Real-Time Behaviour of Dredged Slurry Treated by Air-Booster Vacuum Consolidation

Abstract

The air-booster vacuum preloading method has been applied to slurry ground improvement. It is based on the conventional vacuum preloading method but with an additional injection of pressurised air into the soil via pre-installed conductors. The drainage effect of air-booster vacuum preloading has been demonstrated by past studies; however, direct observations of the real-time behaviour of slurries subjected to boosted air remain lacking. This study used a combined monitoring technique that included particle image velocimetry, pore water/air pressure gauges, a vortex flowmeter and an electronic balance to conduct a laboratory test of air-booster vacuum consolidation of dredged slurry. The tests allowed analyses of (1) the real-time displacement field of the slurry, (2) the pressure–flux relationship of the pressurised air, and (3) the pore water pressure responses during air boosting. The first aspect allowed direct observation of small-crack initialisation and propagation during pressurisation; while the latter two confirmed the crack initiation based on drops in air and pore water pressures. The measured crack initiation pressure was verified by comparison with theoretical predictions. The results demonstrate that pressurised air induces cracks in soil, which promote the drainage consolidation of dredged slurry.

1. Introduction

Tideland reclamation and dredging operations in river channels produce large volumes of dredged slurry characterised by its high water content (up to 120%), large void ratio and high compressibility [1]. The dredged slurry from reclamation sites must be improved before it can be used at a construction site. Similarly, the slurry generated by river mud dredging should be reduced in volume (by drainage) before it is transported and handled. Vacuum preloading is a common engineering practice used to drain and improve soft soil [2]. The vacuum preloading method is generally considered superior to the surcharge preloading method in terms of ground stability. Specifically, vacuum pressure (~85 kPa) can be applied at a single stage for vacuum preloading, while for surcharge preloading, the load has to be applied in several stages to avoid possible stability failure of the soft ground [3,4].

However, when the vacuum preloading method is used for dredged slurry, severe clogging often occurs, such that the rates of water drainage, pore pressure dissipation and settlement decrease substantially, even at the early or middle stage of the designed treatment period [5]. As a result, the improvement in the soil strength is severely limited and the requirements of bearing capacity and postconstruction settlement are difficult to meet. It has been noted that the clogging phenomenon does not exist in naturally consolidated soft soils (as opposed to the artificial ground made by dredging slurry) when treated by vacuum preloading. The mechanisms of clogging are still under investigation [6] and it is generally agreed that the migration of soil particles (driven by vacuum pressure) is the main cause of the clogging problem inherent to dredged slurry [7,8].

Engineering solutions to the clogging phenomenon mentioned above include electro-osmosis [9], lime treatment [5], flocculant treatment [10,11] and air-booster vacuum preloading [1,12,13]. It has been shown in both laboratory and field tests that the air-booster system can promote the drainage consolidation of dredged slurry [13], resulting in the increased settlement, pore water pressure dissipation and shear strength of the soil. Specifically, the influences of pressurisation position [14] and duration [15] on slurry consolidation efficiency have been studied through laboratory tests, based on which optimal positions and duration times have been suggested. There are two explanations for the drainage mechanism of the air-booster system: (1) incremental stress induced by air pressure [1,12] and (2) soil cracks generated by airflow disturbance [13]. The first explanation was ascertained by in situ observations of the pore water pressure (PWP) increment slurry soil [13] during the air-boosting period, which generally lasts for 2–4 h per day for 5–7 consecutive days. However, the second explanation is only conceptual, and no direct observations of cracks have been made.

In this study, a laboratory test of air-booster vacuum consolidation of dredged slurry was carried out. With the help of particle image velocimetry (PIV), the real-time displacement field of the slurry soil during air pressurisation was obtained, and cracks were clearly visible in the test slurry. The real-time air flux, air pressure, and PWP responses were also monitored and analysed. Theoretical predictions of crack-initiation pressure are provided and compared to those obtained from the tests. It is the first time that the cracks induced by the pressurised air are observed, which provides strong evidence for the exploration of drainage-promoting mechanism of the air-booster vacuum preloading method.

