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It is necessary to plan the vibroflotation so that the desired compaction and uniformity is achieved throughout the site. Material compaction is measured in terms of relative density. This is calculated as:

Equation 2: Relative density (D’Appolonia, 1954)

Equation 2: Relative density (D’Appolonia, 1954)

Currently, 80 percent is the general criterion for compaction; this level of compaction is generally deemed acceptable for soils beneath foundations. However, this number can vary considerably from project to project depending on site and project requirements (Bauer Maschinen GmbH, 2012).

Spacing distance and pattern affects the uniformity of the densified material. Typical patterns include square, triangular, and line and spacing distances range between 5 and 10 feet. Typical spacing patterns are presented in Figure 8.  Rectangular and square patterns are used to improve soil beneath spread footings or for small isolated areas of improvement. Equilateral triangle patterns are the most efficient and are commonly used in scenarios with large areas. It has been observed that square patterns require about 5-8% more probe locations to achieve densities equivalent to equilateral triangular patterns (Brown, 1977).

Figure 8: Vibroflotation example patterns (Brown, 1977)

Figure 8: Vibroflotation example patterns (Brown, 1977)

 Design spacing distance is a function of desired relative density, grain size distribution of the material, fines content, and power capabilities of the vibroflotation device. The spacing is chosen so that improved columns from each probe location overlap. The effectiveness of the process decreases exponentially as the radial distance from the vibroflot increases. To determine a suitable spacing, an arbitrary number called an influence coefficient is determined based on the compaction in relation to the radial distance from the probe location. The influence coefficient is a function of distance and relative density for one vibroflotation probe location, and increases as the distance to the probe decreases. For considered design patterns, the influence coefficients are displayed around the probe location and represent an equivalent value at the corresponding radial distance. The critical point is determined based on the greatest distance from the surrounding probe locations. The sum of the coefficients from each of the probe locations must be greater than the required minimum coefficient value. Figure 9 from the International Mineral and Chemical Corporation Phosphate Plant case study shows the sum at the critical point, A, is calculated as 4 + 4 + 4 = 12. For this project, a minimum influence coefficient was determined to be 10, based on achieved relative density. A value of 12 shows that this design spacing is adequate (D’Appolonia et al., 1953).

Figure 9: Triangular spacing pattern showing sum of influence coefficients at critical point (D’Appolonia et al., 1953)

Figure 9: Triangular spacing pattern showing sum of influence coefficients at critical point A (D’Appolonia et al., 1953)

Correlating CPT Results to Relative Density

As noted in the section on 'Quality Control,' the CPT is the most common form of verification testing used today. Data obtained from CPTs is used to measure the relative density of the improved soil. Accurately estimating relative density from CPT results is critical to ensuring the vibroflotation process has achieved the desired densification results.

Research in large calibration chambers has yielded several correlations between cone penetration resistance and relative density. Two of these correlations discussed by Robertson, et al. (1997) are be presented below. It is important to note that most of the testing results used in the development of these correlations was performed on un-aged, clean, fine to medium, uniform silica sands.  Site-specific testing is crucial in developing representative relationships for soil at a site. However, large calibration chamber testing is expensive and often not implemented on projects, this can result in problems later during the verification stage.

The research completed through verification testing has shown that cone penetration resistance is controlled by soil density, sand compressibility, and vertical and horizontal effective stresses. Sand compressibility has been shown to be especially important. Robertson, et al. (1997) discussed a review of calibration chamber test results that demonstrated a lower cone penetration resistance for high compressibility sands compared to low compressibility sands for a constant relative density.  Figure 10 below shows the relationship between relative density and cone resistance for sands of different compressiblities.


Figure 10 : Relationship between relative density and cone penetration resistance for sands of different compressibilities (Robertson et. al, 1997)

The first correlation is presented below (Equation 3) is based on calibration testing of Ticino sand, which considers the effects of compressibility and effective vertical stress, was developed by Baldi et al. (1986).

eqn 1

Equation 3: Relative density and cone penetration resistance correlation (Baldi et al, 1986)

In this correlation, C0, Cand C2 are soil constants whose values can be seen in Figures 11 and 12. The cone penetration resistance is represented by qc and is in units of kilopascals, as is the effective vertical stress, σ'. This correlation was used to develop Figures  11 and 12, which show the relationship between vertical effective stress and cone resistance for both normally consolidated and overconsolidated Tocino sands.


Figure 11: Relationship between Dr, qc, and σ' for normally consolidated Tocino sands (Robertson et. al, 1997)

NC and OC

Figure 12: Relationship between Dr, qc, and σ' for normally and over consolidated Tocino sands (Robertson et. al, 1997)

The second correlation presented (Equation 4) was developed by Kulhway and Mayne (1990).

eqn 2

Equation 4: Relative density and cone penetration resistance correlation (Kulhway & Mayne,1990)

Here qc is the penetration resistance, σv' is the effective vertical stress, Pa is atmospheric pressure, OCR0.18 is the overconsolidation factor, QA is the ageing factor and QC is the compressibility factor whose value ranges from 0.9, for low compressiblity sands to 1.09, for high compressiblity sands.

It is important to reiterate that the correlations presented above are based on testing performed on un-aged, clean, medium to fine, uniform silica sands.  These correlations may be appropriate to apply to reasonably similar soils, however, site-specific calibration testing is crucial for producing accurate and reliable relative density correlations from CPT results.

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