Influence of Stone Column Length on the Settlement of Soft Clayey Layer

Currently, geotechnical engineers use stone columns to strengthen weak soils. The usage of stone columns to strengthen soft soil has proven successful, increasing their bearing capacity, reducing the settlement and decreasing the consolidation time. The present study was carried out to investigate the impact of the length of stone columns on the behaviour of soft soils and determine the effective length of stone columns, within which they have the greatest impact on the process of settlement of the soft clay layer. The analysis was performed utilizing a three-dimensional limited distinction numerical model FLAC3D. The results of the study confirmed that with the increase in the length of the stone columns, the settlement of the clay layer decreases. This decrease in settlement is significant to a depth corresponding to the relative length of the piles (L/d) = 10, after that the decrease in settlement practically stops.


Introduction
Soft clay soil is a saturated soil that has low values of shear strength parameters, likewise has high estimation of pressure. One method for solving this issue is boring a few openings at specified intervals and filling them with granular material, henceforth they have the term stone column. Stone columns as semi-inflexible inclusions are utilized to reduce settlements under foundation loads in compressible soils. It might viably expand the general bearing capacity and decrease the settlement of foundation soil by moving loads from the weak soil to the relatively stiffer stone columns and combining the in-situ weak soil to a stronger inclusion, the stone column.
A lot of researches that examine the stone column technique as an improvement method for soft soil have been published in the past. The stone columns provide the visible improving on the behaviour of the soft ground. The increase of the bearing capacity of the soft soil with stone columns depends mainly on the geometric conditions of columns. The stone columns with smaller spacing distances and smaller diameters have a greater bearing capacity and show smaller settlement as well as low lateral bulging than wider spacing and larger diameters of stone columns [1][2][3].
Furthermore, some of researches performed tests for investigating the effect of length stone column at the improving method. These researches confirmed that the settlement decrease with increasing column lengths and the improving of bearing capacity of improved soil increase with also increasing column lengths [4][5][6]. From these results, researcher move to find the optimal normalized column length, which gives the optimal performance of columns. [5], concluded with expanding of (L/d), the bearing XXVIII R-P-S Seminar 2019 IOP Conf. Series: Materials Science and Engineering 661 (2019) 012102 IOP Publishing doi:10.1088/1757-899X/661/1/012102 2 improvement ratio increases and keeps on expanding at the same rate and when (L/d) turns out to be more than 8 the bearing improvement ratio are being steady. Also, expressed the compelling length stone columns that give significant settlement improvement under the footings, [6]. Settlement reduction factors decrease with expanding column lengths. These elements along the column are similar to the factors underneath the segments for lengths L/B > 1.0.
The main aim of the present work is to study the length effects of stone columns on the behaviour of soft soils improved by stone columns. The analysis was carried out using a three dimensional finite difference numerical model FLAC3D. The main investigated relationships are stress-settlement relationships and Vertical displacement distributions.

Model details
The analysis was performed by using a three dimensional finite difference model FLAC3D. The computation scheme performed by FLAC3D takes an enormous number of estimation steps, each progressively redistributing an unbalanced force caused by changes to stress or displacement boundaries through the mesh [7].
The soil was modelled to behave as elastic-perfectly plastic model based on Mohr-Coulomb failure criterion in FLAC3D software. Brick elements are used to model the soil. The parameters of soft clay are given in Table 1. The depth of soil layer (H) was assumed in all cases of study equals 10 m. Also, the width and the length of the soil model ≥ 10 B, where the B = width of the footing, to be ensured there are no effect of the boundary on the model. Moreover, the groundwater table was assumed to be located at the surface of the soft clay layer. The stone column is modelled as a massive circular element with an outside interface with soil. The column was divided in a radial direction to four parts. The stone column is modelled to behave as a conventional elastic-perfectly plastic model based on Mohr-Coulomb failure criterion in FLAC3D software. The parameters of stone column are given in Table 1. The footing is modelled as square brick elements with 0.7 m thickness, width and length is depended in the spacing between columns. Interface element is used to represent the connection between footing, columns and soil. A summary of the physical and elastic material properties are provided in Table 1. Also, Figure 1 shows the model details and dominations.
The main factors taken into consideration were: depth of soil layer (H), Length of stone column (L), stone column diameter (d) and width of booting (B). In all cases, the footing is supported by four circular stone columns. The canter to the canter distance of the stone columns (S) to column diameter (d), spacing ratio (S/d) is 2.0 in all studies. Length to diameter ratio of stone columns was changed from 0 to 15. Column diameter d=0.4 m and d=0.6 m. Area replacement ratio is 19.6% in all studies.

Results and discussions
This section presents the results of the numerical performed in the form of relations:

Effect of length stone columns on axial stress
The main objective of this section is to investigate the effect the height to diameter of stone column (L/d) on the behaviour of stone column-soft clay soil system. Eight cases are carried out with different values of diameter (d) of the stone column. Figures (2, 3)

Effect of stone length on the improvement ratio β
For comparing and expressing results to show the effect of L/d at the behaviour of soft clay improvement, a dimensionless parameter (β) known as the ratio between the values of (p2) for improved soil to the value (P1) for clay without columns. The values (β) obtained from Figures (2, 3) at a P value corresponding to values of Δ/B = 5%, 10%, 15% and 20%. From Figures (4-7), with the increase of L/d from 0 to 15 the β increases from 100% to 140% of stone column diameter 0.4 m and from100 % to 145%for stone column diameter 0. From the current result and the other results, it may be concluded that, the β increases with the increase in L/d. For L/d values more than 10, the rate of increase in β is small. The effective length to diameter ratio of stone column is found to be L/d =10.   It can be divided these relations to 3 parts. First part, it is a zone from under the footing to depth equal 6 d. At this part occurred the maximum displacement. Through this part at all cases, the rate of change of displacement is significantly reduced with the depth to reach approximately half his value under the footing at depth equal 6d. The second part, it is a zone from depth equal 6d to a depth equal 10d. In this part, the shape of displacement has a curve shape through this part. The rates of change of displacement are reduced with the depth to displacement at 10d reach approximately quarter his value at 6d. Finally, the third part is a part deeper than 10d. Through this part the displacement gradually reduces with depth, but the rate of change is small. And at depth = 10 d the value of displacement reaches the small value it is about (1.5% at d = 0.4 m and 1% at d = 0.6 m) of footing width.
It can be concluded that, at depth = 10 d the value of displacement reaches small value, after that the decrease in settlement practically stops. The effective length to diameter ratio of stone column is found to be L/d =10 and thereafter there is no effect on displacement value.

Conclusion
From the results of the research, several conclusions have been drawn and are summarized as follows:  The settlement of footing decreases with increasing of stone column length to reach the length to stone column diameter ratio L/d=10, then the decrease is very small or virtually has no effect.
 β increases with the increasing L/d. At L/d values more than 10, the rate of increase in β is small.
 At depth = 10 d from the surface, the vertical displacement reaches a negligible value.
 The effective length of stone column was found L/d = 10 and after that does not affect the amount of displacement.