2. Brief Introduction to Air-Booster Vacuum Preloading

The air-booster vacuum preloading method introduces an air-booster system to a conventional vacuum system. Conductors (i.e., booster tubes or plates) are inserted between the prefabricated vertical drains (PVDs) and then connected to the air compressor to produce pressurised air in the slurry. The conductors are generally made of flexible brackets coated with filter cloth, which allows air to flow into the soil. The air pressurisation is generally <40 kPa and lasts for 2–4 h per day for 5–7 consecutive days. The magnitude of the air pressure distinguishes the air-booster vacuum preloading method from the combined method of vacuum preloading and pneumatic fracturing for soft ground improvement [16], which commonly adopts a much higher air pressure (e.g., 500 kPa).

A booster tube was adopted in the original version of the air-booster vacuum preloading method [1]. The tube top needs to be buried at a certain distance below the ground surface (see Figure 1) to prevent the pressurised air from entering the membrane sealing (and losing vacuum pressure). Since the booster tube has a circular cross-section, it cannot be driven by the commonly available machines designed for inserting PVDs (with rectangular cross-sections). Recently, an improved version was designed with the booster tube replaced by a PVD plate [13], which can be readily driven by the machine to the desired depth. The booster plate is designed to have dual functions; that is, it is initially connected to a vacuum pump to facilitate vacuum consolidation of the slurry. Later, the connection is shifted to the air compressor to conduct the pressurised air. The effectiveness of the booster plate in promoting vacuum consolidation of the dredged slurry has been confirmed by field tests [13].

3. Model Test Device

Figure 2 shows the field arrangements of PVDs and booster plates, which are represented by cylindrical cells that include a booster plate at the centre and four PVDs equally spaced around the edges. This can be best represented by a cylindrical model box. However, since a planar observation window is required in the PIV technique, a cuboid model box with transparent glass on its front side was designed and built for this study (Figure 3). The dimensions of the model box are also indicated in Figure 3a. Due to the limited box height, the filling height of the slurry in the model box was 0.45 m. Thus, the model test herein mainly reflects the behaviours of shallow slurry in the field. The model box was connected to the air-boosting system (in red), vacuum system (yellow) and measuring system, shown schematically in Figure 3d. The model box was sealed from the top using an air-tight membrane.

3.1. Vacuum System

The vacuum system included a vacuum pump, air–water separation bottle, vacuum pipes and a hand-shaped connector for connection to the horizontally placed PVD with a length of 650 mm (Figure 3c). The horizontal PVD faced the observation window such that a planar area of evenly strengthened soil was generated to facilitate the PIV observation of the deformation field of the slurry. If the PVD is installed vertically, as in practice, the slurry directly in front of the PVD will be strengthened more than slurries laterally away from it when the observation is made along the planar observation window. This will result in an inhomogeneous slurry, which can hinder the initiation and propagation of soil cracks. The PVD is of the integrated type, i.e., the filter cloth is attached to two surfaces of the plastic core. The engineering properties of the PVD used in this study are summarised in

Table 1. Parameters of PVDs.

Parameter	Value
Width (mm)	100 ± 3
Thickness (mm)	4.2
Equivalent pore diameter (μm)	75
Tensile strength (kN/cm)	0.2
Water flux capacity (cm3/s)	40.9
Permeability coefficient (cm/s)	5 × 10−3

. The air–water separation bottle collects the water discharged during vacuum preloading.

3.2. Air-Boosting System

The air-boosting system included a booster pump, booster pipelines, hand-shaped connector and booster plate, along with a small iron rig to fix them in the model box. The PVD in the vacuum system was used as the booster plate; however, it had a trimmed length (160 mm) comparable to the height of the PIV observation window. It was installed vertically with its two narrow sides fronting the glass and the PVD, respectively, as shown in Figure 3c. Since the PIV camera only captures particle displacements parallel to the observation window, the narrow side of the booster plate needed to face the glass window so that the compressed air will push the surrounding slurry away in an observable direction (Figure 3b).

Moreover, to eliminate possible boundary disturbances, the pressurised air should be controlled such that it will not escape from the plate/connector junction or from the bottom of the model box. Both the top and bottom parts (length = 30 mm) of the booster plate were sealed by glue; that is, the airflow was only allowed in the intermediate part (length = 100 mm) of the booster plate.

3.3. Measurement System

The measurement system included a vortex flowmeter, air-pressure transducer, pore water pressure (PWP) transducers, electronic balance and PIV device. The parameters of the abovementioned transducers, including their measuring range, resolution and sampling frequency, are summarised in

Table 2. Parameters of the monitoring transducers.

