B.7 Aspects of design

B.7.1 Stability

B.7.1.1 Weighted shear strength

Often the purpose of the treated columns is to stabilise slopes, embankments or trench walls. In this case, the columns should preferably be installed in a number of walls on both sides, perpendicular to the slope, the embankment or the trench (see Annex A). The stability is analysed on the basis of the weighted mean strength properties of the untreated soil and those of the columns. Failure is normally assumed to take place along a plane, or curved, failure surface in which the shear strength of the columns and the shear strength of the surrounding soil are both mobilised.

B.7.1.2 Influence of column location along the potential failure surface

In the case of single columns being used for stability purpose the risk of bending failure of the columns need to be considered. The columns will behave differently if situated in the active zone, or in the more or less pure shear zone, or in the passive zone of the potential failure surface (see Figure B.5). In the active zone the axial load on the column contributes to increasing the shearing or bending resistance while in the passive zone the columns may even rupture in tension. Therefore, columns in the active zone benefit most to improving the stability condition. In the shear and passive zones columns arranged as buttress walls or as a block are more effective in preventing shear failure than single columns.

The axial column load in the active zone increases their bending and shearing resistance - In the passive zone the columns may even rupture in tension


  • 1 Passive
  • 2 Shear
  • 3 Active
Figure B.5 — The axial column load in the active zone increases their bending and shearing resistance - In the passive zone the columns may even rupture in tension

B.7.1.3 Overlap of columns

Columns installed for the purpose of improving stability are commonly placed in single or double rows along, and perpendicular to, a slope, an excavation or an embankment. This increases the efficiency in comparison with single columns in that the negative effect of local column weakness is reduced as well as the risk of bending failure of the columns.

The moment resistance of the individual column rows should be sufficiently high not to be the cause of failure. Overlapping of the columns in the individual rows to create a column wall increases the moment resistance and overturning can be avoided by increasing the length of the rows and thus the number of columns in the rows. It is important that the shear strength of the treated soil in the overlapping zone is high enough and that the overlap of the columns is sufficient. It is important that the verticality of overlapping columns is maintained over the whole length. The shear strength of the stabilised soil in the overlapping zone usually governs the lateral resistance of the column rows.

B.7.1.4 Column separation

Failure may occur in the shear zone due to separation of columns in the row when the slip surface is located close to the top of the columns and the tensile resistance is low within the overlapping zone. Such a separation reduces the shear resistance of the column wall. It is expected that the tensile resistance of the treated soil in the overlapping zone is about 5 % to 15 % of the unconfined compressive strength (it can be lower or higher depending upon the quality and efficiency of deep mixing).

B.7.1.5 Dowel action of column rows

The dowel resistance of the columns will be decisive when the failure surface is located close to the bottom of a row. When the columns have separated from the adjacent columns the shear resistance per column in the row will be the same as the shear resistance of single columns.

B.7.1.6 Overturning of a row of end-bearing columns

The axial load on columns situated at the end of a row with end-bearing columns can be very high when the column row is subjected to a rotational movement. The maximum axial load thus obtained should be less than the load corresponding to the unconfined compression strength of the column.

B.7.1.7 Structural wall applications

Structural walls with reinforcement beams are commonly designed using the principle of arching.

B.7.1.8 Block type applications

As the properties of in-situ treated soil are quite different from those of untreated surrounding soil, it is assumed that the treated soil is a rigid structural member buried in the ground to transfer the external loads to a reliable stratum (Kitazume et al., 1996), see Figure B.6. For the sake of simplicity, the design concept is analogous to the design procedure for gravity type structures, such as concrete retaining structures.

The first step in the procedure includes stability analysis of the superstructure to ensure that the superstructure and the treated soil behave as a unit.

The second step includes stability analysis of the treated soil due to external action in which sliding failure, overturning failure and bearing capacity are evaluated.

The third step includes internal stability analysis in which the stresses induced in the treated soil by the external forces are analysed and confirmed to be less than the allowable values. Finally, the displacement of the treated soil is analysed.

In seismic design of the superstructure, the seismic intensity analysis is applied in Japan; the dynamic cyclic loads are converted to static load by multiplying the unit weight of the structure by the seismic coefficient.

In the case of more complex treatment patterns, relying on the interaction between the treated soil and the untreated soil between columns it is desirable to apply more sophisticated 2-D or 3-D elasto-plastic FEM analyses to examine stresses developed in the improved ground and displacement of the improved ground. Of course, the quality of the results is strongly influenced by the correct selection of input parameters.

B.7.2 Settlement

B.7.2.1 Total settlement

The design related to the deformation of mixed-in-place columns or elements or structures used for foundations or retaining walls shall be in accordance with EN 1997-1.

The treated columns, installed in order to reduce settlement of embankments, are mostly placed in some regular triangular or square pattern. Settlement analysis is generally based on the assumptions of equal strain conditions — in other words, arching is presumed to redistribute the load so that the vertical strains at a certain depth become equal in columns and surrounding soil.

For a group of columns the average settlement will be reduced by counteracting shear stresses in the untreated soil, mobilised along the perimeter of the group. Only a small relative displacement (a few mm) is required to mobilise the shear strength of the soil. The counteracting shear stresses will cause angular distortion in the improved soil along the perimeter of the group and, consequently, induce differential settlement inside the group. The counteraction — hence the differential settlement — will be reduced with time by induced consolidation settlement in the surrounding soil. It is therefore usually ignored in the settlement analysis.

Flow of Japanese design procedure for block type stabilisation
Figure B.6 — Flow of Japanese design procedure for block type stabilisation [9]

B.7.2.2 Rate of settlement

In dry mixing where the permeability of the columns may be higher than the permeability of the surrounding soil, the columns may accelerate the consolidation process in a way similar to vertical drains. However, the rate of settlement is not governed by the drainage effect alone. When stiff treated soil and untreated soft cohesive soil co-exist, the dominant phenomenon is the stress redistribution in the system with time. At the instant of loading, the applied load is carried by excess pore water pressure. Owing to gradually increasing stiffness of the columns, a gradual transition of load from the soil to the columns causes a time-bound reduction of the load carried by the soil. In consequence, the excess pore water pressure in the soft soil diminishes rapidly, even without the radial water flow. This stress redistribution is one of the major reasons for the settlement reduction and increased rate of settlement. Therefore, even if the permeability of the columns is of the same order of magnitude as the surrounding soil, the consolidation process is accelerated by the presence of the columns. Thus, the load share between soil and columns increases the average coefficient of one-dimensional consolidation. The column permeability decreases with time and with increasing confining pressure.

In wet mixing the hydraulic conductivity of the treated columns is generally of the same order of magnitude as, or lower than, the hydraulic conductivity of the surrounding untreated soil. Therefore, the consolidation process is governed by vertical one-dimensional water flow only. However, by the stress re-distribution, the rate of settlement is much higher than that calculated by one-dimensional consolidation.

B.7.3 Confinement

A confinement wall is formed by overlapping columns so that no leakage through the wall can take place. It is extremely important that the homogeneity of the columns is guaranteed and that leakage through the column wall is prevented. The thickness of the wall at the overlap and the permeability of overlap joints, have to be given sufficient tolerance in the design. Bentonite is commonly incorporated in wet mixing, in order to reduce the permeability of the treated soil.

If the objective of deep mixing is to create confinement of waste deposits or polluted soils, the durability of the treated soil becomes one of the most important design aspects. The reaction between the treated soil and the contaminant should be studied, especially when the waste has high acidity.

EN 14679:2005 Execution of special geotechnical works — Deep mixing