Geotechnics

Conventional wedge analyses evaluate a block selected before calculation and do not directly resolve competition among finite blocks generated by repeated discontinuities. This study develops a deterministic phase-aware benchmark for an idealized class of rock slopes containing two planar, fully persistent, equally periodic joint systems and restricted to translational closed-contact sliding. The computational novelty is not the rigid-block equilibrium itself, which follows standard single-plane and wedge mechanics, but the explicit treatment of a relative joint-family phase, exhaustive finite-block enumeration at each searched phase, and nested minimization over phase, block and sliding mode. Computational geometry enumerates finite exposed blocks satisfying a prescribed release filter; standard rigid-block equilibrium then evaluates kinematically admissible J₁, J₂ and two-plane wedge sliding with hydrostatic loading and unilateral effective-contact admissibility. Controlled benchmarks recover the prescribed-wedge limit and demonstrate a non-monotonic spacing-dependent lower envelope; after strengthened global phase auditing, the controlled spacing sweep is J₂-controlled at all five tested spacings. A 128-case deterministic database, a 32-case adaptive audit, independent prescribed-polyhedron checks, an end-to-end phase-space stress test, enlarged-domain checks, and external wedge benchmarks support implementation consistency within the adopted model class. States that reach the unilateral contact boundary are flagged separately as ot and require opening/separation analysis rather than assignment of a closed-contact factor of safety. The framework is therefore intended as a transparent deterministic benchmark for two fully persistent periodic joint sets, not as a general model of non-persistent, opening, rotational, toppling, or deformable rock-slope behavior.

Vegetation-based slope stabilisation depends on coupled mechanical and hydraulic processes that vary with soil texture and depth. This study linked a five-month long, 0.5 m column experiment to annual two-dimensional transient seepage and analytical infinite-slope modelling to quantify how alfalfa (Medicago sativa L.) and a mycorrhiza-containing formulation affect shallow root-zone stability in silty clay (SC) and silty sand (SS). Eighteen columns (n = 3 per soil–treatment combination) received unplanted control (C), alfalfa (A), or alfalfa plus mycorrhiza formulation (A + MF). Biomass, saturated hydraulic conductivity (k_s), and saturated direct-shear response at six depths were measured. Relative to A, A + MF increased recovered root dry mass by 24.5% in SC and 53.2% in SS, and k_s by 46.6% and 47.4%. Factorial ANOVA detected a soil × treatment interaction for k_s (p = 0.00052), but not biomass. Exponential apparent-cohesion profiles separated reinforcement amplitude from depth persistence; fitted decay depths for A/A + MF were 0.167/0.176 m in SC and 0.064/0.22 m in SS. The measured mechanical and hydraulic parameters were applied to a 365-day model of a representative 1V:3H natural infinite slope. All planted cases retained higher annual minimum root-zone factors of safety than their controls, but retention, uptake and storm-timing sensitivities changed the A versus A + MF ranking. Reinforcement magnitude, depth persistence, and soil-specific hydrology should therefore be represented together when evaluating biologically treated shallow slopes.

Embankments and other compacted earth structures are widely used in civil engineering, and their mechanical behaviour depends on the properties of compacted soils, which are often affected by unsaturated conditions and matric suction. This study presents an empirical methodology aimed at the preliminary estimation of the peak friction angle of compacted unsaturated soils from cone penetration test (CPT) data, intended to support engineering assessments when laboratory testing and site investigation are limited. The approach was developed using CPT measurements collected at three levee test sites in northeastern Italy (Grizzaga, Panaro, and Tagliamento Rivers), combined with laboratory shear test results on undisturbed samples and supplemented by selected data from the literature. Three empirical equations were proposed and compared using different normalization schemes of cone tip resistance with respect to in situ stress conditions, while considering the influence of matric suction. For the soils examined in this study, the estimated peak friction angles were generally consistent with laboratory results, suggesting that the proposed relationships may provide a reasonable first approximation under similar soil conditions. The proposed procedure is intended as a preliminary engineering tool to complement, rather than replace, detailed laboratory testing in the geotechnical characterization of levees, embankments, and other compacted earth structures.