Monitoring Instrumentation	Accuracy	Range	Sampling Frequency
Vortex flowmeter	1.5% Fs	0~40 Nm3/h	1 Hz
Air pressure transducer	0.2% Fs	0~50 kPa	1 Hz
Pore water pressure (PWP) transducers	0.1% Fs	−100~100 kPa	5 Hz
Electronic balance	0.1 g	0~30 kg	Record when weight changes

. The PIV technique was originally developed in the field of experimental fluid mechanics [17]. It works by using a high-resolution digital camera to photograph tracers, which are evenly spread onto the inner wall of the glass window before the model box is filled with slurry. Silicon grease was smeared onto the inner wall of the transparent glass to hold the initial positions of the tracers. When slurry particles move under vacuum or air pressure, the tracers move with them. The movement is recorded by the PIV camera, which takes photographs at a high frequency. The PIV software divides the images into a grid of test patches according to the image pairs of each tracer. The displacement vector of each patch during the interval between photographs is found by locating the peak of the autocorrelation function of each patch. This peak indicates that the two images of each tracer captured during the flashes overly each other. Then, the displacement vector is obtained as the correlation offset [18]. Due to the resolution requirements, as shown in Figure 3, a rectangular observation window (height = 150 mm and width = 200 mm) with a booster plate located along its central axis is set for the PIV camera. The silicon grease should minimise the negative influence of friction at the slurry/wall boundary.

The vortex flow meter and air-pressure transducer were connected to the booster pipe so they can record the real-time air flux and air pressure, respectively, during the pressurisation operations. There were six PWP transducers arranged symmetrically on both sides of the booster plate, i.e., three transducers on each side located 2.5 cm, 5 cm and 10 cm laterally away from the booster plate. All PWP transducers were 10 cm above the plate bottom. The electronic balance automatically recorded temporal variations in the water discharge during the treatment.

4. Soil Samples

The soil was sampled from a land reclamation site at Wenzhou, a coastal city of Zhejiang Province, China. From the gradation curve in Figure 4, it is seen that the dredged slurry was mainly composed of silt and clay particles. The index properties of the sampled slurry are summarised in

Table 3. Index properties of the sampled slurry.

Parameter	Symbol	Value
Water content (%)	w	70.7
Liquid limit (%)	$w_L$	56.6
Plastic limit (%)	$w_P$	32.5
Specific gravity of soil grain	$G_s$	2.74

. Considering the high water content of the slurry (i.e., w ≈ 1.3 $w_L$) and the nature of the vacuum consolidation, the slurry in the present test can be considered as saturated at the beginning and in the subsequent drainage–consolidation stages.

5. Test Operation Procedures

In practice, the air-boosting system is activated when the slurry has already consolidated to a certain degree. Correspondingly, at the beginning stage of our model test, only vacuum pressure was applied (−85 kPa according to the vacuum pump). When the degree of slurry consolidation reached approximately 70%, the vacuum pump was turned off and the air compressor was turned on to provide pressurised air. The air-boosting duration was set to 10 min; then, the air compressor was turned off, and the vacuum pump switched on to continue the vacuum consolidation.

The main operational steps of the model test are briefly described: (1) Fix the positions of the PVD, iron rig, PWP transducers and booster plate. (2) Connect the PVD and booster plate to the tubes via the hand-shaped connectors. (3) Lead the transducer wires and tubes out from the hole opened in the model box sidewall. (4) Connect the valve, water–gas separation bottle and vacuum pump in sequence to complete the vacuum system. Similarly, connect the valve, air-pressure transducer, vortex flowmeter and air compressor to complete the air-booster system. (5) Connect the PWP transducers, electronic balance and flow meter to computers for automatic data recording and spread the tracers evenly onto the inner wall of the transparent glass. (6) Uniformly mix the dredged slurry and pour it into the model box to a filling height of 0.45 m. (7) Place two layers of air-tight membrane on top of the slurry. Tighten the bolts to ensure that the flange clamps the membrane. (8) Start the vacuum pump to perform vacuum consolidation of the slurry. When the degree of consolidation reaches 70%, the vacuum system is stopped. (9) Activate the air-booster system to start the air pressurisation. Meanwhile, the digital camera takes high-resolution pictures of the slurry displacement field. (10) Turn off the booster pump after 10 min of pressurisation. Then, the vacuum pump is turned on again to continue the vacuum consolidation of the slurry. The flow chart of test operation procedures is showed in Figure 5.

