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Stone column method
Stone column method 6.1
6
Introduction
Stone column method for ground improvement is a vibro-replacement technique, where the weak soil is displaced using a cylindrical vibrating probe (i.e. vibroflot), thus creating a column that is then filled and compacted with good-quality stone aggregates. With the inclusion of stone aggregates to the in situ soil, its stiffness and load-carrying capacity increases. It also helps to reduce the static as well as differential settlement of the soils. Bulging action of the stone columns imparts lateral confinement to the surrounding soils and it also acts as a drainage path accelerating the consolidation of cohesive soils. These stone columns are generally used for soils that are much more compressible but not weak enough to necessitate a pile foundation. Moreover, for the construction of low-to-medium rise buildings on soft soils, pile foundation sometimes becomes expensive. In such cases, stone columns are preferred. Stone columns are very useful for the improvement of cohesive soils, marine/alluvial clays, and liquefiable soils. Stone columns have been used successfully for a wide range of applications from the construction of high-rise buildings to oil tank foundation, and for embankment and slope stabilization.
6.2
Mechanism
As mentioned earlier, the basic mechanisms behind ground improvement using stone columns are (1) soil compaction through the bulging action of the stone columns, (2) soil reinforcement with the inclusion of stone aggregates into the soil mass, and (3) accelerated consolidation of the cohesive soils. The differences between the load carrying mechanism of a pile and that of a stone column are presented in Fig. 6.1. The structural load is mainly carried by the piles only and there is no transfer of stress to the surrounding soil in the case of pile foundations. However, in the case of stone columns, a part of the structural load is carried by the surrounding soil. This is demonstrated in the stress distribution diagram in Fig. 6.1. A single stone column primarily fails by bulging, whereas a group of stone columns may fail by bulging or by shear failure of the soil/columns mass.
6.3
Stone column installation methods
For the installation of stone columns a vibrating poker device is used that can penetrate to the required treatment depth under the action of its own weight, vibrations, and actuated air, assisted by the pull-down winch facility of the rig. This process displaces the soil particles and the voids created are compensated with backfilling of stone aggregates. The vibroflot penetrates the filled stone aggregates to compact it and thus Geotechnical Investigations and Improvement of Ground Conditions. https://doi.org/10.1016/B978-0-12-817048-9.00006-8 © 2019 Elsevier Inc. All rights reserved.
Stress distribution
s
Geotechnical Investigations and Improvement of Ground Conditions
s
50
Structural loading
Shaft resistance
Compaction due to bulging of stone column
GL
(A)
End bearing resistance
(B)
Fig. 6.1 Load carrying mechanism of (A) piles and (B) stone columns.
forces it radially into the surrounding soils. This process is repeated till the full depth of the stone column is completed. The lift height is generally taken as 0.6–1.2 m for the filling and compaction of the stone aggregates. Depending upon the feeding of stone aggregates into the columns there are basically two methods for the installation of stone columns: the top-feed method and the bottom-feed method, as shown in Fig. 6.2. In the top-feed method, the stone aggregates are fed into the top of the hole. The probe is inserted into the ground and is penetrated to the target depth under its own weight and compressed air jetting. However, jetting of water is also done especially when the soil is unstable. This also helps to increase the diameter of the stone columns and to washout the fine materials from the holes. The top-feed method is suitable when water is readily available and there is enough working space to allow for water drainage. Moreover, the soil types should be such that it would not create messy surface conditions due to mud in water. The topfeed method is preferable when a deeper groundwater level is encountered. The bottom-feed method involves the feeding of stone aggregates via a tremie pipe along the vibroflot and with the aid of pressurized air. The bottom-feed method is preferable when the soil is highly collapsible and unstable. However, the stability of holes will also depend upon the depth, boundary conditions, and the groundwater conditions. In areas, where the availability of water and space and the handling of mud in process water are limiting factors, the bottom-feed method can be implemented. Due to limited space in the feeding system, a smaller size of aggregates is used in the bottom-feed method compared with that used in the top-feed method. On the other hand, the flow of stones to the column is mechanically controlled and automatically recorded in the bottom-feed method.
Stone column method
51
Fig. 6.2 Stone columns installation methods: (A) top feed method and (B) bottom feed method.
