The dynamic replacement method is used in many Civil Engineering projects, particularly in cases where traditional foundation methods are not effective due to weak or unstable soils.

Some common applications include:

1) Foundation Improvement

2) Seismic Liquefaction Mitigation

In areas susceptible to liquefaction (where saturated soils lose their strength during earthquakes), DRM can be employed to enhance soil stability. The dynamic compaction of granular materials reduces the risk of soil liquefaction by densifying the soil layers.

3) Marine and Waterfront Projects

In marine construction projects such as docks and ports, dynamic replacement is used to improve the soft, unconsolidated sediments typically found in these areas.

Figure 4 shows the investigated site extent with preliminary field test layout. The encountered ground conditions comprise very loose to loose silty to very silty SAND (up to 6 m thick in some areas) underlain by medium dense to very dense silty to very silty SAND till 10.0 m below ground level. Shallow and surface ground water at lower levelled ground were encountered at the site due to considerable variation in ground elevation at the site (from 9 m to 2 m elevation). Groundwater was encountered at depths between 0.5 m and 4 m below ground level. Sabkha (saline flats) were encountered across the site and easily identified by its characteristic grey and brown colour with varying shades depending upon the proportion of the clay, silt and sand present and proximity of the groundwater table below top of the Sabkha surface.

The project requires soil improvement works by using combination of several soil improvement techniques including but not limited to: Surface/Roller Compaction, Dynamic Compaction (DC), Dynamic Replacement (DR) and Rapid Impact Compaction (RIC) techniques. In order to select the appropriate soil improvement design methodology, an extensive pre-CPTs (prior to soil improvement) campaign following a frequency of 1 PCPT per 1,000 m² was adopted across the site to delineate areas according to applicable methods. This required dividing the site into activity boxes of 1,000 m² each with each having its unique identity as illustrated in Figure 5 below for different improvement methods. The Pre-CPTs will be required for the following:

The project acceptance criteria are target bearing Capacity of 100 kPa for a footing of 3 m × 3 m with embedment depth between 1.5 m to 2 m below rough grade level (RGL). Maximum allowable settlement of 25 mm. Also, minimum Factor of Safety (FOS) of 1.0 against liquefaction (M = 5.5, Pga = 0.096 g after amplification for Site Class D).

The net allowable bearing capacity was calculated in accordance with the methodology proposed by [16] and presented in [17] which relies on the direct approach to estimate the bearing capacity based on CPT results for granular soils.

Net allowable bearing capacity is estimated for a pad footing of 3.0 m by 3.0 m embedded 1.5 m 2.0 m below the finished level with the factor of safety of three by the following equation;

$q_{ultnet}=SCF\cdot k_{\varnothing }\cdot q{t}_{avg}^{rm}$

where:

$k_{\varnothing }$ = coefficient assumed depending on the ratio between width of footing and depth of embedment as well as shape of footing (conservative value of 0.16 will be used in calculations).

$q{t}_{avg}^{rm}$ = rolling mean average tip resistance at the concerned depth considering shell correction factor (SCF) = 1.0.

$q_t=q_c+u_2\left(1-a\right)$

where:

$q_c$ = measured tip resistance at the concerned depth.

$u_2$ = water pore pressure measured behind the cone at the concerned depth.

$a$ = net area ratio determined from laboratory calibration with a value of 0.8.

$q_{allnet}=\frac{q_{ult}}{FoS}$

$q_{ult}$ = ultimate bearing capacity.

$FoS$ = factor of safety (3).

Static settlement was determined according to [18] approach for granular soils as presented in [17] , using footing size of 3.0 m by 3.0 m embedded 1.5 m - 2.0 m below the finished grade level and maximum applied pressure of 100 and 250 kPa. A typical strain influence factor for a foundation width of B is presented in Figure 7 below.

The static settlement will be calculated by the following equation:

$S_{static,total}=C_1{C}_2\left(q-{\sigma }_{v0}^{\iota }\right){\displaystyle {\int }_0^z\frac{I_z}{C_3{E}_s}\text{d}z}$

where:

$C_1$ = depth correction factor.

$C_1=1-0.5\left(\frac{{\sigma }_{v0}^{\iota }}{q-{\sigma }_{v0}^{\iota }}\right)$

${\sigma }_{v0}^{\iota }$ = effective vertical stress at foundation level.

$q$ = foundation load pressure.

$C_2$ = creep correction factor.

$C_2=1+0.2\log \left(\frac{t}{0.1}\right)$

$t$ = time in years.

$C_3$ = correction factor for shape of footing.

$I_z$ = vertical strain influence factor. Maximum vertical strain influence factor is defined within the depth of influence of the applied foundation load.

$I_{z,\max }=0.5+0.1\sqrt{\frac{q-{\sigma }_{v0}^{\iota }}{{\sigma }_{vz\max }^{\iota }}}$

${\sigma }_{vz\max }^{\iota }$ = effective vertical stress at level z = B/2.

Liquefaction analysis was based on the methodology described in “Liquefaction Resistance of Soils: Summary Report from 1996 NCEER & 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils” by [19] .

The analysis is based on the calculation of Cyclic Resistance Ratio (CRR) which expresses the soil strength and Cyclic Strength Ratio (CSR) which expresses the induced seismic load. These values are used to calculate the factor of safety against liquefaction. The soil behavior type index Ic is used to assess the liquefaction potential of certain soil/sub-layer in the soil profile. The factor of safety against liquefaction (FS) defined as follows:

$\text{FS}=\frac{\text{MSF}\cdot {\text{CRR}}_{7.5}}{\text{CSR}}$

Magnitude Scaling Factor (MSF) to be taken into account based on the method recommended by the NCEER [20] . The Cyclic Stress Ratio (CSR) is the seismic demand of the soil layer and is calculated by normalizing the above equivalent shear stress with the initial effective overburden pressure:

$\text{CSR}=0.65\cdot {\alpha }_{\max }\cdot \frac{{\sigma }_{v0}}{{\sigma }_{v0}^{\iota }}\cdot r_d$

where:

${\alpha }_{\max }$ = maximum ground acceleration at the surface.

${\sigma }_{v0}$ = total vertical stress.

${\sigma }_{v0}^{\iota }$ = effective vertical stress.

$r_d$ = depth reduction factor.

Depth reduction factor ( $r_d$) is calculated as recommended by NCEER:

$r_d=\frac{1.000-0.4113z^{0.5}+0.04052z+0.001753z^{1.5}}{1.000-0.4177z^{0.5}+0.05729z-0.006205z^{1.5}+0.001210z^2}$

where:

$z$ = depth.

The Cyclic Resistance Ratio for a magnitude of 7.5 can be related to the normalized and corrected CPT cone tip resistance. The modified flow-chart procedure proposed by [21] was used, and it is based on the recommendations and method proposed in the NCEER. According to the flow-chart procedure proposed by [21] , soils with Ic greater or equal to 2.6 are considered as non-liquefiable. However, based on industry experience soils with Ic greater than 2.4 are non-compactible and non-liquefiable. In this case, a transition zone corresponding to 25 cm above and 25 cm below such soils were not considered in the assessment of compaction.