6. Correspondence between Model Test and Engineering Practice

As mentioned in Section 3.1, the PVD was horizontally laid in the model box, and it only aimed to homogeneously consolidate the slurry around the booster plate. Obviously, the width of model box (26 cm) will not affect the consolidating effect of the test slurry. The box width was controlled such that the planar dimension (i.e., the plane of box height and length) was approximately five times the half width. Half of the box width was considered, because the PVD that was horizontally laid across the box width created two equally strengthened zones, and the booster plate was within one of them. Moreover, silicone grease was smeared onto the inner walls of the model box to minimise the boundary frictions. In this way, the tractions at the front-wall/slurry and back-wall/slurry boundaries can be negligible when compared to the magnitude of air pressurisation within the height–length plane. In viewing of the large dimension ratio (i.e., the height/length over the width) and the negligible boundary frictions, the slurry confined between the booster plate and the box walls would approach the one-dimensional deformation condition, which resembles the soil compression in a horizontally laid oedometer. The one-dimensional deformation condition directs our observations only to the height–length plane, while the variations across the width can be reasonably neglected.

As for the length of model box, it is an important design consideration, because the pressurised air leaves the booster plate and propagates along the length direction. In engineering practice, the spacing between the booster plate and neighbouring PVDs is 50~100 cm; correspondingly, the length of model box was set to a representative value of 70 cm.

7. Test Results

The PWP dissipation occurring during the vacuum consolidation process is presented in Figure 6. The data from the six PWP transducers were averaged. The degree of consolidation of the test slurry was estimated as 70% on the 14th day of vacuum consolidation. Subsequently, the vacuum pump was turned off, and the booster pump was turned on to start the air pressurisation, during which the real-time displacement field, air pressure, air flux and PWP responses, as well as the water yield, were monitored and are presented in this section. A detailed discussion of the observations made in this section is presented in Section 7.

7.1. Flux and Pressure of Boosting Air

The air pressure at the outlet of the boosting pump was set to 20 kPa. However, since pressure is lost due to the airflow and pipe-wall friction, the actual pressure in the booster pipeline (monitored by the air-pressure transducer) will be less than the target value at the outlet. The flux and pressure of the pressurised air, which are recorded by the vortex flow meter and air-pressure transducer, respectively, are shown in Figure 7 for the first 90 s of the boosting duration (i.e., 10 min). It is seen from Figure 6a that the air flux remained low and stable for the first 7 s; meanwhile, an almost linear increase in the air pressure (from 0 to 8 kPa) can be observed in Figure 7b. After, a steep increase in the air flux and a sharp drop in the air pressure can be observed during the time period of 7–10 s. In the following 30 s (i.e., 10–40 s), a steady increase in both the air flux and pressure can be observed, after which they both increased (while fluctuating) and then decreased slightly within the following half minute (i.e., 40–70 s). After 70 s, both the air flux and air pressure became stable. Thus, only the first 90 s of the boosting duration is presented. Figure 7 shows that the stable values of the air flux and air pressure were approximately 0.7 m³/h and 11 kPa, respectively.

7.2. Water Yield

By setting the starting time of the air boosting as t* = 0, the water yield during t* = −3–0 h (i.e., before air boosting) can be evaluated from the records of the electronic balance (

Table 4. Comparison of the water drainage before and after air boosting.

	Time (h)	Discharge of Water (g)
Before air boosting	−3~−2 h	1.7
	−2~−1 h	1.8
	−1~0 h	1.7
After air boosting	0.5–1.5 h	4.2
	1.5–2.5 h	2.8
	2.5–3.5 h	1.7

). For comparison, the water yield during t* = 0.5–3.5 h (i.e., after air boosting) is added. It is noted that the PWP will be influenced during air boosting (as detailed in the following section), and the water yield is dependent on the PWP gradient. Thus, to make a meaningful comparison, the water yield during air boosting (i.e., t* = 10 min = 1/6 h) is not included. Instead, we included the water yield data for the time period after 0.33 h of the vacuum preloading (i.e., t* = 0.5–3.5 h; the vacuum pump was restarted after air boosting). It is noted that the PWP induced by the pressurised air soon disappeared when the air boosting was stopped; that is, the PWP of the slurry at t* = 0.5 h will be the same as that right before boosting (i.e., t* → 0).