6.4
Stone column design parameters
The important parameter information required for the design of stone columns are the diameter and depth of the stone columns, spacing between the stone columns, layout of the stone columns, replacement ratio, stress concentration factor, improvement ratio, etc. The stone columns are very effective up to a depth of 4–10 m. For a depth of >10 m some of the construction problems that might be encountered include the stabilization of the borehole and stone contamination until the bottom of a borehole is reached. The diameter of the stone column depends upon the drilling method adopted, the improvement factor required, and the installation technique used. Generally, the diameter of the stone column is between 0.8 and 1.2 m. The diameter of the wet-feed stone columns is 20%–40% more than the corresponding dry-feed columns. A spacing of about 1.8–2.7 m is adopted depending upon the diameter of the stone columns and the areareplacement ratio. Based upon the concept of improvement factor, the following steps are followed for the design of stone columns. l
l
The settlement of untreated ground is calculated with conventional calculation methods. The ‘settlement ratio’ or ‘improvement factor’, which refers to the ratio of the settlement of untreated ground to that of the treated ground, is evaluated. Also, the improvement factor
52
l
l
l
Geotechnical Investigations and Improvement of Ground Conditions
may refer to the increase in compression modulus of the treated ground. The improvement factor is derived as a function of the area-replacement ratio, angle of internal friction of the column material, and the Poisson’s ratio of the surrounding soils. Charts have been developed by Priebe (1995) correlating these three parameters to the improvement factor. For calculation of the improvement factor, it is assumed that (1) the column is based on a rigid layer (end-bearing), (2) the column material is incompressible, and (3) the bulk density of the column and soil is neglected. Priebe has further considered the effect of the compressibility of the column material and the overburden for calculation of the improvement factor. A detail of the Priebe method is presented later in this section. The reduction of settlement that is required to meet the design requirements is calculated. Based on the contractor’s experience and empirical data it is determined if the stone columns can provide the required reduction of settlement. Typically, the settlement ratios are taken between 2 and 3. The area-replacement ratio necessary to provide the required reduction of settlement is determined. The concept of area-replacement ratio based on the unit cell approach is presented later in this section. For uniformity of settlement between the column and surrounding soil, and the stability of the stone columns, the stress concentration on soil and column is calculated and verified with the ultimate load capacity. The depth of stone column, its diameter and spacing are then determined based upon the area replacement ratio, experience and installation method used by the contractor.
6.4.1 Area replacement ratio The area-replacement ratio, ac is defined as Ac/A, where Ac is the cross-sectional area of one column and A is the total cross-sectional area of the ‘unit cell’ attributed to each column (as shown in Fig. 6.3). Ac/A is related to the column diameter (D) and column spacing (S) as follows: Ac =A ¼ k ðD=SÞ2
(6.1) Area of single stone column, Ac
S S
Triangular grid
CSA of foundation per stone column (unit cell), A
Fig. 6.3 Unit cell in triangular and square grid of stone columns.
Square grid
Stone column method
53
where k is π/4 and π/(2 √ 3) for square and equilateral triangular column grids, respectively. The equivalent diameter of a cylinder enclosing the unit cell may be taken as 1.05S for an equilateral triangular pattern and 1.13S for a square pattern. The ratio of the area of remaining soil in a unit cell (as), i.e. As/A can be calculated as follows: As =A ¼ 1 ac
(6.2)
where As is the cross-sectional area of soil surrounding the column in a unit cell.
6.4.2 Stress concentration Upon placement of a structural load over stone column-treated ground, the concentration of stress over the column and is accompanied by a stress reduction in the surrounding cohesive soil/loose cohesion-less soil, which has a lower load carrying capacity. This distribution of vertical stress within a unit cell can be determined by using a stress concentration factor, n as follows: n ¼ σ c =σ s
(6.3)
where σ c and σ s are the stress in the column and the surrounding soil, respectively. For equilibrium between the vertical loading and the load taken by the unit cell, the following condition must be satisfied: σ ¼ σ c ac + σ s ð1 ac Þ
(6.4)
Eqs (6.3), (6.4) can be rearranged to achieve the stress levels in the column and the surrounding soil as follows: σc ¼
nσ 1 + ðn 1Þac
(6.5a)
σs ¼
σ 1 + ðn 1Þac
6.5b
The value of n is generally assumed to be between 2 and 5.
6.4.3 Improvement factor The basic improvement factor n0 is determined as follows (Priebe, 1995): 2
3 1 + f μ ð , A =A Þ c s Ac 6 7 15 n0 ¼ 1 + 4 2 A Kac f ðμs , Ac =AÞ
(6.6)
54
Geotechnical Investigations and Improvement of Ground Conditions
f ðμs , Ac =AÞ ¼
ð1 μs Þð1 Ac =AÞ 1 2μs + Ac =A
Kac ¼ tan 2 45° ϕc =2
(6.7a) (6.7b)
where Kac is the coefficient of earth pressure and μs is the Poisson’s ratio of the surround soil. By considering the column compressibility, the improvement factor n1 is obtained as follows: 2
3 1 + f μs , Ac =A 6 17 n1 ¼ 1 + Ac =A 4 2 5 Kac f μs , Ac =A Ac =A ¼ Δ
1 A=Ac + ΔðA=Ac Þ
(6.8)
(6.9a)
A 1 1 ¼ Ac ðAc =AÞ1
(6.9b)
4 Kac ð n0 2Þ + 5 1 ðAc =AÞ1 ¼ 2 ð4 Kac 1Þ 2 ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4 Kac ð n0 2Þ + 5 2 16 Kac ð n0 1Þ + 4 Kac 1 4 Kac 1
(6.9c)
Further by considering the overburden, the improvement factor n2 is obtained as follows: n2 ¼ f d n1 fd ¼
(6.10a)
1 K0c Ws =Wc Wc 1+ K0c Pc
(6.10b)
P
Pc ¼ Ac =A +
(6.10c)
1 Ac =A Pc =Ps
1=2 + f μs , Ac =A Pc =Ps ¼ Kac f μs ,Ac =A Wc ¼
X
ðγ c ΔdÞ and Ws ¼
(6.10d) X ðγ s Δd Þ
(6.10e)
Stone column method
K0c ¼ 1 sin ϕc
55
(6.10f)
where P is the foundation load, Ws and Wc are the weights of the soil and column, respectively, and K0c is the earth pressure at rest.
