Designing Vibro Compaction
1 Design goals for Vibro Compaction of granular soils
Generally a denser packing of granular soil particles results in a higher friction angle, higher stiffness modulus and lower water permeability of the compacted soil.
This fundamental change in soil parameters after compaction makes the method ideal in achieving the following results:
• Reduction of static load induced settlements through increased soil stiffness.
> Near-elimination of differential settlements.
• Increased bearing capacity through higher soil friction angle after compaction.
> Bearing capacity in sands of up to 800 kN/m2.
• Reduction of dynamic load induced settlements.
> Dynamic load from earthquake: Prevention of soil liquefaction.
> Dynamic load from machine foundation: Reduction of settlement.
• Reduction of soil permeability (k-value ) tor reduce dewatering volumes and pumping cost.
• Prevention of inundation settlements.
2 Achievable compaction in granular soils
2.1 Compactability and soil fines content
The compactability of a granular soil is a function of its fines content.
The below figure shows the CPT based soil classification chart after Robertson (1986].
The three shaded zones are added from our own experience.
Light shading represents well compactable soil that can be compacted by the Vibro Compaction method without adding gravel to the vibroprobe to aid compaction.
In the medium shaded transition zone Vibro Compaction could deliver on some project the required compaction but in general it is advisable to install stone columns in this zone.
The dark shaded zone requires the installation of Stone Columns and even then the soil is often only marginally compactable.
Correlation of tip resistance and friction ratio with compactability
The shaded zones and their borders were developed using the following experience:
1) A friction ratio of around 0.8 % to 1 % is known as the maximum value for a sand to be well compactable with the Vibro Compaction method. There is an exception to this rule for geologically sedimented soils (not man made fills) that have an initial tip resistance below 3 MPa. The CPT classification indicates silty sand to sandy silt (soil number 7) and if this can be confirmed to be true, then such material is only marginally compactable by Vibro Compaction, even if the friction ratio lies below 1%. In man made fills the low qc –values at low friction ratios are not necessarily indicative for a fine grained soil and therefore the prediction that soils with friction ratios below 1% are not compactable cannot be confirmed in this case. Field trials are suggested to assess the situation in such soil conditions.
2) Data from numerous Stone Column projects suggests Rf = 2 % as the maximum friction ratio for which an increase of CPT tip resistance can be detected a few days after compaction.
3) We applied no shading above the qc = 30 MPa line. A compaction to values over 30 MPa is possible if the soil is a clean sand and enough overburden stress is provided, but such high compaction is hardly ever required, therefore the shading was omitted in that range.
4) The border between the medium and the dark shading was drawn to show that in the upper part (coarser soils) a friction ratio of 1.5 % may still allow some compaction with Vibro Compaction, while in the lower part (finer soils) the border is closer to 1 %.
In summary: The above figure can only be used for general guidance. Site specific soil conditions such as a high shell content, high mica content, extremely angular our very round grain shapes can change the soil behavior drastically such that the above figure might not be applicable to estimate compactability.
2.2 Estimating the compaction grid spacing
Some sources in the literature pretend the compaction grid can be estimated from a simple chart showing the achievable sand densification (mostly given in Relative Density Dr) as a function of vibrator grid spacing.
The more elaborate of these charts give three different curves: One for clean sand, medium clean sand and marginal sand.
The problem with these charts is their limited applicability and hence large risk of using them without enough experience. Some of these charts may work reasonably well for a specific machine type in specific (mostly clean silica sand) soil conditions.
However, the world’s largest Vibro Compaction projects are not in clean silica sands but in man-made reclamations and sands with elevated carbonate content.
We therefore encourage the reader to not trust those charts but rather give us an e-mail or call one of our experienced engineers to give expert support in estimating compaction grid spacing based on site specific soil information.
On large projects, we would in any case recommend a trial compaction similar to the one shown in the next figure, rather than guessing the grid from charts or contractor experience only.
Example for a Vibro Compaction trial grid
3 Design for Load Settlement Reduction
3.1 Admissible stresses for footings on sand
The chart gives allowable soil pressure for a sand with ground water level below 2B from ground level, with B = foundation width.
Allowable stresses are calculated such that total settlements do not exceed 1 inch and differential settlements stay below 3/4 inch.
Clearly this graph, although widely used, is purely indicative and must be double-checked by settlement estimation for the actual load geometry and soils data whenever such information is available.
