PSI - Issue 84

Federico Foria et al. / Procedia Structural Integrity 84 (2026) 304–312

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Fig. 5. Identification of three main discontinuity sets (bedding planes and fractures) from point cloud analysis, and their spacing.

The uniaxial compressive strength (UCS) can be derived from the rebound index (R) obtained through Schmidt hammer tests (refer to the ISRM guidelines for the detailed work-flow), by means of empirical correlation proposed by several authors according to the lithology involved and the boundary conditions (e.g. Irfan & Dearman 1978, Sachpazis 1990, Katz, 2000).

2.3.2 Evaluation of possible collapsing/sliding mechanisms

The estimation of defects is part of the calculation of the overall vulnerability class. Two classes are considered: detachment of weathered rock (Defects 1.9 of the guidelines) and detachment of portions of tabular/stratified rock (Defects1.10 of the guidelines). According to the guidelines, each tunnel segment should be assigned with a defect severity class, G (four levels, increasing in severity), based on the measured extension (k1) and intensity (k2) of the defect. Here we propose an approach aimed at ensuring that observations are consistent, comparable, and repeatable over time, enabling an objective evaluation of defects and their progression. Regarding Defect 1.9, these parameters are quantitatively determined based on the statistical distribution of the failure mechanisms (kinematic stability analysis) identified by comparing the distribution and orientation of discontinuities obtained from the geomechanical survey (point cloud analysis integrated with traditional in-situ survey) with the planes that best approximate the sidewalls and the crown of the tunnel. The kinematic stability analysis is conducted using the Markland test (Markland 1972) which enables the assessment of whether the existing discontinuities may result in planar sliding or wedge sliding mechanisms when intersecting a plane, considering an assumed friction angle. The purpose of this approach is to quantify the structural elements that are found to be kinematically unstable expressed in percentage. In practical terms, the crown geometry is approximated by two principal planes. The kinematic analysis is then conducted for both mechanisms (planar and wedge sliding) on each of these two planes, and for the two planes representing the sidewalls. K1 (Extension) is intended to identify the presence of the phenomenon. A Boolean approach (0/1) is applied to each of the two surfaces representing the crown: for each kinematic mechanism, a value of 0 is assigned when no unstable elements are detected, and 1 when at least one unstable element is present. The same procedure is applied to the two surfaces that represent the sidewalls of the tunnel. K2 (Intensity) measures the magnitude of the phenomenon. The percentages of unstable elements detected by the Markland's tests are used, with a graduated scoring system (from 0 to 3).