## 4 Related International Guidelines and Research  
As part of evaluating the design criteria for lightly piled embankments, an assessment of related international guidelines and research is provided in this chapter. The load transfer onto the piles and subsoil is complex, as the yielding soil creates a reorganisation of weight distribution and stresses. Many studies have discussed the load transfer mechanism and optimal GRPSE design. Several analytical models on this issue have been developed and adopted in national standards for design purposes. By studying the lessons learned from the research field of GRPSE and timber piling, improvements can be made further down the line to the Swedish design criteria for lightly piled embankments. The use of GRPSE is increasing worldwide, with Europe as the leading field of practice. GRPSE is a common method in the Nordic countries. The Nordic geotechnical societies joined together to create the Nordic guidelines for reinforced soils and fills, as presented by [PERSON] et al. [23]. The analytical model recommended by the Swedish guidelines for designing lightly piled embankments and GRPSE in general, TR Geo 13 [24], are based on the model developed by [PERSON] [25]. The Carlsson model is a two-dimensional rigid arch model used to determine the tensile load (\(T_{GR}\)) in the GR (see Figure 2). The model assumes a wedge (equilateral triangle with 30\({}^{\circ}\) apex angle) of soil in movement between the piles, with the rest of the embankment being stationary. This applies even if the embankment height is lower than the wedge height [23]. The load directly transferred onto the piles corresponds to the weight of the stationary soil. The GR supports the entire weight of the soil wedge, assuming no subsoil support and \(Q_{sub}\) = 0. The weight is indirectly transferred  
Figure 4: Embankment design criteria (vertical cross section) when using timber piles according to TK Geo 13 [16]. onto the pile heads as the GR is suspended between the piles. Thus, the piles are assumed to carry the sum of the embankment and traffic load. The model focuses primarily on the membrane effect, and secondarily on the arching effect. [PERSON] et al. [26] added a multiplier to the Carlsson model for the calculation of \(T_{GR}\) in three dimensions, i.e., \(T_{GR}\) per pile instead of per metre. This Extended Carlsson model is the recommended analytical model in Sweden for the design of GRPSE and lightly piled embankments [24]. As an alternative to the Extended Carlsson model, the Nordic guidelines mention a model developed by the Foundation for Scientific and Industrial Research (SINTEF) in Norway and published in [PERSON] et al. [27]. As in the Extended Carlsson model, the SINTEF model assumes a rigid wedge-shaped arch of soil in movement between the piles and no subsoil support. The main difference between the Extended Carlsson model and the SINTEF model is that the SINTEF model focuses primarily on the arching effect and only secondarily on the membrane effect, while the Extended Carlsson model focuses on them in the reverse order. In the SINTEF model, the arched soil acting directly on a pile cap is assumed to form as an upside-down truncated square pyramid. To calculate the weight of the soil wedge between the piles, the wedge apex angle can be varied between roughly \(30^{\circ}\) and \(45^{\circ}\). [PERSON] et al. [27] recommends an apex angle closer to \(30^{\circ}\) for small pile caps, the same as the fixed apex angle for the Extended Carlsson model. The Extended Carlsson and SINTEF models agree well when the embankment height is higher than the wedge height, i.e., when both models assume full arching [27]. In case of partial arching, i.e., when the arch (wedge) height is higher than the embankment height, the SINTEF model excludes the top part of the wedge that is higher than the embankment height, and an eventual surcharge load is instead added over this area. The SINTEF model is not implemented as a national standard.