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Design of Vibro ReplacementBy Heinz J Priebe, GEOStat

The application of Priebes method to ex-

tremely soft soils, floating foundations and

proof against slope or embankment failure

Introduction

Vibro Replacement is an accepted method for subsoil improvement, whereby large columnsof coarse backfill material are installed in the ground using special vibrators [1]. The bearing

behaviour of this composite system, consisting of stone columns and soil, cannot be reliably

determined by simple investigation methods. Theoretically, however, the efficiency of vibro

replacement can be reliably evaluated. Probably, the most commonly applied method is that

developed by Priebe [2] and [3].

However, questions concerning the application of this method to extremely soft soils, float-

ingcolumns and for the proof of safety against slope or embankment failure were not dis-

cussed in previous publications.

1 Extremely Soft Soils1.1 Preliminary remarks

In Germany, the first guidelines for the application of deep vibratory compaction techniques

in general and for the vibro replacement technique in particular were published in 1976 by

the German institution Forschungsgesellschaft fr das Straenwesen [4]. Within this, the

application of vibro replacement was restricted to soils with an undrained shear strength, c u,

of at least 15 kN/m2to 25 kN/m2.

1.2 Comment

Vibro replacement suffers from this very conservative value. Although the technique had

already grown out of its infancy by the time the guidelines were published, there were still

some uncertainties over both design and performance. Taking this into account, some cau-

tion was still justified.

However since then design methods and, to a greater extent, equipment have been im-

proved to allow stone columns to be installed safely and to perform reliably, even in very

soft soils. In such cases soil improvement is achieved by drainage rather than by reinforce-

ment.

In fact, even soils with an undrained shear strength as low as cu= 5 kN/m (ie soils which in

their natural state can scarcely allow a person to walk on them) can be treated and im-

proved by vibro replacement. This is not just based on sporadic experiences in Germany,

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Design of Vibro Replacement

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where extremely soft soils do not play an important role in structural engineering, but

moreover on extensive application on highway projects in South East Asia [5].

It goes without saying that the treatment of extremely soft soils requires utmost care and

the suitability of the method to a project has to be carefully examined. But it is not justified

to cling to formerly defined values based on different circumstances.

Finally, the design method described here may be particularly suitable for extremely softsoils as it hardly allows a serious misjudgement. This is because it does not deliver absolute

improvement values but only a relative improvement value which always refers to the origi-

nal state of the soil.

2 Floating Columns2.1 Preliminary Remarks

The starting point of Priebes design method is the examination of a unit cell as part of an

unlimited load area on an unlimited column grid. The evaluation, simplified by the following

three restrictingconditions, gives the basic improvement value, n0.

The column material is incompressible The bulk density of column and soil is ignored

The column is founded on a rigid layer

The second step of the method considers the compressibility of the column material,

ie the first restricting condion is abandoned. The result is the reduced improvement value,

n1.

The third step refers to the influence of the bulk densities of column and soil which is con-

sidered by the depth factor, fd. The product of fdand n1gives the final improvement value n2

which - at least - is recommended for settlement calculations.

With regard to the last restricting condition, this was not considered in [2] because this

condition is met in most practical cases. However, it is not met when using floating col-umns. Here additional evaluations are required. The following formulae, their context and

application are subject to the same terms as in [2].

2.2 General Aspects

Vibro replacement rightly stands for ground improvement. Although the installed stone col-

umns of coarse backfill material present stiffer structural members, they still depend on the

support of the surrounding soil. This interaction is the reason that, for example in the case

of vibro replacement for the foundation of a road embankment, there is hardly ever any

danger of column punching. Some waviness at foundation level will certainly occur but will

if at all hardly be noticeable at the embankment surface.A similar situation occurs for stone columns ending above a soft layer which is not suitable

to bear concentrated loads. At the boundary between the columns and the underlying soil

there is a balancing of stress and strain.This balancing takes place more or less in both zones,

ie in the upper treated soil as well as in the soil below.

To approach the floating case of columns in poor soil the obvious thing to do would be to

assume that the balancing takes place solely either in the upper treated zone or in the un-

treated zone below.

2.3 Balance of stress in the upper treated zone

In this case it is assumed that the treated depth can be divided into a zone with full effictive-ness of the columns and a transitional zone. Above the transitional zone the stress within

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Heinz J. Priebe, GEOStat, Bad Bodenteich

3

the unit cell is distributed in the way derived from normal calculations, ie with the propor-

tional load on the columns, m (In [2] m was reduced in comparison to m). At the bottom

of the transitional zone, ie at the end of the column, there exists, according to the assump-

tion, a uniform stress p, if disregarding the unit weight of column and soil. That means that a

difference, P, has to be transferred from the column to the soil.

