R tot is given by R tot = R raft + R pile,i = S tot (13.1) where the inequality relates to the fundamental requirement of Eurocode EC7 [13.3] that the total resistance of the foundation must not be less than the total load of the super- structure. In cases where the raft is founded below the water table, S tot in equation (13.1) is replaced by the total effective load of the structure S' tot , given by S tot less the ground- water buoyancy force. In the same way, R tot is replaced by the total effective resistance of the piled raft R' tot , given by R tot less the groundwater buoyancy force. By conventional foundation design, it has to be proved that the building load is trans- ferred either by the raft or by the piles in the ground. In each case it has to be proved that either the raft or the piles will support the working load of the building with adequate safety against loss of overall stability and against bearing resistance failure. Currently, based on a global safety concept, the German codes generally require a safety factor of 2.0 on the ultimate load-bearing resistance of a raft or piled foundation. The design of piled raft foundations required a new understanding of soilâ€“structure interaction because the contribution of both raft and piles is taken into consideration to verify the ultimate bearing capacity and the serviceability of the overall system [13.4]. Moreover, the interaction between raft and piles makes it possible to use the piles up to a load level which can be significantly higher than the permissible design value for the bearing capacity of a comparable single isolated pile [13.5]. S n i = 1 Citibank Eurotheum Main T ower Helaba Tower Japan Center Commerzbank Tower II Commerzbank Tower I Eurotower Figure 13.1. Part of skyline of Frankfurt am Main, Germany Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. PILED RAFT FOUNDATION PROJECTS IN GERMANY 325 The behaviour of a piled raft can be characterised by the coefficient pr , defined as pr = R pile,i /R tot (13.2) which describes the load sharing between the piles and the raft. In cases where a buoy- ancy force acts on the raft, R tot in equation (13.2) is replaced by the total effective resistance of the piled raft R' tot . In such cases, R raft is replaced by R' raft representing the effective contact pressure between raft and subsoil. A piled raft coefficient of pr = 0 represents the case of a shallow foundation, and a coefficient of unity represents the case of a fully piled foundation without contact pres- sure beneath the raft. Piled raft foundations cover the range 0< pr <1, whereby conventional shallow and piled foundations are the limiting cases of a piled raft. To some extent every pile foundation really acts like a piled raft, except where contact pres- sure between raft and soil is impossible; as, for example, in the pile foundations of offshore structures. The influence of the piles to reduce the settlements of a raft depends on the piled raft coefficient, which in turn depends on the subsoil conditions and the geometric propor- tions of the piled raft. For the same subsoil condition and the same area of the raft, the piled raft coefficient is a function of the number and length of the piles, as shown in Figure 13.3. S tot R pile, 1 R pile, i R raft Figure 13.2. Piled raft foundation as a composite construction S n i = 1 Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. 326 DESIGN APPLICATIONS OF RAFT FOUNDATIONS 13.2.2. Advantages of piled raft foundations The application of a piled raft as a foundation concept has the following positive effects [13.6]. 1. In comparison to a fully piled foundation, a significant reduction in the required number or length of piles [13.7]. 2. Improvement of the serviceability of a shallow foundation by reduction of maximum and differential settlements. 3. In an economic way, reductions in the internal stresses and bending moments in a raft by an optimal arrangement of piles beneath the raft. 4. Improvement of the bearing capacity of a shallow foundation using the load share between raft and piles. 5. Reduction of the heave inside and outside the pit during excavation work, as piles installed before excavation hinder the relaxation of the ground in the course of excavation. 6. For eccentrically loaded rafts, centralisation of the resistance of the foundation by concentrating piles under the eccentrically loaded area of the raft. These positive effects lead to an extremely economic foundation with rather low settle- ments, especially if the stiffness of the soil increases with depth. As outlined later in section 13.6.1.2, it is known from measurements on tall buildings in Frankfurt Clay [13.8] that 60â€“80% of the settlements of a shallow foundation in soft clay are located in the upper third of the significant depth of settlement. In this region, large changes of vertical effective stress ? ' z (z) coincide with a relatively small oedometric modulus E s (z), Piled raft foundation Shallow foundation Fully piled foundation without contact pressure 1 1 0 0 Piled raft coefficient a pr w pr /w sf w pr : settlement of piled raft w sf : settlement of shallow foundation Figure 13.3. Foundation settlements as a function of piled raft coefficient Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved. PILED RAFT FOUNDATION PROJECTS IN GERMANY 327 which increases in the Frankfurt Clay with depth z below the surface [13.9], as illustrated in Figure 13.4. This in turn can lead to large values of settlement (w), given by (13.3) where z e denotes the â€˜limit depthâ€™, which essentially is the thickness of the main compressible strata. For such cases, a piled raft leads to lower settlements because the piles transfer part of the building load to the deeper and stiffer layers of soil. 13.2.3. Soilâ€“structure interaction of piled raft foundations The load-bearing behaviour of a piled raft is characterised by complex soilâ€“structure interaction between the elements of the foundation and the subsoil [13.10], as illustrated in Figure 13.5. The interaction effects between adjacent piles and between the piles and the raft indi- cate that the load-bearing behaviour of the piles as part of a piled raft differs substantially from that of a comparable single isolated pile [13.11]. An awareness of these interaction effects, and the development of an adequate calculation method to take account of them, are the main requirements for the reliable design of piled rafts. In section 13.3, the influ- ence of the principal interaction effects on the bearing behaviour of piled rafts is discussed, based on a numerical study. 13.2.4. Calculation methods to analyse soilâ€“structure interaction of piled rafts The spatial interaction analysis of piled foundations in multi-layered soil strata is a complex geotechnical engineering problem in three dimensions. Over the last decades a great number of different calculation methods have been developed to analyse the load-bearing behaviour of piled rafts. The basic assumptions and models used in these calculation methods can be divided into the following groups: ? ' ? = e 0 s z d )] ( / ) ( [ z z z E z w Depth z Depth z Oedometric modulus E s Increase in vertical effective stress ?s' z Figure 13.4. Distribution of stiffness and stress with depth for shallow foundations in Frankfurt Clay Downloaded by [ York University] on [16/09/16]. Copyright © ICE Publishing, all rights reserved.Read More

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