6.4.4 Load carrying capacity The vertical stress on a single column can be calculated as follows: σ 1 1 + sin ϕc ¼ σ 3 1 sin ϕc
(6.11)
where σ 1 and σ 3 are the vertical and lateral stress respectively. Based upon the tests conducted, Hughes and Withers (1974) have proposed the following equations: qa ¼
1 + sin ϕc 0 σ r0 + 4c 1 sin ϕc
(6.12) 0
where qa is the allowable bearing capacity of the stone column, c is cohesion, and σ r0 is the average effective radial stress over a depth of four times the diameter of column. The drained cohesion value may be considered for small column spacings, whereas the undrained value is considered if the column spacing is more (about >2 m). A factor of safety varying from 1.5 to 3 is generally applied to the value of qa obtained from Eq. (6.12). Also, qa ¼ Cs As + Ac cp Nc =FS
(6.13)
where cp is cohesion at the column base; As is the average stone column perimeter area; and Nc is taken as 9 for clay, if the length/column ratio is 3 and is taken between 5.4 and 9 and if the ratio is less. Further, as per Barksdale and Bachus (1983a,b), the bearing capacity of an isolated stone column or a stone column located within a group can be expressed in terms of an ultimate stress applied over the stone column: qult ¼ cNc
(6.14)
Nc is generally taken to be between 18 and 22. For soils having a reasonably high initial stiffness (e.g. inorganic soft to stiff clays and silts), an Nc of 22 is recommended. On the other hand, for soils with low stiffness (e.g. peats, organic cohesive soils and very soft clays with plasticity index >30), an Nc of 18 is recommended.
56
Geotechnical Investigations and Improvement of Ground Conditions
Example 1. Bearing Capacity Determine what height of fill the stone column-improved ground can safely support. Both a general shear failure and a local bulging failure in a deep, very soft clay layer (Fig. 6.4) must be considered. Assume the stone column has an angle of internal friction ϕc of 42°, and an equilateral triangular pattern of columns is used having a spacing, s, of 2 m. Solution ac ¼ π= 2√3 ðD=SÞ2 ¼ 0:907 0:25 ¼ 0:227 Ac ¼ 3:14 ð1=4Þ ¼ 0:785 m2 A ¼ ðAc =ac Þ ¼ 0:785=0:227 ¼ 3:458 m2 Assuming that a bulging failure occurs in the upper three stone column diameters of depth, the ultimate capacity of a stone column can be calculated as: qult ¼ cNc ¼ 22 22 ¼ 484 kPa
H
sc
ss
Clay (°sat = 15.7 kN/m3 PI = 25, c = 22 kPa)
1m
2.5 m
6m
GL
Fill (°wet = 19.6 kN/m3
1.5 m
Clay (°sat = 15.7 kN/m3 PI = 40, c = 10 kPa) Clay (c = 22 kPa)
Firm bearing strata 2m
Fig. 6.4 Example 1. Based on Barksdale, R.D., Bachus, R.C., 1983a. Design and Construction of Stone Columns, Volume I, Appendixes, Report No. FHWA/RD-83/026, Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC; Barksdale, R.D., Bachus, R.C., 1983b. Design and Construction of Stone Columns, Volume II, Report No. FHWA/RD-83/027, Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC.