Allowable soil pressure for footings on sand on
the basis of SPT, from Terzaghi, Peck (1967)
General considerations regarding settlement estimation procedures:
1) What settlements and/or differential settlements are acceptable by the structure?
2) Gather all soil information relevant for settlement estimation.
Sieve analysis, Oedometer, PMT, CPT, SPT, full load tests, plate load test
3) Find out about the stress history of the site.
Is an excavation made where the foundation will be located?
Is the soil over-consolidated (OC) or normally consolidated (NC)?
4) Find the exact dimensions and loads of the foundation.
Does the design still allow changes to adapt for Vibro Compaction?
5) Find out if the load on the foundation is only reloading or also virgin loading.
Reloading gives 5 - 10 times smaller settlements than virgin loading.
6) Find out if the total load is near to the failure load.
For F < 1.2 settlements from mobilization of shear forces may be even larger than settlements from elastic compression.
7) Carry out settlement calculations after Schmertmann or with classical method.
8) Always keep in mind that all settlement "calculations" are estimations rather than calculations.
3.2 Settlement estimation procedure after Schmertmann (1970)
After Schmertmann (1970) the settlements of a rigid footing over granular soil is given by
where C1 = Correction factor for footing depth = with
P0 = Effective overburden pressure at foundation level
ΔP = Net foundation pressure
C2 = Correction factor for creep =
t = Time in years from application of P0 + ΔP
Iz = Strain influence factor at the center of each assumed constant-qc sub layer
n = Number of qc sub layers to depth below foundation
Es = Young's Modulus of compacted sand (say Es = 2 -3 x qc)
∆Z = Thickness of the n sub layers
The strain influence factor Iz is introduced in order to consider the fact, that the strains along the centerline under a rigid footing are distributed such that maximum strains occur in a depth of about 0.5 to 1.0 times the footing width B depending on the geometry of the footing being axisymmetric or plane strain.
The maximum value of the strain distribution factor is given by
It is understood, that the creep factor C2 is a highly empirical value, and the approximation given here according to Schmertmann (1970) may be subject to variations depending on local experience.
Modified strain influence factor diagrams after Schmertmann (1970)
4 Vibro Compaction for foundation and slope stability
4.1 Foundation stability
According to common experience settlement, rather than stability criteria are rele-vant for the design of foundations, when the least width of a foundation over sand exceeds 1 m to 1.5 m. However, most national design standards ask for the proof of sufficient stability in-dependently of such considerations.
A stability calculation for a foundation soil improved by Vibro Compaction can be carried out as for a "normal" sandy or gravely soil, but the shear parameters must be adapted to the higher values reached by the compaction effort.
The following table cannot replace a carefully established site-specific assessment of the possible increase of soil friction as a consequence of soil compaction. However, it gives a first idea of the effect of Vibro Compaction on the shear strength increase in granular soils.
Friction angle j' and relative density Dr
4.2 Slope stability
Vibro Compaction can increase the stability of slopes in granular soils, since the friction angle dra-ma-tically increases with the compaction of the soil. However, it must be evaluated cautiously that through all states of the compaction process the factor of safety within the slope remains above a tolerable level.
In the Lusatia (Lausitz) area of Germany very large volumes of sand slopes are stabilized by Vibro Compaction, the major concern there being the working safety during execution of the works, i.e. the danger of a sudden collapse of the slope during compaction.
At the “Restloch Sedlitz” the company BUL-Brandenburg compacted a total of two million cubic meters of “hidden dam”.
The principals of our company were involved from the beginning in this project, supplying the specially adapted compaction equipment to master the required world-record depths.
The purpose of the hidden dam is to ensure that shear failures on the shoreline remain local and do not propagate into the hinterland.
Open pit shoreline, with 56 m deep “hidden dam” for landslide stabilization
Compaction blasting and Vibro Compaction
Before the introduction of Vibro Compaction as the method of choice, the reclaimed fill has for several years been compacted by compaction blasting. However, if compaction blasting is carried out near the shoreline, the energy induced by the explosives is transferred into the soil within seconds, whereas, for the same energy, a vibroprobe needs one or more days. Consequently the risk of initiating a slope failure like the one on the following photo is very low with the Vibro Compaction system. The same cannot be said for compaction blasting.
Typical landslide in the Lusatian mining area
(Location: Restloch Sedlitz)
5 Vibro Compaction to prevent soil liquefaction
The design against soil liquefaction is covered in a separate chapter “Liquefaction Mitigation”.
The reason for this separation lies for one part in the increasing importance of this field of activity, but also in the technical fact that Vibro Compaction and Stone Columns often are combined in projects for liquefaction mitigation.
