In order to study the deformation and failure characteristics of rocks under different cyclic loading and unloading paths, three stress path tests were conducted, and acoustic emission (AE) monitoring was conducted simultaneously. The mechanical characteristics and AE characteristics under different stress paths were analyzed, and the influences of the different stress paths on the energy dissipation and deformation damage were investigated. The law of energy evolution considering viscoelasticity under different stress paths was obtained. The concept of ultimate damage energy and its calculation method was proposed. The results show that the “hardening effect” of sandstone and granite under the constant lower limit (CLLCL) is the most significant in maximizing the mechanical property. The CLLCL imparts a stronger elastic property to rocks than the variable lower limit (VLLCL) does, while the VLLCL causes more damage to rocks than the CLLCL. A significant linear relationship between the proportion of damage energy and the proportion of elastic energy was discovered. Based on this linear relationship, the ultimate damage energy can be calculated for sandstone and granite. The evolution of the damage variable based on damage energy was compatible with the real damage condition, which validates the ultimate damage energy calculation method. The research results lay a theoretical foundation for the design and construction of geotechnical engineering.

As a new type of retaining structure, lattice beams with tie-back anchor cables have been increasingly used in slope reinforcement and have achieved improved prevention effects. However, the simplified load distribution method (SLDM) at the node, which is the theoretical basis of internal force analysis for lattice beams, is not perfect at present. An alternative new load distribution method (NLDM) at the node based on the force method for the lattice beam was therefore introduced in this paper. Taking into account the loads acting on other nodes of the beams in both directions and according to the static equilibrium condition and deformation compatibility condition at the nodes, NLDM assigns the loads acting on the nodes to the cross beams and vertical beams, respectively, by constructing and solving a system of linear equations. In order to verify the superiority of NLDM, a case of slope reinforced by a lattice beam was introduced in this paper, and the load distribution of the nodes under the design condition was carried out based on both methods. Then, the deflections at the nodes of the lattice beam resting on the Winkler foundation, loaded with the known loads, were analyzed by the superposition method. The results of the deformation analysis showed that the deflections at the same nodes of the beams in both directions based on NLDM were almost equal, thus demonstrating the superiority of NLDM in terms of deformation compatibility. In addition, a comparative analysis of the theoretical bending moments of the lattice beam under the design and the actual working conditions based on both methods was also carried out. The results of the bending moment analysis showed that the bending moments of the cross beam differed significantly in the middle third of the beam length, while the bending moments of the vertical beams differed significantly at the beam sections where the maximum bending moments are located, and the theoretical bending moments under the actual working condition were in relatively good agreement with the measured values. Consequently, NLDM for the lattice beam was self-consistent in terms of the deformation compatibility at the node, and therefore the introduction of this new method provides an important theoretical basis for the accurate internal force analysis of lattice beams.

In consideration of the temporary stability of the cutting slope during construction and its permanent stability under long-term service, a new technique of lattice beam construction with anchors pre-set in the slope from the original ground surface before cutting was proposed, and its construction process was briefly introduced. Compared with the model without pre-set anchors, the effectiveness of pre-setting anchors to strengthen the cutting slope during multi-excavation was verified in the numerical software FLAC^3D. Various factors such as the factor of safety (FOS) and the maximum shear strain increment (MSSI) as well as the displacement for different stages were discussed. The results show that the anchors pre-set in the slope provide reinforcement step-by-step with excavations which changes the mechanical responses of the cutting slope and increases the factor of safety with a variation of 15.9–44.1% compared to the case without setting anchors. In addition, with excavations, the axial forces of the anchors pre-set in the stratum increase gradually, and the positions of the maximum axial forces gradually transfer from the vicinity of the cutting surface to the depth of the design slope. Numerical simulations prove that this new technique is beneficial for ensuring the temporary stability of the slope during excavations and is especially suitable for the advance anchorage of the cutting slope, in which the inclined original ground surface is cut at an angle steeper than it can stand safely and is close to the design slope surface after cutting. After the completion of slope excavation, the cast-in-place concrete lattice beam is immediately set on the design slope surface and connected with the anchor heads exposed on the cut slope surface to ensure the permanent stability of the slope. Therefore, this new technology has important guiding significance for both the temporary stability of slopes during construction and the permanent stability of slopes in service.

