Convergence-Confinement Tunnel Calculator
Underground design & NATM tunneling: Calculate the Ground Reaction Curve (GRC), critical yield pressure ($p_{cr}$), plastic zone radius ($R_{pl}$), and wall convergence ($u_r$).
Tunnel & Geotechnical Input Data
Plastic Zone & Convergence Performance
Critical Support Pressure $p_{cr}$
--
MPa (elastic-plastic threshold)
Plastic Zone Radius $R_{pl}$
--
meters ($R_{pl} / a$ ratio)
Wall Radial Displacement $u_r(a)$
--
mm (inward convergence)
Relative Strain $\epsilon_t$
--
% ($u_r / a$)
Elastic Wall Displacement $u_{r,el}$
--
mm (@ $p_i = p_{cr}$)
Passive Coeff $k_p$
--
$(1+\sin\phi)/(1-\sin\phi)$
Ground Reaction Curve ($p_i$ vs $u_r$)
Ground Reaction Curve shows how rock mass relaxes as support pressure decreases. The intersection with the Support Characteristic Curve (SCC) defines the equilibrium point.
The Convergence-Confinement Method (CCM)
The Convergence-Confinement Method is the theoretical cornerstone of the New Austrian Tunneling Method (NATM). In an elastic rock mass, radial displacement obeys Hooke's Law:
$$u_{r,el} = \frac{1 + \nu}{E} a (p_0 - p_i)$$
$$p_{cr} = \frac{2 p_0 - \sigma_c}{k_p + 1}, \quad \text{where } k_p = \frac{1 + \sin\phi}{1 - \sin\phi}, \; \sigma_c = \frac{2 c \cos\phi}{1 - \sin\phi}$$
When $p_i < p_{cr}$, plastic yielding initiates. The plastic zone extends to radius $R_{pl} = a \left[ \frac{2(p_0 + c \cot\phi)}{(k_p + 1)(p_i + c \cot\phi)} \right]^{\frac{1}{k_p - 1}}$, generating non-linear volumetric dilation and accelerated wall convergence.
Recommended Tools & Equipment
Tested hardware and components for high reliability
100% Free Tool
Zero Sign-Up