DISTRIBUTION OF STRESSES BELOW FOOTINGS SUPPORTED BY …

Journal of Engineering Science and Technology Vol. 16, No. 2 (2021) 1719 - 1732 © School of Engineering, Taylor’s University

1719

DISTRIBUTION OF STRESSES BELOW FOOTINGS SUPPORTED BY STONE COLUMNS

AMEER A. AHMED*, MOHAMMED Y. FATTAH

Department of Civil Engineering, University of Technology, Baghdad, Iraq *Corresponding Author: [email protected]

Abstract

The behaviour of a circular footing supported by a single floating stone column in soft clay soils of low undrained shear strength, cu = 20 kN/m2, is studied through finite element analysis to determine the effect of soil improvement on the distribution of stresses below the isolated footings supported by the composite soil system. The studied cases consist of 1 m diameter circular stone column Ds having different lengths Ls of (4, 6 and 8) m. The studied diameters of footing Df are (1.0 , 1.2 , 1.4 , 1.6 , 1.8 , 2.0, 2.5 and 3.5) m which cover the range of area ratios, Ar%=(Area of stone column)/(Area of footing) , from (8.16 to 100)%. A total of 36 cases were analysed by ANSYS 18 workbench CAD program for treated and untreated soil to investigate these cases. The adopted axisymmetric modelling takes into account the contact between the target stone column and the surrounding contact clay soil. The results of the study revealed that the stress distribution below footings is not uniform in both stone and clay areas and the value of the stress concentration ratio (n) is dependent on the normalized normal stress q/cu levels and n increase with the increasing of the area ratio.

Keywords: Area ratio, Finite element, Stone column, Stress concentration ratio.

1720 A. A. Ahmed and M. Y. Fattah

Journal of Engineering Science and Technology April 2021, Vol. 16(2)

1. Introduction Soft soils are presented in many places around the world, these soils are characterised by their low mechanical shear strength, typically cu ≤ 25 kN/m2 and high compressibility which in turn leads to many foundation problems from the geotechnical engineering point of view. Many techniques were adopted for the sake of enhancing the properties of these soils to enhance its mechanical properties. The best technique used for the improvement of these soils depends on the project’s importance and budget. The stone column is one of these methods used to increase the load carrying capacity and reduce the value and time of settlement of soft soil especially for large areas and under embankments because of its low costs in comparison with other used techniques.

The use of the stone column technique for the treatment of soft soil has proven to be successful in increasing bearing capacity, reducing total and differential settlements and decreasing the time of consolidation and enhancing slope stability of both embankments and slopes. These columns are made of granular compacted material, cheaper and easy to install. In addition, the stone columns are environmentally friendly in comparison with other ground improvement techniques.

Stone columns repeatedly used for the stabilization of soft soils. For the support of different structures, the use of stone columns is increasing day by day [1, 2].

One of the earliest studies was carried out by Hughes and Withers [3], they reported that the bulging failure is the dominated type of failure in stone columns when the critical length (4 × stone diameter) is exceeded they arrived at this conclusion through model and field observations.

The stress concentration ratio “n” is defined as the ratio of the stresses on stone column’s area divided by the stresses on the soft clay area it is an indicator of the degree of improvement of stone columns since the stresses will passes through the stiffer material hence reducing the amount of settlement of the soft clay area [4].

Fattah et al. [4] studied the value of stress concentration ratio, n through a laboratory model test. The load applied through a specially manufactured setup to measure the load applied directly on stone column and the total load applied to the composite soil-stone system through two proving rings. The foundation steel plates have 220 mm diameter and 5 mm thickness. These plates contain 1, 2, 3, and 4 holes. The centre to centre spacing between all holes are equals twice the stone column diameter, D. Crushed stone was installed in very soft clays having undrained shear strength ranging between 6 and 12 kPa. The stone columns made of. Two lengths to diameter ratios L/D = 6 and 8, respectively. The experimental tests showed that the stone columns with L/D = 8 provided a stress concentration ratio n of 1.4, 2.4, 2.7, and 3.1 for the soil having a shear strength cu=6 kPa, treated with single, two, three, and four columns, respectively. The values of n were decreased to 1.2, 2.2, 2.5, and 2.8 when the L/D = 6. The values of n increase when the shear strength of the treated soil was increased to 9 and 12 kPa.

