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:
where
is the minimum principal stress in soil before air pressurisation;
and
are the cohesion and friction angles of the soil, respectively; and
is the tensile strength of soil. Generally,
is small for soft soil, and a range of
)
can be adopted [
23], where
denotes the unconfined uniaxial compression strength of soil. For the undrained behaviour of saturated cohesive soil,
.
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.,
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,
:
where
is the expansion displacement of the cavity along the radial direction;
is the cavity radius;
is the hydrostatic stress of the soil before pressurisation;
is the shear modulus of the soil, which is related to Young’s modulus
by
; and
is the Poisson’s ratio. When the expansion displacement is sufficiently large, the internal expansion pressure will reach its limit
:
It is noted that soil fracturing may occur before large radial displacement occurs. Thus, 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,
and
can be assumed. The cohesion,
, 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:
where
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,
and
= 1.21 kPa can be estimated.
The Young’s modulus,
, of the test soil can be estimated based on the unloading strain of the soil or by the empirical formula (Mori and Tamura, 1987):
from which
242 kPa can be obtained.
It is known that vacuum consolidation will not change the total stress state of the soil. The vertical stress
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.,
. 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,
, of the test soil is taken as
. Thus, the minimum principal stress
can be determined. The values of the abovementioned parameters are summarised in
Table 5.
Substituting the parameters in
Table 5 into Equations (1)–(5), the crack initiation pressure of the test soil can be quantified (
Table 6). For Equation (4),
at
is taken as the crack initiation pressure. From
Figure 7, the expansion displacement
can be obtained. The initial cavity radius,
, 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.