6 Vibro Compaction to reduce soil permeability
6.1 Theory of permeability of granular soils
Soil is a three-phase system of solid (soil grains), liquid (mostly water, sometimes also oil or other pollutant liquids) and gas (air). Although most soil mechanical calculations assume the existence of a continuum, the distribution of the three phases within the soil mass is of very high importance to many soil mechanical calculations.
The success of any compaction, be it with Vibroprobe procedures or any other method, is always accompanied by the reduction of the portion of the liquid and/or gaseous phase (Vv ) of the soil, while the solid portion (Vs ) remains constant. Whether a soil is compactable by vibration depends finally on the permeability of the soil, i.e. if during compaction the water/gas phases can drain quickly enough from the soil mass.
Soil element, separated into three phases
After Lambe/Whitman (1969) the water permeability of a soil depends on the following factors:
1. Grain size
3. Type of grain size distribution (well or poorly graded)
4. Structure of grains
5. Saturation of soil
All the following approximations take into account only a few of these parameters, and are therefore not very accurate.
After Cozeny-Karman it is:
k0 = shape factor, depending on pore shape
S = specific surface
Beyer (1964) found for granular soils with 0.06 mm < d10 < 0.6 mm and U = d60 / d10 < 20 that the k-value can be
approximated as follows:
with d10 in cm and k in m/s.
The constants A, B and C depend on the density according to the following table:
Coefficients A, B and C to estimate permeability k
According to Carrier/Beckmann (1984) the permeability of fine-grained soils is estimated as
, with wp and Ip in % and k in m/s.
6.2 How to quantify Permeability reduction by Vibro Compaction
Compacting a soil of equally sized ideally round grains in loosest deposit (n = 48% , e = 0.923) to the largest possible
density (n = 26% , e = 0.35) gives a reduction factor of the k-value of
Which factor of reduction will be reached in a real soil depends on the initial density before compaction, the grain size distribution, and the grain size of the backfill compared with the in-situ soil. If a backfill material coarser than the in-situ soil is used, even an increase in permea-bility may be reached, which in special cases may be desirable.
From past projects, it is believed that the range of possible permeability reduction factors lies between 1 and 100.
(1 = no improvement, 100 = 100 times less permeable)
1 to 5:
This range can be expected in poorly graded sand and gravel, which is already in a medium dense state before compaction.
50 - 100:
This range can be expected in well-graded sandy gravel, which is in a very loose to loose state before compaction.
Further research is needed to more precisely assess the permeability reduction of granular soils due to com-pac-tion than is possible today. This research is especially needed since there is no satisfactory way of testing the success of a compaction for the purpose of permeability reduction prior to the actual dewatering of the excavation, by which time it is often too late for any remedies.
No responsible contractor or engineer can therefore give any guarantees for a specific permea-bility improvement factor to be safely reached after treatment.
CPT or SPT tests are not suitable for testing permeability reduction, since the correlation factor between density, as measured in these tests, and permeability is highly imprecise.
In other words: CPT and SPT test a compaction effort, not an effort in permeability reduction. Although compaction and permeability reduction are positively coupled phenomena, the degree of coupling is very much in question.
6.3 Example for Vibro Compaction to reduce permeability
Tessuti housing complex, Switzerland
For the shopping and apartment complex "Tessuti" in Locarno, Switzer-land, a permeability reduction had to be achieved in order to reduce the water to be pumped during excavation.
The sieve analysis of the soil shows very coarse gravel with 52 % > 31.5 mm and 28 % > 63 mm.
The whole excavation was 55 x 110 m. The amount of water that was allowed to be pumped was 15'000 liters/min, which corresponds with a k-value of
A pump test showed a natural k-value in the order of .
The excavation was to be made five meters deep and the five meters be-low the excavation level had to be com-pac-ted. Compaction was carried out from a level of 2 meters below surface.
In order to fill the pores of the in-situ soil, a well-graded sandy gravel was used as backfill material.
Too fine backfill is not practical, since it will not have enough weight to fall down the hole along the vibroprobe, while too coarse back-fill does not reduce permeability far enough.
The compaction pattern was chosen to 2.4m triangular. Per lineal meter, 0.5 m3 of backfill have been used, filling the pores of the in-situ soil with the finer backfill material. Compaction was carried out by specifying pulling amperage of the vibroprobe motor of 150 A.