A review to analyse the behaviour of stone columns used in different types of constructions such as oil storage tanks, embankments, buildings etc was presented by Singh and Sahu [5]. The consequence of without encased and encased stone columns on several types of construction are studied. The effect of various diameters with various depths in the ground also reviewed. For the encasement

Distribution of Stresses Below Footings Supported by Stone Columns 1721


different types of geosynthetics are used for improvement of the results. For the prediction of the settlement of foundations reinforced with stone column number of numerical and physical approaches are done. The work dealt with several theories that exist from past to present which helps in understanding the enhancements by stone columns in boosting soft soils. In the development of geotechnical properties, physical modelling has an important role.

Znamenskii and Sayed [6] carried out three-dimensional numerical studies on a stone column under footing on the composite soil. A comparison between the numerical model and different analytical methods to represent a footing on the soft clay soil reinforced by a group of stone columns. Numerical results showed good convergence with experimental.

The main goal of this research is to clarify the variation of stresses below a foundation supported by a single floated stone column in soft clay. These stresses variation will suggest, if it is suitable, to adopt a single constant value for stress in the stone and clay area and the reliability of adopting this approximation.

2. Verification of ANSYS Program The output results of the ANSYS 18 Workbench were validated by comparing the results obtained from a finite element model of an axisymmetric single floated stone column with experimental load-settlement test carried out by Rao et al. [7]. The experimental model consists of a single floated stone column of 25 mm in diameter and 225 mm in length constructed at the centre of the bed of clay of height 350 mm inside a cylindrical steel tank of diameter of 650 mm. The load was gradually applied through a rigid steel plate of diameter 50 mm. Table 1 shows the properties of stone column and soft clay materials.

A similar validation work was carried out by Ambily and Gandhi [8], they validated PLAXIS program with the load-settlement results from the experimental work of Rao et al, their PLAXIS axisymmetric finite element model and result are shown in Fig. 1 along with the current results of ANSYS 18. The ANSYS 18 finite element results show a good agreement with experiment’s results conducted by Rao et al. [7] indicating the accuracy of the model in this study.

Table 1. Physical properties of the soft clay and stone materials for experimental work of Rao et al. [7].

Material Clay Stone column Young’s Modulus (kN/m2) 4000 45000 Poisson’s Ratio 0.45 0.3 Initial Cohesion (kN/m2) 20 0 Angle of Internal Friction (Deg.) 0 38



(a) Ambily geometry, mesh and dimensions.

(b) Compare of results between Rao’s experimental

work VS PLAXIS and ANSYS 18 Workbench.

Fig. 1. Validation of ANSYS program with Rao et al experimental work.

3. Problem Description The variation of stresses beneath the footing which is supported by the composite of clay and stone columns is studied by using ANSYS Workbench 18.0 software. The problem consists of a single circular concrete footing of thickness 500 mm and having different diameters of (1.0, 1.2, 1.4 ,1.6, 1.8, 2.0, 2.5 and 3.5 m). The footing is supported by a single floating stone column of diameter 1.0 m and having length(s) of 4, 6 and 8 m, these lengths are beyond the critical length (4Ds) as suggested by Hughes and Withers [3] to ensure that the failure will be in bulging of stone column. The clay boundary is 8.0 m in diameter from the Y-axis symmetry line and 12.0 m in depth. The schematic dimensions are shown in Fig. 2 which shows half the structure due to using axisymmetric analysis instead of using 3D analysis, this simulation will minimize the time and amount of data required to solve the problem. The soft clay material has an undrained shear strength of 20 kN/m2 and Poisson’s ratio of 0.499. Bowels [9] stated that the modulus of elasticity of soft clay is assumed to be 500 times its shear strength as suggested by empirical correlations. The physical properties of the soft clay and backfill material of the stone column are shown in Table 2.

