3.3.3 Determination of the Eruption of Slurry
The actual split of slurry shield occurs when the pressure of slurry is greater than that of formation.From the above results of shield model test，it can be seen that：①in the case of upper load on the surface，the split occurs in the vertical direction；②When there is no upper load，the split occurs oblique upward.The former is equivalent to the case ofσ1＞σ3，that is to say，it is equivalent to the case of thicker overburden；the latter is equivalent to the case of σ1＜σ3，that is to say，the overburden is thinner.According to the diameter of shield，it can be considered that the thickness of overburden is 1D or less than 1D.
When the splitting occurs on the cutting surface，whether the splitting crack tip stops in overburden or spreads to the surface to produce mud eruption depends on the relationship between the time ts when the splitting reaches the surface and the time t0 when the mud pressure acts on the splitting opening under a certain splitting extension speed.Time t0 is closely related to the speed of shield tunneling，that is，if the split occurs in shield tunneling，with the continuous excavation of shield machine，the shell of shield body reaches the split hole，blocks the split hole，and the slurry pressure cannot continue to act，and the split extension will stop.The longest distance from the cutting surface to the front of the shield tunneling（Fig.3.13），that is，the maximum distance L（m）is the distance from the front end of the tool to the front end of the shield shell.Therefore，the operating time of the slurry pressure at the opening of the split can be expressed as：
Vs—Driving speed of shield（cm/s）.
On the other hand，there is
t—Split continuation time；
Ø—Fig.3.14 shows the angle of oblique upward split extension.
Lt increases with time，and become Ls when it reaches the surface.At this time，mud water erupts.If it is assumed that the time for the fracture to extend to the ground is t，then Ls can be expressed as
Fig.3.13 Schematic diagram of the distance from the front end of the tool to the front end of the shield shell
Fig.3.14 Oblique upward split shape
From the formula（3.10），we can see that the expression of（ts）is
By comparing ts andt0，we can judge whether there can be slurry eruptions：ts＜t0，slurry erupts；ts＞t0，slurry eruptions will not occur.