PSI - Issue 84

Gerardo Sorrentino et al. / Procedia Structural Integrity 84 (2026) 1071–1078

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removed, the material first expands elastically and then reaches an inelastic state where dilation is restrained. Under these conditions, a parabolic separation curve develops, extending (from the crown) to the intersection with the sliding planes. Its height can be derived from the maximum pressure recorded at the crown. Starting from Ritter’s work, Kommerell (1912) proposed a method for evaluating the equivalent loading body for all soil types. According to him, the height of the parabolic solid could be determined by measuring the tunnel crown subsidence (which is responsible for displacement in the overburden) and the percentage of volumetric increase in the soil. The solid was approximated by an ellipse extending only across the width of the lining from the crown to the sidewall. Giovannini (1936) provided a critical review of tunnel design methods, while in the same year Corini (1936) proposed a procedure to integrate Ritter's theory. Corini’s approach applies even to completely cohesionless soils, enabling the determination of both vertical and horizontal loads acting on the lining. Following Giovannini’s work, Desimon (1939) proposed an approach that links the lining thrust to a detached portion of rock and the energy stored during its formation, assuming this energy drops to zero upon material settlement. He argued that within the detached zone, internal stresses and cohesion are reduced or vanish, so the behavior is governed mainly by friction and self weight. Desimon described the isolated nucleus as an ellipse whose size depends on the tunnel geometry. Terzaghi (1943) proposed expressions to compute pressures on the tunnel’s roof in sandy soils and lately proposed a largely used classification for determining the equivalent loading body height in different types of rocks (Proctor, 1946). Later Caquot and Kérisel (1956) proposed revised expressions to estimate tangential and radial pressures in materials at plastic equilibrium, distinguishing between cohesive and cohesionless soils. Lotti (1958) highlighted the central role of experimental data in defining soil parameters, as cohesion and friction angles, from in-situ tests. He argued that, while earlier theoretical formulas offer acceptable estimates when used with reliable parameters, on-site measurements remain fundamental in their absence. Falchi Delitala (1971) provided a critical assessment of earlier methods, grouped by soil type. He considered Terzaghi and Caquot–Kérisel to be reliable for cohesionless soils. For cohesive soils, he considered Caquot–Kérisel’s expressions to be conservative and thus suitable for deep excavations. Conversely, he noticed that the application of Ritter’s and Kommerell’s theories was limited by the difficulty of defining cohesion and friction angles with adequate precision. For rock masses, Heim’s theory (Heim, 1950) was considered valid but only as long as transverse pressures remained below the rock’s tensile strength. The chronological

evolution of these methodologies is reported in the timeline of Figure 1 . For the evolution of these methods up to the present day, see (Barla, 2005).

Figure 1 Timeline about the different methods for evaluating loads acting on tunnels

In this paper two widely used tunnel design methods from the past are compared: the Sidewall Rotation Equilibrium (SRE) method proposed by Kommerell (1912) and the Soil-Thrust Wedge (STW) method proposed by Desimon (1939). These methods were selected because they define the boundaries of the structural design principles applied to