Stone column method
57
Hence, Pult ¼ qult Ac ¼ 484 0:785 ¼ 380 kN Checking for the possibility of bulging failure in very soft clay located at a depth of 6 m, the ultimate stress the stone column can carry can be calculated as follows: 1 + sin ϕc 1 + sin ϕc ¼ 9c ¼ 90 5:04 1 sin ϕc 1 sin ϕc ¼ 454kPað< 484 kPa, hence it governsÞ:
qult ¼ σ 3
The maximum stress the clay surrounding the stone column can take is σ s ¼ 5c ¼110 kPa. Now assuming a value of 3 for the stress concentration factor, n: σc ¼
nσ σ ¼ 2:06σ and σ s ¼ ¼ 0:688σ 1 + ðn 1Þac 1 + ðn 1Þac
σ c Then σ s ¼ 0:688 2:06 ¼ ð0:688 454Þ=2:06 ¼ 152 kPa. Since 152 kPa is >110 kPa, σ s ¼5c ¼ 110 kPa is the ultimate stress the clay can carry. The ultimate load that can be applied to the unit cell area in the fill is now calculated as: Pult ¼ σ c Ac + σ s As ¼ ½454 0:785 + ½110 ð3:458 0:785Þ ¼ 356 + 294 ¼ 650 kN Using a factor of safety of 2.0, the allowable load, Pall is 325 kN per unit cell. Hence, the safe height of the fill is Pall/(unit weight of the fill area of unit cell) ¼ 325/ (19.6 3.458) ¼4.8 m. Example 2. Settlement Estimate the primary consolidation settlement of the stone column-improved silty clay layer, as shown in Fig. 6.5. Assume the water table to be at ground level and the stone columns are in an equilateral triangular grid. Solution The stress exerted by the embankment along with the sand blanket on top of the stone columns σ is (3.7 18.8) + (0.8 17) ¼83.16 kPa. Area-replacement ratio ac ¼ π/(2 √ 3) (D/S)2 ¼ 0.907 0.25 ¼ 0.227. The initial effective stress σ 0 at the centre of the silty clay layer is σ 0 ¼ 3 ð15 9:81Þ ¼ 15:57 kPa: Using the one-dimensional consolidation theory, the primary settlement, st, can be calculated as follows: cc σ 0 + Δσ st ¼ H log 10 1 + e0 σ0
58
Geotechnical Investigations and Improvement of Ground Conditions
0.8 m
4.5 m
Embankment (°wet = 18.8 kN/m3)
Sand blanket (°wet = 17.0 kN/m3)
GL
Soft silty clay eo = 2.0 6m
Cc = 0.7 °sat = 15 kN/m3 c = 19 kPa
1m
Firm to dense sand 2m
Fig. 6.5 Example 2. Based on Barksdale, R.D., Bachus, R.C., 1983a. Design and Construction of Stone Columns, Volume I, Appendixes, Report No. FHWA/RD-83/026, Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC; Barksdale, R.D., Bachus, R.C., 1983b. Design and Construction of Stone Columns, Volume II, Report No. FHWA/RD-83/027, Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC.
0 st ¼
cc B H log 10 @ 1 + e0
σ0 +
1 σ 1 + ð n 1Þ ac C A σ0
0 st ¼
B 0:7 6 log 10 B @ 1 + 2:0
St ¼ 0:810 m ¼ 81 cm:
15:57 +
1 83:16 1 + ð5 1Þ 0:227C C A 15:57
Stone column method
6.5
59
Field inspection and execution
During the installation of stone columns it is very important to have control of the diameter of the columns, spacing between two columns, lift thickness of each stone column, quantity of fill aggregates fed into the column, etc. A real-time computerized monitoring system can be employed for this purpose. Generally, a difference occurs between the theoretical volume of the filled materials calculated and the actual volume used in the site. This is mainly due to the lateral movement of the materials penetrating into the surrounding soils and the extent of compaction given to the materials. Hence, generally a reduction factor is used, which is about 1.3 to 1.5 for the top-feed method and 1.2 for bottom-feed method. At the start of any stone-column project, trial tests are necessary to validate the material quality and to verify the expected ground response with installation of the stone columns. In addition, the following points need to be taken care of: l
l
l
l
l
The granular material fed into the column must be clean and free from any fine content or foreign materials. The materials should be of good quality and durable. The sensitivity of the soil must be checked to ensure that it is <3. A higher sensitivity of soil causes problems in regaining shear strength. Moreover, the lateral earth pressure exerted by the surrounding soils is a determining factor in the construction of stone columns. Hence, stone columns are not effective in peats, waste dumps and organic soils, or in soils with a loss of ignition value >5%. To facilitate the drainage of in situ pore water and to avoid the ill effects of water accumulation at the top of the stone columns, a blanket drainage layer of sand or cohesionless soil should be provided. The circulation of bentonite must be avoided to protect the stability of the columns, because it blocks the flow of soil pore water into the stone column and hence its drainage. Instead, casing may be used. In cohesive soils, preloading is essential in combination with the stone column. This is to take accommodate residual settlements that may be greater than permissible limits.
References Barksdale, R.D., Bachus, R.C., 1983a. Design and Construction of Stone Columns, Volume I, Appendixes. Report No. FHWA/RD-83/026. Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC. Barksdale, R.D., Bachus, R.C., 1983b. Design and Construction of Stone Columns, Volume II. Report No. FHWA/RD-83/027. Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC. Hughes, J.M.O., Withers, N.J., 1974. Reinforcing of soft cohesive soils with stone columns. Ground Eng. 7 (3), 42–49. Priebe, H.J., 1995. The design of vibro replacement. J. Ground Eng. 28 (12), 31–37.
60
Geotechnical Investigations and Improvement of Ground Conditions
Further reading Chummar, A.V., 2000. Ground improvement using stone column: problems encountered. In: ISRM International Symposium, 19–24 November 2000, Melbourne, Australia. IS 15284 Part I, 2003. Design and Construction for Ground Improvement-Guidelines, Part I Stone Columns. . McCabe, B.A., McNeill, J.A., Black, J.A., 2007. Ground improvement using the vibro-stone column technique. In: Joint Meeting of Engineers, Ireland West Region and the Geotechnical Society of Ireland, NUI Galway, 15 March 2007. Taube, M.G., Herridge, J.R., 2002. Stone columns for industrial fills. In: Presented at the 33rd Ohio River Valley Soil Seminar (ORVSS), October 18, 2002.