It is clear from Table 4 that the rate of water yield reached a stable value (~1.7 g/h) before air boosting. However, after air boosting, there was an obvious increase in the water yield, i.e., the rates during t* = 0.5–1.5 and t* = 1.5–2.5 h reached 4.2 g/h and 2.8 g/h, respectively. Finally, during t* = 2.5–3.5 h, the rate of the water yield returned to that before air boosting. The increased water yield rate indicates that the drainage consolidation of the dredged slurry was promoted, even though the pore water pressure gradients were the approximately the same for the time periods before and after air boosting.

7.3. Displacement Field of the Slurry

From Section 7.1, it is clear that the entire air-boosting duration (10 min) can be divided into different stages, i.e., 0–7 s and 7–10 s, etc., according to the characteristics of the air pressure/flux variations. Accordingly, during the first stage (i.e., 0–7 s), a horizontal displacement field of the slurry can be constructed using the PIV technique, as shown in Figure 8a. The coloured contour shows a nearly symmetric deformation pattern; that is, the slurries on the right and left sides of the booster plate moved to the right (red colour) and left (blue), respectively. The amplitudes of both the right- and leftward displacements were the same, i.e., 1.5 mm. Since the displacement was small, no observable change happened to the slurry (see Figure 8b) at time t* = 7 s compared to the instant before air boosting (i.e., t* = 0 s). The randomly distributed cavities in the picture (indicated by the dashed circles) were due to the detachment of the soil from the glass window during the vacuum consolidation of the slurry.

A displacement field and image of the slurry are presented in Figure 9 for the time period 7–10 s of air boosting. There is an increase in the amplitude of the horizontal displacements: 3.5 mm in Figure 9a compared to 1.5 mm in Figure 8a. More importantly, the slurry above the booster plate has been mobilised by the pressurised air, contrasting with the observation from Figure 8a that observable displacements are concentrated only in zones fronting the booster plate. From the slurry image taken at t* = 10 s, small vertical cracks (extending along the axis of the booster plate) and oblique cracks (originating near the top of the booster plate) can be observed.

From the horizontal displacement contour constructed for the time period 10–40 s (Figure 10a), it can be seen that the slurry was compressed with an incremental displacement amplitude of 1.5 mm. The displacement field has a more even distribution; that is, the slurry at the boundary of the observation window (x = 12 mm and x = 188 mm) was also effectively compressed compared to that at time period 7–10 s (Figure 9a). A closer observation of Figure 10a reveals that there were localised blue/red coloured zones within the red/blue coloured zones, which indicates opposite displacements occurring along the zone boundaries. This can be confirmed from the slurry picture taken at t* = 40 s (Figure 10b) in which oblique cracks to both sides of the booster plate can be clearly observed. It is understood that the slurries on the two sides of the oblique crack should move in opposite directions. By comparing Figure 9b and Figure 10b, it is observed that the vertical crack extends upward to connect with the oblique cracks. Moreover, there was an obvious increase in the opening widths of both the vertical and oblique cracks.

Within the following 30 s of air pressurisation (i.e., time period 40–70 s), the dominant slurry displacement field shrinks to be close to the booster plate (Figure 11a), with the largest displacement increments existing along lines oblique to the axis of the booster plate. Actually, as can be seen in Figure 11b, the displacement increments are contributed to by the elongated and widened oblique cracks. The vertical crack was largely the same as that in Figure 10b. The vertical and oblique cracks were more connected during the present time period and formed a Y-shaped channel for the pressurised airflow.

The horizontal displacement field of the slurry for a time period of 70–90 s is presented in Figure 12a. A negligible incremental displacement occurred to the slurry during this period. From the slurry picture taken at t* = 90 s (Figure 12b), the overall appearance of the cracks resembled those in Figure 11b. Thus, it is understood that the cracks enter a steady state.

In the remaining air-boosting time (i.e., t* > 90 s), there was basically no observable displacement increment or crack development. Thus, the corresponding displacement contour and slurry pictures are omitted. It is noted that the displacement field immediately after air boosting (Figure 13a) showed a contrary pattern to that during boosting; that is, the slurry to both sides of the booster plate moved towards the plate. As a result, cracks with smaller widths can be observed in Figure 13b.