Table 2. Physical properties of the soft clay and stone materials. Material Clay Stone column Unit Weight (kN/m3) 19 21 Young’s Modulus (kN/m2) 10000 100000 Poisson’s Ratio 0.4999 0.35 Initial Cohesion (kN/m2) 20 0 Angle of Internal Friction (Deg.) 0 45 Dilatancy Angle (Deg.) 0 15 Residual Cohesion (kN/m2) 20 0 Residual Friction Angle (Deg.) 0 30



Fig. 2. Problem schematic diagram.

4. Program Data The Ansys 18 workbench software is used in the analysis of the problem. The Mohr-Coulomb failure criterion is adopted for the clay and stone materials. The element used in the analysis is (PLANE183) with the axisymmetric option, the degrees of freedom for the element Ux and (Ux and Uy) is restrained in the right and bottom boundaries, respectively. The element size is 100 mm in length to obtain a regular and uniform shape for all elements and to increase the accuracy of the output. The total number of elements is ranging from 4674 to 4739 while the total number of nodes is ranging from 14501 to 14722 due to changing in footing’s diameter. The surface-to-surface contact elements (CONTA172) and (TARGE169) are used to simulate the boundary between stone column and clay soil and also between the concrete footing and stone and clay, the type of the contact was chosen as bonded type as the stone will penetrate the clay layer.

Figure 3 represents the finite element mesh. A construction geometry path was inserted between two points starting from the symmetry line of the bottom of footing and the edge of the footing, the number of points between these limits was chosen in such a manner that the length of each segment will be 10 mm in length so that for different footing diameters, the induced stresses and deformations can be compared for the same point location. So, for a footing of diameter 600 mm, the number of points is 59 to produce a total number of 60 sublines of the length of 10 mm for each.



Fig. 3. Finite elements mesh for stone and concrete and the clay materials.

The boundary condition was applied to the structure by assuming the inner and outer vertical lines with zero horizontal displacements (Ux = 0) and free to displaced in the Y-direction for the clay and concrete while the bottom boundary of the clay was assumed with both horizontal and vertical displacement equal to zero (Ux = Uy = 0). During the non-linear loading process, the load was applied gradually to the top of concrete footing in the global Y-direction in one ramped single step in the form of pressure stresses so that the pressure for every sup-step is equal to (1.0 kN/m2), for all load cases until reaching the desired total load or reaching a high value of deformation. This means that for a total pressure of 600 kN/m2, the number of sub-steps was 600 in total, therefore the auto time stepping was turned to off during the solution process.

5. Results and Discussion After the completion of the data insertion, the solving process was started until obtaining a solution for the problem. The results of the load-deformation were normalized to get a better understanding of the effect of variation of stresses beneath the footing in both the stone and soft clay areas. The applied stresses were normalized by dividing them by the clay shear strength (q/cu) and the vertical axis was normalized by dividing the deformation values by the diameter of the isolated footing (s/Df) to have dimensionless values which will be more efficient in comparison between the different cases.

Figure 4 shows the results of normalized treated and untreated load-settlement curves. It is worth mentioning that the untreated load settlement relation consists of six curves representing the variant diameters of the single footing but when they are normalized, they are transformed into one curve.

From Fig. 4, it is clear that under the same normalized q/cu values, the normalized settlement decreases with decreasing the footing’s diameter. On the other hand , for the same normalized s/Df values, the normalized q/cu increases with decreasing the footing’s diameter, this is because with quantizing the diameter of stone column (Ds) and increasing the footing’s diameter, and for the same stress values applied on the footing, the corresponding area ratio Ar%=(Area of stone column)/(Area of footing) will decrease and this will result in increasing the stresses transmitted to the clay area and increasing the amount of deformation of the composite structure.



Fig. 4. Normalized pressure-settlement chart

for different area ratio on treated soil, Ls/Ds = 8.