6
Introduction
Stone column method for ground improvement is a vibro-replacement technique, where the weak soil is displaced using a cylindrical vibrating probe (i.e. vibroflot), thus creating a column that is then filled and compacted with good-quality stone aggregates. With the inclusion of stone aggregates to the in situ soil, its stiffness and load-carrying capacity increases. It also helps to reduce the static as well as differential settlement of the soils. Bulging action of the stone columns imparts lateral confinement to the surrounding soils and it also acts as a drainage path accelerating the consolidation of cohesive soils. These stone columns are generally used for soils that are much more compressible but not weak enough to necessitate a pile foundation. Moreover, for the construction of low-to-medium rise buildings on soft soils, pile foundation sometimes becomes expensive. In such cases, stone columns are preferred. Stone columns are very useful for the improvement of cohesive soils, marine/alluvial clays, and liquefiable soils. Stone columns have been used successfully for a wide range of applications from the construction of high-rise buildings to oil tank foundation, and for embankment and slope stabilization.
6.2
Mechanism
As mentioned earlier, the basic mechanisms behind ground improvement using stone columns are (1) soil compaction through the bulging action of the stone columns, (2) soil reinforcement with the inclusion of stone aggregates into the soil mass, and (3) accelerated consolidation of the cohesive soils. The differences between the load carrying mechanism of a pile and that of a stone column are presented in Fig. 6.1. The structural load is mainly carried by the piles only and there is no transfer of stress to the surrounding soil in the case of pile foundations. However, in the case of stone columns, a part of the structural load is carried by the surrounding soil. This is demonstrated in the stress distribution diagram in Fig. 6.1. A single stone column primarily fails by bulging, whereas a group of stone columns may fail by bulging or by shear failure of the soil/columns mass.
6.3
Stone column installation methods
For the installation of stone columns a vibrating poker device is used that can penetrate to the required treatment depth under the action of its own weight, vibrations, and actuated air, assisted by the pull-down winch facility of the rig. This process displaces the soil particles and the voids created are compensated with backfilling of stone aggregates. The vibroflot penetrates the filled stone aggregates to compact it and thus Geotechnical Investigations and Improvement of Ground Conditions. https://doi.org/10.1016/B978-0-12-817048-9.00006-8 © 2019 Elsevier Inc. All rights reserved.
Stress distribution
s
Geotechnical Investigations and Improvement of Ground Conditions
s
50
Structural loading
Shaft resistance
Compaction due to bulging of stone column
GL
(A)
End bearing resistance
(B)
Fig. 6.1 Load carrying mechanism of (A) piles and (B) stone columns.
forces it radially into the surrounding soils. This process is repeated till the full depth of the stone column is completed. The lift height is generally taken as 0.6–1.2 m for the filling and compaction of the stone aggregates. Depending upon the feeding of stone aggregates into the columns there are basically two methods for the installation of stone columns: the top-feed method and the bottom-feed method, as shown in Fig. 6.2. In the top-feed method, the stone aggregates are fed into the top of the hole. The probe is inserted into the ground and is penetrated to the target depth under its own weight and compressed air jetting. However, jetting of water is also done especially when the soil is unstable. This also helps to increase the diameter of the stone columns and to washout the fine materials from the holes. The top-feed method is suitable when water is readily available and there is enough working space to allow for water drainage. Moreover, the soil types should be such that it would not create messy surface conditions due to mud in water. The topfeed method is preferable when a deeper groundwater level is encountered. The bottom-feed method involves the feeding of stone aggregates via a tremie pipe along the vibroflot and with the aid of pressurized air. The bottom-feed method is preferable when the soil is highly collapsible and unstable. However, the stability of holes will also depend upon the depth, boundary conditions, and the groundwater conditions. In areas, where the availability of water and space and the handling of mud in process water are limiting factors, the bottom-feed method can be implemented. Due to limited space in the feeding system, a smaller size of aggregates is used in the bottom-feed method compared with that used in the top-feed method. On the other hand, the flow of stones to the column is mechanically controlled and automatically recorded in the bottom-feed method.
Stone column method
51
Fig. 6.2 Stone columns installation methods: (A) top feed method and (B) bottom feed method.
