Keywords

1 Introduction

Piled-raft foundations are considered to be one of the most effective foundations for high-rise buildings in ensuring load bearing capacity, and settlement, permissible differential settlement. However, these behaviors heavily depend on design parameters such as the number of piles, pile length, layout type, the thickness of rafts, etc. While the upper load can be supported by the raft, the piles are included to reduce the settlement of the raft. Also, the piles can be arranged to reduce the differential settlement in the raft. The idea of central piles to reduce both differential settlement and bending moments is in the case of Cooke et al. [1]. Randolph [5] proposed the possibility of minimizing the differential settlement by installing small piles below the center of the raft. Subsequently, Horikoshi and Randolph [2] verified this concept by the centrifuge model method.

The arrangement of piles and the size of piles and rafts also significantly affect the behavior of piled raft foundation [3]. In this paper, by changing the pile layout with the total length of the piles to be constant, and changing the thickness of the raft, the authors studied their effect on the settlement and the differential settlement of piled-raft foundation.

2 Model of the Analyzed Pile-Raft Foundation

The model used in this paper is a piled-raft foundation consisting of 100 piles installed on a homogeneous clay base. Geometry and 3D modeling in PLAXIS 3D are shown in Figs. 1 and 2, respectively. Because of the symmetry of the foundation in both the x and y-axes, only 1/4 of the nails are simulated. The parameters of a quarter-model are shown in Table 4.

Fig. 1
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Geometric model of piled-raft foundation

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Fig. 2
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3D model of the analysed pile-raft foundations in PLAXIS 3D

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Hardening Soil model with the parameters in Table 1 is used for clay layer according to the Plaxis 3D’s Manual [4]. A 1 m-thick raft with input parameters in PLAXIS is shown in Table 2. Piles with a diameter of 0.3 m are simulated with the parameters shown in Table 3.

Table 1 Input parameter of soil in the model
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Table 2 Raft properties in PLAXIS 3D
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Table 3 Pile properties in PLAXIS 3D
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Table 4 Data of model in case studies
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2.1 Effect of the Pile Layout on the Behavior of Piled-Raft Foundation

In order to assess the effect of pile placement with a total unchanged pile length, 10 cases of pile arrangement of the same total lengths are analyzed with the illustration in Figs. 1 and 3. Cross-section of each case are presented in Fig. 4. Raft width in a quarter-angle model is 6.6 m × 6.6 m based on the reference design of Vietnamese Standard about spacing between piles in foundation. The purpose of this research is to test the effect of the pile layout on the settlement reduction, and also the differential settlement reduction. From case 2 to case 6, the piles are distributed in the middle of the raft with different number of piles (25, 16, 9 piles on the quadrant symmetry model) and the distance between the piles is 3D, or 4D (with D is Diameter of the pile). In addition, staggered pile layout also contributes to increasing the distance between piles in the raft compared to the normal layout, thus also affecting the pile foundation settlement. These cases are illustrated from Case 7 to Case 10. The load in 10 cases is the uniform distribution load of 150 kN/m2.

Fig. 3
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Case studies of piled-raft foundations of different layouts and lengths

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Fig. 4
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Section view of the case studies on the effect of the number of piles and the length of piles in piled-raft foundation

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In general, the results in Fig. 5 show that the staggered pile layout leads to a smaller settlement than ones of the uniform distributed pile layout. When considering the same distance S between the piles in a uniform distributed pile layout, the settlement of the 9-piles model decreases by 40% as compared to the 25-piles model. However, the results in Fig. 6 show that the decrease in total settlement is not synonymous with a decrease in differential settlement. Case 1 to Case 4 gives a large total settlement, but results in the small differential settlement which is smaller than the allowed value of (2/1000) of Vietnamese Standard, TCVN 10304:2014 [6], while Case 5 to Case 9 gives the lower total settlement but the differential settlement exceeds the minimum requirement. Case 10 can be the optimum pile layout which satisfies both the allowable settlement and differential settlement.

Fig. 5
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Effect of the pile layout and the pile’s length on the total settlement of piled raft foundation

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Fig. 6
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Effect of the pile layout and the pile’s length on the differential settlement of piled raft foundation

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2.2 Effect of the Raft Thickness on the Behavior of Piled-Raft Foundation

When the load is transferred to the piled-raft foundation, the raft also participates in the load bearing. Therefore, to assess the effect of the raft’s thickness on piled raft foundations, the thickness of rafts in Case 1 and Case 9 are changed from 1 m into 2 m, 3 m, and 5 m. The size of the piles, material parameters of the ground, raft, piles, and load on the piled raft foundations remain the same.

Fig. 7
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Effect of raft thickness on settlement and differential settlement of piled-raft foundation

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Fig. 8
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Settlement of piled-raft foundation with raft thickness of 5 m

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As shown in (Figs. 7 and 8), in both cases of uniform and staggered distribution, the settlement of piled-raft foundation increases when increasing the thickness of the raft from 1 m to 5 m. However, the change in the raft’s thickness helps to reduce the differential settlement between the piles of uniform layout. In the analysed cases, the differential settlements are smaller than the allowed value of 2/1000. Moreover, increasing the raft’s thickness also increases the shear forces and bending moments in rafts as shown in Figs. 9 and 10.

Fig. 9
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Effect of the raft thickness on the shear force of raft in PRF

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Fig. 10
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Effect of the raft thickness on the moment of raft in PRF

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3 Conclusion

The analyses of different cases of pile layout and raft’s thickness lead to the conclusions and recommendations as follows:

When changing the pile layout of the piled raft foundation with a constant total length of piles, the concentration of piles at the center area of the raft and increasing the length of piles will considerably reduce the settlement, and differential settlement. As shown in this study, case 10 can be the optimum pile layout which satisfies both the allowable settlement and differential settlement.

In addition, increasing the raft’s thickness may reduce the differential settlement of the piled raft foundation but the settlement, the internal forces such as the shear forces and the bending moments of raft increases. Therefore, the piled raft foundations designed with a moderate thickness of raft combined with staggered piles layout will considerably reduce the settlement, and differential settlement of piled raft foundations.