This study addresses the reliance on empirical methods in the structural analysis of hinged prefabricated frame beam (HPFM) structures by proposing a theoretically rigorous analytical framework based on the Winkler foundation model. The proposed analytical framework comprises three main steps: (a) The HPFB structure is discretized into individual beam segments supported on a Winkler foundation, based on the locations of anchorage points and hinge connections; (b) A system of linear equations is formulated using static equilibrium and deformation compatibility conditions at both anchorage points and hinge joints. Solving this system yields the distribution of concentrated loads—applied perpendicular to the slope surface at anchorage points—among horizontal and longitudinal beam segments of the cross beams, and simultaneously determines the shear forces transferred through hinge joints to adjacent beam ends; and (c) The deflection and internal forces for each Winkler-supported beam segment are evaluated using the computed loads and beam-end shear forces obtained in the previous step. To evaluate the validity and practical applicability of the proposed framework, a simplified HPFB structure was analyzed in terms of load distribution, beam-end shear forces, deflections, and internal forces. The results were compared with those from a traditional frame beam (TFB) structure under identical conditions to assess differences in mechanical behavior between the two structures. Deformation analysis at both the anchorage points and hinge joints indicates that the proposed analytical framework inherently satisfies deformation compatibility conditions at the anchorage points and hinge joints. Consequently, the results demonstrate improved accuracy compared to those derived from empirical methods. Comparative analysis reveals that, relative to the TFB structure, the HPFB structure exhibits larger deflections near the beam ends and smaller deflections in regions farther away from the beam ends, along with a reduced maximum negative bending moment, an increased maximum positive bending moment, and lower maximum shear forces. These results suggest that the HPFB structure offers improved mechanical performance. A sensitivity analysis was further performed to quantify the influence of the subgrade reaction coefficient on the mechanical behavior of the HPFB structure. As the subgrade reaction coefficient increases multiplicatively, the concentrated loads allocated to the shorter horizontal beam segments and their corresponding beam-end shear forces exhibit a progressive increase. Conversely, the loads assigned to the longer longitudinal beam segments and the associated beam-end shear forces demonstrate a consistent decrease.Variations in beam loading induced by a multiplicative increase in the subgrade reaction coefficient significantly influence beam deflection, yet exert only a minimal effect on both the bending moment and shear force. Consequently, the proposed analytical framework establishes a robust theoretical foundation for the rational design of HPFB structures, diminishing the dependency on empirical approaches and enhancing the reliability of structural performance predictions.

Conventional structural analysis of hinged precast frame beams (HPFB) often relies on a simplified load distribution method that may not fully account for deformation compatibility, potentially affecting result accuracy. To address this limitation, this paper develops a rigorous analytical framework based on the Winkler foundation model. The framework explicitly incorporates soil-structure interaction (SSI) and enforces static equilibrium and deformation compatibility at all structural nodes and hinges, thereby enabling a mechanically consistent prediction of structural responses. A comprehensive comparative analysis with a traditional frame beam (TFB) reveals the unique mechanical behavior of the HPFB system. Key findings demonstrate the HPFB configuration achieves a drastic reduction in maximum negative bending moment (63.5–83.5%) and shear force (7.8–22.8%), while increasing the maximum positive bending moment by 46–62%. This fundamental shift in internal forces occurs in conjunction with a characteristic segmented deflection profile. Sensitivity analysis further indicates that while the subgrade reaction coefficient significantly influences deflection patterns, its effect on bending moments and shear forces remains marginal. The proposed framework provides designers with a robust and theoretically sound tool for the analysis and design of HPFB structures, ensuring performance reliability while addressing limitations observed in current analytical approaches.