6.4
Stone column design parameters
The important parameter information required for the design of stone columns are the diameter and depth of the stone columns, spacing between the stone columns, layout of the stone columns, replacement ratio, stress concentration factor, improvement ratio, etc. The stone columns are very effective up to a depth of 4–10 m. For a depth of >10 m some of the construction problems that might be encountered include the stabilization of the borehole and stone contamination until the bottom of a borehole is reached. The diameter of the stone column depends upon the drilling method adopted, the improvement factor required, and the installation technique used. Generally, the diameter of the stone column is between 0.8 and 1.2 m. The diameter of the wet-feed stone columns is 20%–40% more than the corresponding dry-feed columns. A spacing of about 1.8–2.7 m is adopted depending upon the diameter of the stone columns and the areareplacement ratio. Based upon the concept of improvement factor, the following steps are followed for the design of stone columns. l
l
The settlement of untreated ground is calculated with conventional calculation methods. The ‘settlement ratio’ or ‘improvement factor’, which refers to the ratio of the settlement of untreated ground to that of the treated ground, is evaluated. Also, the improvement factor
52
l
l
l
Geotechnical Investigations and Improvement of Ground Conditions
may refer to the increase in compression modulus of the treated ground. The improvement factor is derived as a function of the area-replacement ratio, angle of internal friction of the column material, and the Poisson’s ratio of the surrounding soils. Charts have been developed by Priebe (1995) correlating these three parameters to the improvement factor. For calculation of the improvement factor, it is assumed that (1) the column is based on a rigid layer (end-bearing), (2) the column material is incompressible, and (3) the bulk density of the column and soil is neglected. Priebe has further considered the effect of the compressibility of the column material and the overburden for calculation of the improvement factor. A detail of the Priebe method is presented later in this section. The reduction of settlement that is required to meet the design requirements is calculated. Based on the contractor’s experience and empirical data it is determined if the stone columns can provide the required reduction of settlement. Typically, the settlement ratios are taken between 2 and 3. The area-replacement ratio necessary to provide the required reduction of settlement is determined. The concept of area-replacement ratio based on the unit cell approach is presented later in this section. For uniformity of settlement between the column and surrounding soil, and the stability of the stone columns, the stress concentration on soil and column is calculated and verified with the ultimate load capacity. The depth of stone column, its diameter and spacing are then determined based upon the area replacement ratio, experience and installation method used by the contractor.
6.4.1 Area replacement ratio The area-replacement ratio, ac is defined as Ac/A, where Ac is the cross-sectional area of one column and A is the total cross-sectional area of the ‘unit cell’ attributed to each column (as shown in Fig. 6.3). Ac/A is related to the column diameter (D) and column spacing (S) as follows: Ac =A ¼ k ðD=SÞ2
(6.1) Area of single stone column, Ac
S S
Triangular grid
CSA of foundation per stone column (unit cell), A
Fig. 6.3 Unit cell in triangular and square grid of stone columns.
Square grid
Stone column method
53
where k is π/4 and π/(2 √ 3) for square and equilateral triangular column grids, respectively. The equivalent diameter of a cylinder enclosing the unit cell may be taken as 1.05S for an equilateral triangular pattern and 1.13S for a square pattern. The ratio of the area of remaining soil in a unit cell (as), i.e. As/A can be calculated as follows: As =A ¼ 1 ac
(6.2)
where As is the cross-sectional area of soil surrounding the column in a unit cell.
6.4.2 Stress concentration Upon placement of a structural load over stone column-treated ground, the concentration of stress over the column and is accompanied by a stress reduction in the surrounding cohesive soil/loose cohesion-less soil, which has a lower load carrying capacity. This distribution of vertical stress within a unit cell can be determined by using a stress concentration factor, n as follows: n ¼ σ c =σ s
(6.3)
where σ c and σ s are the stress in the column and the surrounding soil, respectively. For equilibrium between the vertical loading and the load taken by the unit cell, the following condition must be satisfied: σ ¼ σ c ac + σ s ð1 ac Þ
(6.4)
Eqs (6.3), (6.4) can be rearranged to achieve the stress levels in the column and the surrounding soil as follows: σc ¼
nσ 1 + ðn 1Þac
(6.5a)
σs ¼
σ 1 + ðn 1Þac
6.5b
The value of n is generally assumed to be between 2 and 5.
6.4.3 Improvement factor The basic improvement factor n0 is determined as follows (Priebe, 1995): 2
3 1 + f μ ð , A =A Þ c s Ac 6 7 15 n0 ¼ 1 + 4 2 A Kac f ðμs , Ac =AÞ
(6.6)
54
Geotechnical Investigations and Improvement of Ground Conditions
f ðμs , Ac =AÞ ¼
ð1 μs Þð1 Ac =AÞ 1 2μs + Ac =A
Kac ¼ tan 2 45° ϕc =2
(6.7a) (6.7b)
where Kac is the coefficient of earth pressure and μs is the Poisson’s ratio of the surround soil. By considering the column compressibility, the improvement factor n1 is obtained as follows: 2
3 1 + f μs , Ac =A 6 17 n1 ¼ 1 + Ac =A 4 2 5 Kac f μs , Ac =A Ac =A ¼ Δ
1 A=Ac + ΔðA=Ac Þ
(6.8)
(6.9a)
A 1 1 ¼ Ac ðAc =AÞ1
(6.9b)
4 Kac ð n0 2Þ + 5 1 ðAc =AÞ1 ¼ 2 ð4 Kac 1Þ 2 ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4 Kac ð n0 2Þ + 5 2 16 Kac ð n0 1Þ + 4 Kac 1 4 Kac 1
(6.9c)
Further by considering the overburden, the improvement factor n2 is obtained as follows: n2 ¼ f d n1 fd ¼
(6.10a)
1 K0c Ws =Wc Wc 1+ K0c Pc
(6.10b)
P
Pc ¼ Ac =A +
(6.10c)
1 Ac =A Pc =Ps
1=2 + f μs , Ac =A Pc =Ps ¼ Kac f μs ,Ac =A Wc ¼
X
ðγ c ΔdÞ and Ws ¼
(6.10d) X ðγ s Δd Þ
(6.10e)
Stone column method
K0c ¼ 1 sin ϕc
55
(6.10f)
where P is the foundation load, Ws and Wc are the weights of the soil and column, respectively, and K0c is the earth pressure at rest.