7.4. Excess Pore Water Pressure

The excess PWP variations recorded during the first 90 s of air boosting are shown in Figure 14. In general, the temporal variation in the excess PWP resembles that of air pressure (Figure 7); that is, the excess PWP increased steeply over t* = 0–7 s and then suddenly dropped in the following 3 s. Within the next 5 s, the excess PWP increased gradually, although with an amplitude slightly smaller than that before the drop. During the remaining air-boosting time, the excess PWP gradually decreased. The above observation was within expectations, since the soil surrounding the boosting plate should undergo undrained deformation when it is subjected to a short period of boosting loading (i.e., 90 s). When Figure 14 is compared to Figure 6, the maximum air pressure reads as 11 kPa, while the PWP peaks are within 7 kPa. The gap between the air and pore water pressures can be attributed to the geometric attenuation effect of the soil. At t* = 7 s, it is observed from Figure 13 that the farther the PWP transducer is away from the booster plate, the lower the PWP peak. However, after the initiation and propagation of cracks (i.e., t* > 10 s), the slurry becomes inhomogeneous, which may explain the abnormal PWP responses (P_2L > P_1L) during the time period t* = 10–90 s.

8. Discussion

8.1. Stages of Soil Behaviour Subjected to Air Pressurisation

According to the real-time observations of the boosting air flux and pressure, the displacement contours of the soil and excess PWP responses and the soil behaviours under air pressurisation can be qualitatively divided into four stages:

(i)

Cavity expansion stage (0–7 s): The soil surrounding the booster plate expands radially in this stage, i.e., the pressurised air continuously compresses the surrounding soil along the direction perpendicular to the face of the booster plate. As a result, the soils to the left and right sides of the booster plate move to the left and right, respectively, as shown in Figure 8. The farther the soil is from the booster plate, the smaller its displacement is. No cracks are generated in this stage, since the air pressure rises steeply, while the air flux is negligible (Figure 7).

(ii)

Crack initiation stage (7–10 s): The air pressure drops suddenly and the air flux increases substantially, which indicates that cracks have been generated in the surrounding soil, which provides airflow paths. Accompanying the increased air flow, the air pressure drops [19,20,21]. Figure 9b shows an image of the cracks. Combined with the displacement contours in Figure 9a, it is found that a vertical crack was generated in the soils right in front of the booster plate. An oblique crack appears in the soil on top of the plate, as schematically shown in Figure 15. The vertical and oblique cracks might be caused by tensile and shear failures of the soil, respectively. From Figure 7b, the crack initiation pressure of the slurry soil can be estimated as 8 kPa.

(iii)

Crack propagation stage (10–70 s): With continuous air inflation, the vertical and oblique cracks become elongated and connected, as shown in Figure 10b. The air flux increases due to the greater number of connected crack channels, as indicated in Figure 16. In addition, the air pressure increases, since additional pressure is needed for continuous soil fracturing at the crack tips (Figure 7). In the first 30 s of this stage, crack propagation is mainly reflected as a widening of the cracks, as shown in Figure 11b. Correspondingly, steady increases in both the air flux and pressure can be observed. For the remaining 30 s of this stage (i.e., t* = 40–70 s), the vertical and oblique cracks propagate and become connected. Thus, the air flux increases slightly in a fluctuant manner, while the air pressure decreases gradually. Figure 7b shows that the pressure required for the formation of Y-shaped cracks is approximately 11 kPa.

(iv)

Crack stabilisation stage (70 s and after): The air pressure and flux remain almost constant during 70–90 s of air boosting (Figure 7). Moreover, the cracks in the image in Figure 12b are almost the same as those in Figure 11b. These observations indicate that the soil cracks have entered into a steady state. The air pressure required to maintain the crack opening is approximately 10.5 kPa (Figure 7b), which is slightly less than that required for crack propagation.

At the end of pressurisation, elastic rebound will occur in the soils on both sides of the cracks, since the supporting air pressure is lost. After elastic rebound, the Y-shaped crack remains; however, its opening width reduces significantly, as shown schematically in Figure 17. The unclosed cracks serve as a fast track for pore water transportation, which promotes seepage consolidation of the slurry during the vacuum preloading period following air boosting. This explains the variations in water yield described in Section 7.2.

Figure 15. Schematic view of the crack distributions during the soil cracking stage.

Figure 15. Schematic view of the crack distributions during the soil cracking stage.

Figure 16. Schematic view of the connected cracks during the crack propagating stage.

Figure 16. Schematic view of the connected cracks during the crack propagating stage.

Figure 17. Schematic view of the connected cracks at the end of the air pressurisation.

Figure 17. Schematic view of the connected cracks at the end of the air pressurisation.