Figure 5 shows the stress contour at q/cu = 12 for the composite structure for two cases of area ratio Ar% of 16% and 51% respectively having the same length to diameter ratio Ls/Ds of 8 and stone diameter of 1 m. These figures show that the stresses within stone column is larger than the stresses within the clay soil because of the stiffer material of the stone.

(a) Area ratio = 16%. (b) Area ratio = 51%.

Fig. 5. Stress contours for stone column having Ds = 1 m, Ls/Ds = 8 and q/cu = 12.

Figure 6(a) shows the vertical stresses distribution beneath the circular footing, for low stresses q/cu ≤ 5 kN/m2, for Ls/Ds = 8 case. These stresses are transferred from the concrete circular footing(s) to the stone column and the surrounding soft clay soil. It is noticed that the vertical stress is almost uniform within the interior zone of footing above the stone column area, the largest the footing size, the most uniform and flatten value of stresses for approximately 80 percent of the footing



diameter, after that the stresses increase until reaching the edge of the stone column when the stress increases rapidly to its maximum value for all different types of footings diameters. Then the stress decreases rapidly to its minimum value when passing the stone column zone and reaching soft clay zone, the stresses within the clay zone in general, tend to vary from increasing to decreasing until reaching the edge of the footing when the stresses again increase to a maximum value and sometimes higher than that recorded for the columns zone when the footing diameter is larger two times than the stone diameter.

Figure 6(b) shows the vertical stresses distribution beneath the circular footing, for high stresses q/cu > 5 kN/m2, these stresses are transferred from the concrete circular footing(s) to the stone column and the surrounding soft clay soil. It is noticed that the vertical stress distribution is similar in behaviour for that described for low stresses but there are differences between the maximum stresses at the contact area between the stone column and soft clay.

The stresses are falling from their maximum values to their minimum values, this is because the column undergoes the large portion of the stresses in comparison with the weaker clay layer. Then the stresses increase to their maximum values within soft clay zone, the stresses in general tend to increase until reaching the edge of the footing when the stresses show their maximum values. Figures 7-12 show the same behaviour for footing diameter 1.4, 1.6, 1.8, 2.0, 2.2, 2.5 and 3.5 m, respectively.

Fig. 6(a). Stress

distribution for Df = 1.2 m, q/cu = (1-5). Fig. 6(b). Stress

distribution for Df = 1.2 m, q/cu = (1-15).

Fig. 7(a). Stress

distribution for Df = 1.4 m, q/cu = (1-5). Fig. 7(b). Stress

distribution for Df = 1.4 m, q/cu = (1-15).



Fig. 8(a). Stress distribution for Df = 1.6 m, q/cu = (1-5).

Fig. 8(b). Stress distribution for Df = 1.6 m, q/c = (1-15).


Fig. 9(b). Stress distribution for Df = 1.8 m, q/cu = (1-15).

Fig. 10(a). Stress distribution for

Df = 2.0 m, q/cu = (1-5). Fig. 10(b). Stress distribution for

Df = 2.0 m, q/cu = (1-15).

Fig. 11(a). Stress distribution for

Df = 2.5 m, q/cu = (1-5). Fig. 11(b). Stress distribution for

Df = 2.5 m, q/cu = (1-15).




Fig. 12(b). Stress distribution for Df = 3.5 m, q/cu = (1-15).

The stress concentration ratio (n) is used to define the benefit of using stone columns by comparing the ratio of stresses transferred to stone or sand column to the stresses transferred to the surrounding clay layer in the unit cell concept, which represents the group of stone columns spread in the large area i.e., n = (stresses on stone column)/(stresses on soft clay). The area ratio (Ar%) is also used in the unit cell to describe the area of stone column to that of the total area of the unit cell. However, for a single stone column, the boundary condition is not the same as the unit cell concept and we need to adjust the equation into a more presenting form which simulates the existing case, but the derivation of the equation is the same.

