Water and mud inrush is a common geological disaster in the completely weathered granite tunnel during construction.The key factor leading to the expansion of water inrush channel is the loss of soil particles

where the starting velocity is the critical condition of its loss.By considering the water erosion and particles adhesion

the particle 3D force in the water inrush channel cross-section was analyzed

and the function of particles starting velocity was established.The function includes the following factors

namely

the particle diameter

the particle position of channel cross-section and relative exposure degree of the particle.Meanwhile

numerical simulation was conducted to analyze the effect of the above three factors on the starting velocity.Numerical results showed that the starting velocity decreased initially and then increased with the increase of particle diameter.Furthermore

the starting velocities of channel cross-section at different positions were symmetry

and they were increased with the increase of relative exposure degree generally.By combining with orthogonal tests to analyze the sensitivity to starting velocity for the above three factors

the results showed that the diameter was the most sensitive factor.Accordingly

by considering the minimum starting velocity standard of channel cross-section and the randomness of relative exposure degree

the factors of particle position of channel cross-section and relative degree of exposure were simplified

and a simplified theoretical formula of the starting velocity was developed.Finally

the rationality of the starting velocity formula was verified by the laboratory test and field investigation.