Convergence–confinement (circular tunnel) calculator

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Worked example — results

• ✓ Strain < 1% (few support problems, Hoek)

Method, formulas and assumptions

• k = (1 + sinφ)/(1 − sinφ) = (1+SIN(RADIANS(30)))/(1-SIN(RADIANS(30))) = 3
• σcm = 2c cosφ/(1 − sinφ) = 2*0.8*COS(RADIANS(30))/(1-SIN(RADIANS(30))) = 2.7713 MPa
• pcr = (2p0 − σcm)/(1 + k) = (2*5-2.7713)/(1+3) = 1.8072 MPa
• Plastic radius = IF(0.3>=1.8072,4,4*(2*(5*(3-1)+2.7713)/((1+3)*((3-1)*0.3+2.7713)))^(1/(3-1))) = 5.5051 m
• Wall displacement = IF(0.3>=1.8072,4*(1+0.3)/3000*(5-0.3),4*(1+0.3)/3000*(2*(1-0.3)*(5-1.8072)*(5.5051/4)^2-(1-2*0.3)*(5-0.3)))*1000 = 11.417 mm
• Strain ui/r0 = 11.417/1000/4*100 = 0.28542 %

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