Because the stresses are not uniformly distributed above the columns and clay layer therefore to calculate the stress concentration ratio (n) we should calculate the summation of the stress’s areas of that of stone column and clay separately for a given chart.

In a single stone column, the stress concentration ratio will be equal to the summation of stresses, obtained from the program, transferred to the stone column divided by the summation of stresses transferred to the clay, i.e.,

𝑛𝑛 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝐴𝐴𝐴𝐴𝑠𝑠𝑠𝑠𝐴𝐴𝑠𝑠 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑜𝑜𝑜𝑜𝐴𝐴 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐𝑐𝑐𝑜𝑜𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝐴𝐴𝐴𝐴𝑠𝑠𝑠𝑠𝐴𝐴𝑠𝑠 𝑜𝑜𝑜𝑜 𝑠𝑠𝑜𝑜𝑜𝑜𝑠𝑠 𝑐𝑐𝑐𝑐𝐴𝐴𝑐𝑐 𝑏𝑏𝐴𝐴𝑐𝑐𝑜𝑜𝑏𝑏 𝑜𝑜𝑜𝑜𝑜𝑜𝑠𝑠𝑓𝑓𝑜𝑜𝑓𝑓

(1)

The area ratio for a single stone column should be as described in Eq. (2),

𝐴𝐴𝐴𝐴% = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑜𝑜𝑜𝑜𝐴𝐴 𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐𝑐𝑐𝑜𝑜𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑜𝑜𝑜𝑜 𝑜𝑜𝑜𝑜𝑜𝑜𝑠𝑠𝑓𝑓𝑜𝑜𝑓𝑓

(2)

Figures 13-15 show the variation of stress concentration ratio, n with the normalized applied stresses (q/cu) plotted for different area ratios Ar% which are calculated according to Eq. (2).

Figure 13 shows the results for stone column of length to diameter ratio, Ls/Ds = 8, it is clear that for a given area ratio Ar% and normalized vertical stresses up to q/cu = 5, the stress concentration ratio, (n) is generally constant, with the increasing of the applied vertical stresses, the n values increase linearly with the increase of the applied stresses. The higher the normalized stress, the higher the stress concentration ratio value. This suggests that for a given area ratio, (n) value is dependent on the stress level and it is not constant during the entire loading process except at low-stress level q/cu < 5.



For a given stress level, the maximum area ratio exhibits the maximum n values for all normalized stress levels. The effect of area ratio on the n values is clear in the high-stress levels in comparison with that calculated at low stresses.

For Ls/Ds = 8, the n values (for area ratio of 69.44%) increases from minimum of 5.38 at q/cu = 3 to 19.26 at q/cu = 25 while its values (for area ratio of 39.06%) increases from minimum of 1.67 at q/cu = 2 to 9.98 at q/cu = 25.

Fig. 13. Variation of n with q/cu for different area ratios, Ls/Ds = 8.

Figures 14 and 15 show the variation of (n) with q/cu for Ls/Ds = 6 and Ls/Ds = 4, both figures have a similar behaviour to Fig. 13.

For Ls/Ds = 6, the n values (for area ratio of 69.44%) increases from a minimum of 5.23 at q/cu = 3 to 18.45 at q/cu = 25 while its values (for area ratio of 39.06%) increases from a minimum of 1.69 at q/cu = 2 to 9.78 at q/cu = 25.

For Ls/Ds = 4, the n values (for area ratio of 69.44%) increases from a minimum of 6.26 at q/cu = 2 to 18.95 at q/cu = 25 while its values for area ratio of 39.06% increases from a minimum of 1.68 at q/cu = 2 to 9.59 at q/cu = 25.





Figure 16 shows the variation of stress concentration ratio (n) with area ratio Ar% for different normalized loading levels q/cu for the case of stone length to diameter ratio Ls/Ds = 8, the figure reveals that the n value increases with the increasing of the area ratio and it is dependent on the stress level, the higher the stress level, the higher the n values. This is true for all area ratios. At low-stress level q/cu < 5, the behaviour is convergent.