8.2. Crack Initiation Pressure

Both vertical and oblique cracks were observed in the PIV model test. The vertical cracks were parallel to the booster plate, and their positions basically overlapped the projection of the booster plate, as indicated in Figure 15, Figure 16 and Figure 17. In comparison, oblique cracks emerged only in soils above the head of the booster plate. With these crack shapes in mind, it would be straightforward to attribute the vertical and oblique cracks to tensile and shear strength failures of the slurry soil, respectively. Zhang et al. [22] proposed two equations for evaluating crack-initiation pressures for the tensile and shear failures of soils when high-pressure air is injected into a borehole:

$$P_{\mathrm{f}}=2{\sigma }_3+{\sigma }_t,$$

(1)

$$P_{\mathrm{f}}=\left(1+\sin \phi \right){\sigma }_3+c\cos \phi$$

(2)

where ${\sigma }_3$ is the minimum principal stress in soil before air pressurisation; $c$ and $\phi$ are the cohesion and friction angles of the soil, respectively; and ${\sigma }_t$ is the tensile strength of soil. Generally, ${\sigma }_t$ is small for soft soil, and a range of ${\sigma }_t=(\frac{1}{6}\mathrm{to}\frac{1}{5}$) $q_{\mathrm{u}}$ can be adopted [23], where $q_{\mathrm{u}}$ denotes the unconfined uniaxial compression strength of soil. For the undrained behaviour of saturated cohesive soil, $q_{\mathrm{u}}=2c$.

Mori and Tamura [23] proposed a unified equation for determining the hydrofracturing pressure of cohesive soil, regardless of whether the fracture surface is vertical, horizontal or oblique, i.e.,

$$P_{\mathrm{f}}={\sigma }_3+q_{\mathrm{u}},$$

(3)

As indicated by the authors, the horizontal and oblique cracks are initialised by the shear failure of the soil near the borehole. Before fracture, soil displacements may already be observed during the pressurisation process. Under the small strain assumption of the soil, Carter et al. [24] derived an explicit solution for the expansion displacement of cylindrical cavities in cohesive soil subjected to an internal pressure, $p$:

$$\frac{\delta }{a}=\frac{c}{2G}\exp (\frac{p-p_0}{c}-1),$$

(4)

where $\delta$ is the expansion displacement of the cavity along the radial direction; $a$ is the cavity radius; $p_0$ is the hydrostatic stress of the soil before pressurisation; $G$ is the shear modulus of the soil, which is related to Young’s modulus $E$ by $G=E/2\left(1+\vartheta \right)$; and $\vartheta$ is the Poisson’s ratio. When the expansion displacement is sufficiently large, the internal expansion pressure will reach its limit $p_L$:

$$p_L=c\left[1+\ln \left(\frac{G}{c}\right)\right]+p_0,$$

(5)

It is noted that soil fracturing may occur before large radial displacement occurs. Thus, $p_L$ can serve as the upper limit of the crack initiation pressure of soil. Equations (4) and (5) are applicable to the undrained behaviour of saturated soil. Since fracturing happens within a short time, the soil surrounding the booster plate in our model test should be undrained. At the same time, the slurry soil is consolidated by vacuum pressure before air pressurisation, thus guaranteeing saturation of the soil.

For the undrained behaviour of the saturated cohesive soil, $\phi =0$ and $\vartheta =0.5$ can be assumed. The cohesion, $c$, of the test soil is best determined using an in situ test, e.g., cross-vane shear. However, the vane would puncture the membrane and cause air leakage because the vacuum consolidation is restarted directly after air boosting. Instead, we use the empirical formula of Leroueil et al. [25] to estimate the cohesion of the test soil:

$$c=\frac{1}{{\left(I_L-0.21\right)}^2},$$

(6)

where $I_L$ is the liquidity index. The initial water content of the test soil is given in Table 3. During the vacuum consolidation process before air boosting, the water yield is recorded as 8610 g. Accordingly, the water content of the test soil at the moment of air boosting can be determined as 59.4%. Thus, $I_L=1.12$ and $c$= 1.21 kPa can be estimated.

The Young’s modulus, $E$, of the test soil can be estimated based on the unloading strain of the soil or by the empirical formula (Mori and Tamura, 1987):

$$E=100q_u$$

(7)

from which $E=$242 kPa can be obtained.