P = p A (m - AC/A) = p A [(n 1)/n AC/A]

Figure 1: Vertical stress distribution with stress equalisation in the upper treated layer.

The differential load, P, has to be transferred from the column to the soil by shear resis-

tances R. These consist of cohesion, cS, and Friction, F, in the soil.

R = diaC (cS+ F) diaC= column diameter

The friction results from the lateral support of the soil and its friction angle, S. It is far too

conservative to ascertain lateral support from the proportional external load on the soil

between the columns, pS, only. On the other hand, it is questionable whether at the prede-

termined value of K = 1 additionally the total weight of the soil should be considered.

However, the height of the transitional zone amounts to h = P/R and, on the condition of a

linearly decreasing improvement, the settlement of this zone has to be calculated with a re-

duced average improvement factor of n = (1+n)/2.

p p

uniformly distributed load p

transitionzone

pC

pS

improvedlayer

Underlying layer

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2.4 Balance of stress in the untreated underlying zone

In this case it is assumed that the load on the column is transferred down to the entire

depth of the treated layer.

Thus, logically, the column is pressing the underlying soil with its increased load and causes a

depression. Only in the widest sense this effect may be described as punching.As already indicated, failure-like processes similar to those experienced with sinking piles are

not possible with vibro replacement because of the transfer of load to the surrounding soil.

Therefore, the depression caused by a single column in the underlying soil can be compared

with the settlement of a circular footing and calculated accordingly.

It is sufficient to calculate this settlement with the total proportional load of the column and

not with the difference in pressure between the column and the soil, but then to only use

the depth where the pressure has decreased by load distribution to the value of p.

Figure 2:Vertical stress distribution with stress equalisation in the substratum.

p p

uniformly distributed load p

pC pS

im

provedlayer

depth ofinfluence

calculated

press. area

underlyi

nglayer

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2.5 Assessment of the approaches

Settlement calculations are generally performed using the deformation moduli or compres-

sion index and initial void ratio only. Consequently, the first approach is disadvantageous, for

the simple reason that more or less vague values with regard to shear resistance also have

to be considered.As already mentioned, the balance in stress and strain takes place in zones both above and

below the bottom of the stone columns. If either of the approaches is used, the obtained

settlements will always turn out to be too high which is even in the sense of being inten-

tionally on the safe side not always acceptable.

In the first case of the assumed balancing solely in the upper, improved zone the inaccuracy

increases with the growing stiffness of the underlying stratum. In the second case, assuming

balancing solely in the lower, untreated zone, inaccuracy increases with growing initial stiff-

ness of the upper treated soil.

In the second case, however, the limitation of inaccuracy is relatively simple: the punching

has to be limited to the very value which the upper treated strata without improvement

will allow.This is because the punching into the lower soil is coupled with an equal verticalcompression of upper soil.

sP= sP s0/ (sP+ s0)

sP = calculated punching value

s0 = settlement of the treated layers without improvement

sP= reduced punching value

Consequently, it is simpler and more accurate to use to the second approach, applying the

reduction procedure. The author has calculated settlement this way using the GRETA pro-

gram software developed by the author not only for vibro replacement but extended to

nearly all kinds of vertical foundation members.

Thus the entire settlement of vibro replacement projects consists of three parts:

Settlement of the treated soil

Additional settlement by punching into the layer directly below the treated soil

Settlement of all layers below the treatment depth

s = su+ sP+ sl

su=calculated settlement of upper treated soil (e g Priebes method)

sl =calculated settlement of lower layers

3 Embankment or Slope Failure3.1 Preliminary Remarks

Excessive building settlement may cause substantial structural damage. Fortunately, such

damage can often be avoided as there is advance warning of problems in most cases.

The situation is completely different with regard to stability failure. Generally, there is no

warning and thus no chance for damage limitation. Here, calculations have to be on the safe

side. Therefore, for economic reasons the calculation should be as reliable as possible.

Unfortunately, in cases of ground improvement by vibro replacement, frequently the proof

of sufficient safety is unknowingly based on overestimating the improvement achieved by thetreatment. This problem was not dealt with in [2].