6.4.4 Load carrying capacity The vertical stress on a single column can be calculated as follows: σ 1 1 + sin ϕc ¼ σ 3 1 sin ϕc
(6.11)
where σ 1 and σ 3 are the vertical and lateral stress respectively. Based upon the tests conducted, Hughes and Withers (1974) have proposed the following equations: qa ¼
1 + sin ϕc 0 σ r0 + 4c 1 sin ϕc
(6.12) 0
where qa is the allowable bearing capacity of the stone column, c is cohesion, and σ r0 is the average effective radial stress over a depth of four times the diameter of column. The drained cohesion value may be considered for small column spacings, whereas the undrained value is considered if the column spacing is more (about >2 m). A factor of safety varying from 1.5 to 3 is generally applied to the value of qa obtained from Eq. (6.12). Also, qa ¼ Cs As + Ac cp Nc =FS
(6.13)
where cp is cohesion at the column base; As is the average stone column perimeter area; and Nc is taken as 9 for clay, if the length/column ratio is 3 and is taken between 5.4 and 9 and if the ratio is less. Further, as per Barksdale and Bachus (1983a,b), the bearing capacity of an isolated stone column or a stone column located within a group can be expressed in terms of an ultimate stress applied over the stone column: qult ¼ cNc
(6.14)
Nc is generally taken to be between 18 and 22. For soils having a reasonably high initial stiffness (e.g. inorganic soft to stiff clays and silts), an Nc of 22 is recommended. On the other hand, for soils with low stiffness (e.g. peats, organic cohesive soils and very soft clays with plasticity index >30), an Nc of 18 is recommended.
56
Geotechnical Investigations and Improvement of Ground Conditions
Example 1. Bearing Capacity Determine what height of fill the stone column-improved ground can safely support. Both a general shear failure and a local bulging failure in a deep, very soft clay layer (Fig. 6.4) must be considered. Assume the stone column has an angle of internal friction ϕc of 42°, and an equilateral triangular pattern of columns is used having a spacing, s, of 2 m. Solution ac ¼ π= 2√3 ðD=SÞ2 ¼ 0:907 0:25 ¼ 0:227 Ac ¼ 3:14 ð1=4Þ ¼ 0:785 m2 A ¼ ðAc =ac Þ ¼ 0:785=0:227 ¼ 3:458 m2 Assuming that a bulging failure occurs in the upper three stone column diameters of depth, the ultimate capacity of a stone column can be calculated as: qult ¼ cNc ¼ 22 22 ¼ 484 kPa
H
sc
ss
Clay (°sat = 15.7 kN/m3 PI = 25, c = 22 kPa)
1m
2.5 m
6m
GL
Fill (°wet = 19.6 kN/m3
1.5 m
Clay (°sat = 15.7 kN/m3 PI = 40, c = 10 kPa) Clay (c = 22 kPa)
Firm bearing strata 2m
Fig. 6.4 Example 1. Based on Barksdale, R.D., Bachus, R.C., 1983a. Design and Construction of Stone Columns, Volume I, Appendixes, Report No. FHWA/RD-83/026, Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC; Barksdale, R.D., Bachus, R.C., 1983b. Design and Construction of Stone Columns, Volume II, Report No. FHWA/RD-83/027, Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC.