It is known that vacuum consolidation will not change the total stress state of the soil. The vertical stress ${\sigma }_1$ of the slurry at the mid-height of the booster plate, where the cracks first appear, can be estimated according to the self-weight; i.e., ${\sigma }_1=\gamma h=1600\frac{\mathrm{kN}}{{\mathrm{m}}^3}\times 0.4 \mathrm{m}=6.4 \mathrm{kPa}$. Since the water content of the slurry soil at the end of vacuum consolidation is still higher than the liquid limit, the lateral pressure coefficient, $K_0$, of the test soil is taken as $K_0=1$. Thus, the minimum principal stress ${\sigma }_3=K_0{\sigma }_1=6.4\mathrm{kPa}$ can be determined. The values of the abovementioned parameters are summarised in

Table 5. Intermediate parameters.

Parameter	Symbol	Value
Minimum principal stress (kPa)	${\sigma }_3$	6.4
Vertical stress (kPa)	${\sigma }_1$	6.4
Lateral pressure coefficient	$K_0$	1
Unconfined uniaxial compression strength (kPa)	$q_{\mathrm{u}}$	2.42
Tensile strength	${\sigma }_t$	$(\frac{1}{6}$$~\frac{1}{5}$$)q_{\mathrm{u}}$
Cohesion (kPa) of soil	$c$	1.21
Friction angle of soil	$\phi$	0
Liquidity index	$I_L$	1.12
Unit weight of soil (kN/m3)	$\gamma$	1600
Thickness of soil (m)	h	0.4
Shear modulus of the soil (kPa)	$G$	80.67
Young’s modulus (kPa)	$E$	242
Poisson’s ratio	$\vartheta$	0.5
Expansion displacement (mm)	$\delta$	1.5
Cavity radius (mm)	$a$	3.66
Internal pressure (kPa)	$p$	8
Hydrostatic stress (kPa)	$p_0$	6.3
Limit value of internal expansion pressure (kPa)	$p_L$	12.6

.

Substituting the parameters in Table 5 into Equations (1)–(5), the crack initiation pressure of the test soil can be quantified (

Table 6. Estimations on crack initial pressure of slurry soil.

Source	Mechanism	Value (kPa)
Equation (1)	Tensile failure	13.2
Equation (2)	Shear failure	7.6
Equation (3)	Tensile/shear failure	8.8
Equation (4)	Cavity expansion	10.9
Equation (5)	Limit cavity expansion	12.6

). For Equation (4), $p$ at $t^{*}=7\mathrm{s}$ is taken as the crack initiation pressure. From Figure 7, the expansion displacement $\delta =1.5\mathrm{mm}$ can be obtained. The initial cavity radius, $a$, can be determined according to the area equivalence between the circular cavity section and the rectangular section of the booster plate (sectional dimensions given in Table 1).

From Table 6, it is clear that Equations (2) and (3) provide the closest crack initiation pressure to that observed in our model test, i.e., 8 kPa (Figure 7 and Figure 9). The crack initiation pressure estimated from the cavity expansion displacement is approximately 36% higher than 8 kPa. This discrepancy may be due to the fact of an overestimated shear modulus or to the shape effect of the PVD section.

9. Conclusions

A laboratory test was used to investigate the real-time behaviour of the air-boosted vacuum consolidation of dredged slurry. A measuring system incorporating the PIV technique, a vortex flowmeter, pore water/air pressure gauges and an electronic balance allowed real-time monitoring of the soil and pressurised air during the air-boosting process. The PIV technique obtained the displacement field of the test slurry, which provided direct observations of crack initiation and propagation. The pressure/flux of the pressurised air and PWP read from the gauges and vortex flowmeter help understand the undrained soil behaviours under pressurised air based on which the air-boosting process can be divided into different stages. The total water discharge read from the balance confirms that the air-booster vacuum preloading promoted consolidation of the dredged slurry. The crack initiation pressure observed from the model test was compared with theoretical predictions. The following conclusions can be drawn:

(1)

When subjected to pressurised air, the soil surrounding the booster plate undergoes four stages of deformation: cavity expansion, crack initiation, crack propagation and crack stabilisation.

(2)

Both vertical and oblique soil fractures can be induced by pressurised air and connected to form a Y-shaped crack. The vertical crack occurs parallel to the booster plate, and its position basically overlaps the booster plate axis. Oblique cracks only emerge in soils above the head of the booster plate.

(3)

A sudden drop and increase in the air/pore water pressure and air flux indicate the initiation of soil cracks. Crack initiation is due to the fact of either the tensile or shear failure of the soil under undrained conditions.

(4)

The air-booster system can induce cracks in treated soil, which promote the drainage consolidation of the dredged slurry.