Fig. 16. Variation of n with area ratios for different q/cu, Ls/Ds = 8.





Figures 17 and 18 show similar behaviour for variation of stress concentration ratio n with area ratio for length to diameter Ls/Ds of 6 and 4, respectively.

Fattah et al. [10] concluded that the value of stress concentration ratio n increases with increasing the shear strength of the treated soil.

Paul and Sindhu [11] concluded that the n value was found to increase as the number of columns was increased. Also, an l/D (length to diameter) ratio of 6 showed more n value than an l/D of 5. Also, triangular pattern of arrangement showed more n value than square pattern.

6. Conclusions All the results obtained in this study are from finite element analysis for the soil properties and boundary conditions. So, the results are restricted to these conditions.

• Under the same normalized q/cu values, the normalized settlement decreases with decreasing the footing’s diameter. On the other hand, for the same normalized s/Df values, the normalized q/cu increases with decreasing the footing’s diameter.

• The vertical stress is almost uniform within the interior zone of footing above the stone column area, the largest the footing size, the most uniform and flatten value of stresses for approximately 80 percent of the footing diameter, after that the stresses increase until reaching the edge of the stone column when the stress increases rapidly to its maximum value for all different types of footings diameters.

• The stress concentration, n value is initially constant for all area ratios when q/cu ≤ 5, after that it increases with the increase of the stress level and it is dependent on the stress level, the higher the stress level, the higher the n values.

• For a given stress level, the maximum area ratio exhibits the maximum n values.



References 1. Bergado, D.T.; Anderson, L.R.; Miura, N.; and Balasubramaniam, A.S. (1996).

Soft ground improvement in lowland and other environments. New York: American Society of Civil Engineers.

2. Fattah, M.Y.; Al-Neami, M.A.; and Al-Suhaily, A.S. (2017). Estimation of bearing capacity of floating group of stone columns. Engineering Science and Technolgy, an International Journal, 20(3), 1166-1172.

3. Hughes, J.M.O.; and Withers, N.J. (1974). Reinforcing of soft cohesive soils with stone columns. Ground Engineering, 7(3), 42-49.

4. Fattah, M.Y.; Shlash, K.T.; and Al-Waily, M.J.M. (2011). Stress concentration ratio of model stone columns in soft clays. Geotechnical Testing Journal, 34(1), 50-60.

5. Singh, I.; and Sahu, A.K. (2019). A review on stone columns used for ground improvement of soft soil. Proceedings of the 4th World Congress on Civil, Structural, and Environmental Engineering (CSEE’19). Rome, Italy, ICGRE 132(1-5).

6. Znamenskii, V.V.; and Sayed, D.A. (2019). Comparison between analytical method and numerical model for footings on soft clay supported by stone columns. Journal of Physics: Conference Series, 1425(1), 12075.

7. Rao, S.N.; Madhiyan, M.; and Prasad, Y.V.S.N. (1992). Influence of bearing area on the behaviour of stone columns. Proceedings of the Indian Geotechnical Conference. Calcutta, India, 235-237

8. Ambily, A.P.; and Gandhi, S.R. (2007). Behavior of stone columns based on experimental and FEM analysis. Journal of Geotechnical and Geo Environmental Engineering, 133(4), 405-415.

9. Bowles, J.E. (1997). Foundation analysis and design (5th ed.). Singapore, : McGraw-Hill Companies, Inc.

10. Fattah, M.Y.; Shlash, K.T.; and Al-Waily, M.J. (2013). Experimental evaluation of stress concentration ratio of model stone columns strengthened by additives. International Journal of Physical Modelling in Geotechnics(ICE), 13(3), 79-98.

11. Paul, J.; and Sindhu, A.R. (2018). Study on stress concentration ratio of stone column reinforced soft clay. International Research Journal of Engineering and Technology (IRJET), 5(4), 3535-3539.

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DISTRIBUTION OF STRESSES BELOW FOOTINGS SUPPORTED BY …