Stone column method
57
Hence, Pult ¼ qult Ac ¼ 484 0:785 ¼ 380 kN Checking for the possibility of bulging failure in very soft clay located at a depth of 6 m, the ultimate stress the stone column can carry can be calculated as follows: 1 + sin ϕc 1 + sin ϕc ¼ 9c ¼ 90 5:04 1 sin ϕc 1 sin ϕc ¼ 454kPað< 484 kPa, hence it governsÞ:
qult ¼ σ 3
The maximum stress the clay surrounding the stone column can take is σ s ¼ 5c ¼110 kPa. Now assuming a value of 3 for the stress concentration factor, n: σc ¼
nσ σ ¼ 2:06σ and σ s ¼ ¼ 0:688σ 1 + ðn 1Þac 1 + ðn 1Þac
σ c Then σ s ¼ 0:688 2:06 ¼ ð0:688 454Þ=2:06 ¼ 152 kPa. Since 152 kPa is >110 kPa, σ s ¼5c ¼ 110 kPa is the ultimate stress the clay can carry. The ultimate load that can be applied to the unit cell area in the fill is now calculated as: Pult ¼ σ c Ac + σ s As ¼ ½454 0:785 + ½110 ð3:458 0:785Þ ¼ 356 + 294 ¼ 650 kN Using a factor of safety of 2.0, the allowable load, Pall is 325 kN per unit cell. Hence, the safe height of the fill is Pall/(unit weight of the fill area of unit cell) ¼ 325/ (19.6 3.458) ¼4.8 m. Example 2. Settlement Estimate the primary consolidation settlement of the stone column-improved silty clay layer, as shown in Fig. 6.5. Assume the water table to be at ground level and the stone columns are in an equilateral triangular grid. Solution The stress exerted by the embankment along with the sand blanket on top of the stone columns σ is (3.7 18.8) + (0.8 17) ¼83.16 kPa. Area-replacement ratio ac ¼ π/(2 √ 3) (D/S)2 ¼ 0.907 0.25 ¼ 0.227. The initial effective stress σ 0 at the centre of the silty clay layer is σ 0 ¼ 3 ð15 9:81Þ ¼ 15:57 kPa: Using the one-dimensional consolidation theory, the primary settlement, st, can be calculated as follows: cc σ 0 + Δσ st ¼ H log 10 1 + e0 σ0
58
Geotechnical Investigations and Improvement of Ground Conditions
0.8 m
4.5 m
Embankment (°wet = 18.8 kN/m3)
Sand blanket (°wet = 17.0 kN/m3)
GL
Soft silty clay eo = 2.0 6m
Cc = 0.7 °sat = 15 kN/m3 c = 19 kPa
1m
Firm to dense sand 2m
Fig. 6.5 Example 2. Based on Barksdale, R.D., Bachus, R.C., 1983a. Design and Construction of Stone Columns, Volume I, Appendixes, Report No. FHWA/RD-83/026, Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC; Barksdale, R.D., Bachus, R.C., 1983b. Design and Construction of Stone Columns, Volume II, Report No. FHWA/RD-83/027, Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC.
0 st ¼
cc B H log 10 @ 1 + e0
σ0 +
1 σ 1 + ð n 1Þ ac C A σ0
0 st ¼
B 0:7 6 log 10 B @ 1 + 2:0
St ¼ 0:810 m ¼ 81 cm:
15:57 +
1 83:16 1 + ð5 1Þ 0:227C C A 15:57
Stone column method
6.5
59
Field inspection and execution
During the installation of stone columns it is very important to have control of the diameter of the columns, spacing between two columns, lift thickness of each stone column, quantity of fill aggregates fed into the column, etc. A real-time computerized monitoring system can be employed for this purpose. Generally, a difference occurs between the theoretical volume of the filled materials calculated and the actual volume used in the site. This is mainly due to the lateral movement of the materials penetrating into the surrounding soils and the extent of compaction given to the materials. Hence, generally a reduction factor is used, which is about 1.3 to 1.5 for the top-feed method and 1.2 for bottom-feed method. At the start of any stone-column project, trial tests are necessary to validate the material quality and to verify the expected ground response with installation of the stone columns. In addition, the following points need to be taken care of: l
l
l
l
l
The granular material fed into the column must be clean and free from any fine content or foreign materials. The materials should be of good quality and durable. The sensitivity of the soil must be checked to ensure that it is <3. A higher sensitivity of soil causes problems in regaining shear strength. Moreover, the lateral earth pressure exerted by the surrounding soils is a determining factor in the construction of stone columns. Hence, stone columns are not effective in peats, waste dumps and organic soils, or in soils with a loss of ignition value >5%. To facilitate the drainage of in situ pore water and to avoid the ill effects of water accumulation at the top of the stone columns, a blanket drainage layer of sand or cohesionless soil should be provided. The circulation of bentonite must be avoided to protect the stability of the columns, because it blocks the flow of soil pore water into the stone column and hence its drainage. Instead, casing may be used. In cohesive soils, preloading is essential in combination with the stone column. This is to take accommodate residual settlements that may be greater than permissible limits.
References Barksdale, R.D., Bachus, R.C., 1983a. Design and Construction of Stone Columns, Volume I, Appendixes. Report No. FHWA/RD-83/026. Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC. Barksdale, R.D., Bachus, R.C., 1983b. Design and Construction of Stone Columns, Volume II. Report No. FHWA/RD-83/027. Federal Highway Administration Office of Engineering and Highway Operations Research and Development, Washington, DC. Hughes, J.M.O., Withers, N.J., 1974. Reinforcing of soft cohesive soils with stone columns. Ground Eng. 7 (3), 42–49. Priebe, H.J., 1995. The design of vibro replacement. J. Ground Eng. 28 (12), 31–37.
60
Geotechnical Investigations and Improvement of Ground Conditions
Further reading Chummar, A.V., 2000. Ground improvement using stone column: problems encountered. In: ISRM International Symposium, 19–24 November 2000, Melbourne, Australia. IS 15284 Part I, 2003. Design and Construction for Ground Improvement-Guidelines, Part I Stone Columns. . McCabe, B.A., McNeill, J.A., Black, J.A., 2007. Ground improvement using the vibro-stone column technique. In: Joint Meeting of Engineers, Ireland West Region and the Geotechnical Society of Ireland, NUI Galway, 15 March 2007. Taube, M.G., Herridge, J.R., 2002. Stone columns for industrial fills. In: Presented at the 33rd Ohio River Valley Soil Seminar (ORVSS), October 18, 2002.