After excavation of the whole site, 9'000 liters/min. instead of the required 15'000 had to be pumped. This means, that an average k-value of 2.5 . 10-5 has been achieved.
6.4 The dynamic effect of vibrations on neighboring structures
The German standard DIN 4150, part 3 shows the following limit values for vibration veloci-ties vi in mm/s, which according to recent experience, when not exceeded, safely prevent damages.
Table after DIN 4150, showing tolerable vibration velocities
Bertok and Barron (1985) have reported about extensive vibration measurements for Vibro Compaction works carried out near the control tower of Vancouver Airport with its sensitive electronic instrumentation.
For the buildings 25 mm/s steady state peak particle velocity were adopted as the damage criteria, while the maximum permitted impact excitation was set to 75 mm/s.
The ground water level on the site was at about 0.76 m below existing grade.
The left figure shows the vibration velocities measured in 2 m to 6 m distance from the installation of a vibro replacement probe, using a vibroprobe with 50 Hz frequency as compared to the vibration velocity created by a Vulcan air hammer pile driver with 20.34 kJ energy per blow with 60 blows per minute.
Both foundation installations were well below the critical values. However, the vibro equipment showed markedly lower readings than the pile driving.
Vibration intensities, from Bertok and Barron (1985)
6.5 The static effect of Vibro Compaction on neighboring structures
Besides the more obvious dynamic effect of a Vibroprobe on nearby structures, the static effect is at least as important, although it is in practice much less discussed.
"Static effect" shall mean a deformation of the subsoil and structures buried in or standing on such subsoil.
The deformations can be divided in "active" deformations of the soil towards the vibroprobe and "passive" deformations away from the vibroprobe.
The sketch below shows the conditions for loose sand if it is compacted to a depth of 10 m and the compaction is achieved mainly by self-feeding of the in-situ soil towards the vibroprobe.
The compaction points are executed in rows vertical to the drawing plane of the sketch.
As the sand flows towards the vibroprobe, an active failure plane develops quite precisely under an angle of . Settlements are ob-served in a range of 5 % to 15 % of the original treated sand layer thickness, depending on the initial state of density. In order to achieve 15 % settlements, the original density must be very loose to loose and the final density must be dense to very dense.
Settlements in front of a Vibro Compaction field
At the Chek Lap Kok site, we observed up to 5 cm wide cracks on the sand surface. These cracks aligned perfectly parallel to the front most line of compaction points. The fur-thest reaching cracks were found at a distance of ± 1 m around the active shear plane for sand with .
The rule of thumb, which says that the distance bet-ween a building and a vibroprobe should be greater than 7 m, is supported by the above sketch and the fact that in most projects the maximum treatment depth is less than 14 m. However, it is equally ob-vious that if the depth of treatment is greater than 14 m, this rule of thumb is no longer valid.
In fully saturated cohesive soils the Dry Bottom Feed Stone Column (Vibro Displacement) method is used instead of the Vibro Compaction method. For these soils the deformation behavior is opposite to the behavior in loose sand with self-feeding.
The stone column installation leads to a displacement of the in-situ soil away from the treatment zone.
If the soft soil layer is covered by a harder crust, as this was the case for a site in Virginia, USA, the lateral deformations within the subsoil can reach an unexpectedly far distance from the treatment area. In this case, a pipeline more than 30 m away was moved due to the installation of stone columns.
If such a condition is encountered, the easiest remedy is by reversing the direction of stone column installation progress away from the pipeline instead of in the direction towards the pipeline.
Bertok, J.; Barron, K.E.: Vibration measurement during foundation test installation at Vancouver International Airport; Can. Geotechnical Journal, Vol. 22, pp. 258-263, 1985
Beyer, W. : Zur Bestimmung der Wasserdurchlässigkeit von Kiesen und Sanden aus der Kornverteilungskurve, Wasserwirtschaft u. -technik 14, 1964
Carrier, W.F.; Beckmann, J.F.: Correlation between index tests and the properties of remolded clays, Geotechnique 34, pp. 211-228, 1984
Lambe, Whitman: Soil Mechanics, John Wiley & Sons, New York, 1969
Robertson, P.K.: In situ testing and its application to foundation engineering; Can. Geot. Journ. , Vol. 23, p 573-594, 1986
Schmertmann, J. H. : Static cone to compute static settlement over sand, ASCE Journ. of Soil Mech. and Found. Eng, p 1011-1043, May 1970
Terzaghi, K. ; Peck, R. B.: Soil mechanics in engineering practice, Wiley, 2nd Ed., 1967