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3.2 Explanation

According to Priebes design method, the shear values of improved ground are not averaged

proportionally to the cross-section of the stone columns and the soil in between but pro-

portionally to their loads. That means the high friction value of the stone columns does not

only contribute according to their cross-section but also according to their load. However,this is valid for external loads on the columns only after installation.

If now, for example to prove the safety against failure of an embankment slope, the shear

values averaged this way are thoughtlessly assigned to the sliding surface in treated ground,

this results in an inaccuracy on the unsafe side. This may be substancial, particularly where

there are deep sliding surfaces.

The fact is, because the approach would implicitly require that not only the deposited load

of the embankment, but also the entire load of the improved soil above the sliding surface, is

mainly borne by the columns which, at best, could be anticipated in exceptional cases only.

However, to avoid the described inaccuracy it is unjustified to average right from the be-

ginning the shear values in proportion to the cross-section of the columns and the sur-

rounding soil. If the proof of safety is based as usual on a plane system, two approacheswhich provide sufficient safety may be taken into account: either to apply adjusted loads or

to correct the averaged shear values.

As to the following formulae and their context the same terms as in [2] apply.

Figure 3: Related surcharges in the treated layer with safety design against slope failure.

p

fpC

fpS

actual embankment line

Assumed embankment line

Improved width

Embankment

C C C C C

S S, c

S S, c S S, c S S, c S S, c S S, c

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3.3 Adjusted Loads

This approach requires the slice method to be applied to prove safety against embankment

or slope failure. Columns and soil are then transformed into equal area strips forming indi-

vidual slices, each with their attributed properties (ie their own characteristic unaltered

shear values). In this case, the load and weight of the embankment is distributed on the col-umn and soil slices according to the Priebemethod. For that, the portion of the slice load

which lies above the improved stratum has only to be multiplied by corresponding factors

for the column and soil slices respectively.

( )AAmf CC 11 =

( ) ( )AAmf CS = 111 1

This approach, with different loads on column and soil slices, is plausible and relatively accu-

rate, if the simplifications and approximations in the determination of the value m1 is disre-

garded. Admittedly, the input of slices for the calculation may be a bit time consuming, alldepending on the program which will be used.

3.4 Corrected Shear Values

The corrected shear values approach does not necessarily depend on column and soil slices.

It is based on the assumption of averaged shear values of the improved stratum, determined

on the basis of a reduced load on the columns. It is recommended to calculate the propor-

tional load on the columns, m1, from the ratio between the load and weight of the em-

bankment, QC, and the total load and weight of the sliding mass, Q.

( ) QQAAmAAm CC1C1 += With this reduced proportional load on the columns the shear values can be averaged as

usual.

Even if this method does not require the sliding body to be subdivided into slices and by no

means into slices depending on the grid of columns, it is advisable to calculate with slices

bringing it close to the method of adjusted loads and consequently is more accurate.

3.5 Ground Failure

Though with reservations ground failure beneath foundations is comparable with em-

bankment or slope failure, usually safety is proved rather differently. It is not necessary to gointo detail here as [2] outlines how it can be proved in case of vibro replacement.

With regard to overestimating the degree of improvement using vibro replacement, principi-

ally the same situation as for embankment or slope failure applies, but the possible inaccu-

racy in the procedure outlined in [2] is far less.

This is because a considerable portion of the failure line outside of the foundation is in any

case calculated with the initial shear values of the untreated soil. The remainder of the sliding

mass beneath the foundation does not play such an important role in comparison to load

and weight of the foundation itself to justify any exaggerated accuracy.

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References

[1] Kirsch K (1993). Die Baugrundverbesserung mit Tiefenrttlern, 40 Jahre Spezialtiefbau:

1953-1993. Festschrift, Werner-Verlag, Dsseldorf.

[2] Priebe HJ (1995). The design of vibro replacement, Ground Engineering, December1995, pp31 - 37.

[3] Priebe HJ (1995). Die Bemessung von Rttelstopfverdichtungen, Bautechnik 72, H3.

[4] Forschungsgesellschaft fr das Straenwesen: Merkblatt fr die Untergrundverbesserung

durch Tiefenrttler (1979).

[4] Raju VR (1997). The behaviour of very soft cohesive soils improved by vibro

replacement. Ground improvement conference, London, 1997.

Heinz Priebe is founder of GEOStat. He worked previously at Keller Grundbau,

Germany, for 35 years, specialising in ground improvement techniques and the

design of vibro replacement.

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