The key issue in the 3-D seismic exploration of geothermal reservoirs is to determine how the petrophysical properties of geothermal reservoirs change with temperature. In this paper, physical experiments on six rock samples from the Yunnan Lufeng geothermal field were used to analyse the effect of temperature on the elastic moduli of dry rock. The laboratory measurements show that under formation pressure conditions, the bulk modulus and shear modulus of the studied rock decrease linearly with increasing temperature, and the rock moduli exhibit approximately linear relationships with temperature. Gassmann's equation can be used to predict the influence of pore fluid on the P- and S-wave velocities of the rocks. To include the temperature effect in Gassmann's equation, we separately considered the rock matrix and pore fluid; we combined thermoelastic theory to introduce the influence of temperature on the rock into Gassmann's equation and directly considered the influence of temperature on the pore fluid. The effects of fluid on the physical properties of rocks were evaluated based on Gassmann's equation while considering the effect of temperature. The results show that the rock shear modulus is affected by temperature more than the bulk modulus is, which implies that the S-wave information is more sensitive to temperature. When the uniform water saturation is less than 95 per cent, temperature is the main factor influencing the rock bulk modulus. When the uniform water saturation is greater than 95 per cent, the fluid is the main factor influencing the rock bulk modulus, and the rock shear modulus is affected by only temperature. Fluid replacement with Gassmann's equation achieves results that are more consistent with laboratory measurements when the influence of temperature is considered. Gassmann's equation considering the effect of temperature reveals crucial dependences of the seismic wave velocities and elastic moduli on temperature and fluid content.

Coal is a complex viscoelastic porous medium with fractal characteristics at different scales. To model the macroscale structure of coal, a fractal viscoelastic model is established, and the P-wave velocity dispersion and attenuation characteristics are discussed based on the complex modulus derived from this model. The numerical simulation results indicate that the fractional order α and relaxation time τ greatly affect the P-wave velocity dispersion and attenuation. The fractal viscoelastic model indicates a full-band velocity dispersion between 1 Hz and 104 Hz. Meanwhile, the P-wave velocity has a weaker dispersion with the fractal viscoelastic model than with the Kelvin-Voigt model and Zener model between 1 Hz and 104 Hz for the same relaxation time and elastic modulus, but the velocity at 1 Hz based on the fractal viscoelastic model is higher with the Kelvin-Voigt model and Zener model. Simultaneously, the velocities of five coal samples are tested, and the attenuation factor is calculated using a low-frequency system. The experimental results indicate a strong dispersion in coal in the range of 10–250 Hz. The classic Kelvin-Voigt model and Zener model cannot describe the dispersion characteristics of coal, but the fractal viscoelastic model can describe them well by using the appropriate fractional order and relaxation time.

As a typical porous medium, unsaturated loess demonstrates critical hydro-mechanical coupling properties that fundamentally influence geohazard mitigation, groundwater resource evaluation, and foundation stability in geotechnical engineering. This investigation develops a novel theoretical framework to overcome the limitations of existing models in converting electrical resistivity tomography (ERT) profiles into water content distributions for unsaturated loess through quantitative inversion modeling. Systematic laboratory investigations on remolded loess specimens with controlled density and water content conditions revealed distinct resistivity–water interaction mechanisms. A characteristic two-stage decay pattern was identified: resistivity exhibited an exponential decrease from 420 Ω·m (water saturation (S_w = 10%)) to 90 Ω·m (S_w = 40%), followed by asymptotic stabilization at S_w ≥ 40%. The derived quantitative correlation provides a robust mathematical basis for water content profile inversion. Field validation through integrated ERT and borehole data demonstrated exceptional predictive accuracy in shallow strata (<20 m depth), achieving mean absolute errors of 20 m), primarily attributed to density-dependent charge transport mechanisms. This underscores the necessity of incorporating coupled thermo-hydro-mechanical processes for deep-layer characterization. This study provides a robust framework for engineering applications of ERT in loess terrains, offering significant advancements in geotechnical monitoring and geohazard prevention.

Accurate prediction of post-construction settlement in high-speed railway (HSR) soft foundations is critical for operational safety yet challenging due to the non-equidistant and non-stationary nature of observation data. This study systematically evaluated the robustness and accuracy of settlement prediction models using a Monte Carlo simulation approach. A numerical model incorporating the permeability characteristics of soft foundations was established to simulate stochastic system responses. Furthermore, an innovative multi-metric evaluation framework was constructed using the entropy weight method, integrating goodness-of-fit, prediction accuracy (systematic error), and stability (random error). Four classical empirical models—Hyperbolic, Exponential Curve, Asaoka, and Hoshino—were assessed. The results indicate that: (1) The Hyperbolic Method significantly outperformed other models ($p<0.01$) in goodness-of-fit (mean correlation coefficient: 0.983 ± 0.006) and accuracy (systematic error: 3.2% ± 1.1%); (2) The Hoshino Method exhibited optimal stability, characterized by the lowest random error (3.8 ± 2.0 mm); and (3) Model performance showed a significant positive correlation with the permeability coefficient ($R^2>0.92$). Validated by five distinct engineering cases, the comprehensive performance ranking was determined as: Hyperbolic > Hoshino > Exponential Curve > Asaoka. These findings provide a scientific strategy for model selection under non-stationary conditions and offer theoretical support for refining railway deformation monitoring standards.

Attenuation refers to any decrease in the power of a propagated signal through a medium. Attenuation measurement techniques include ultrasonic, resonance bar, and stress-strain methods. The stress-strain method measures elastic and viscoelastic properties in the seismic frequency range. The signals received via attenuation measurement systems using the stress-strain method can be considerably weak. Moreover, the noise in these signals causes errors when estimating the signal phase-angle difference between the sample signal and probe signal, thereby reducing system precision and measurement accuracy. Accurate measurements of such phase differences are essential to the measurement of attenuation. A seismic-wave attenuation with frequency-dependent measurement based on the stress-strain method and digital signal processing techniques has been performed. The system estimates the attenuation of a rock by measuring the phase shift in the stress-strain cycle. As a preprocessing method, the finite impulse response band-pass filters are designed to eliminate the influence of noise and direct current offset while ensuring that the phase difference of the measured signal remains unchanged. Three methods for phase difference estimation, i.e., crosscorrelation, fast Fourier transform (FFT), and Hilbert transform are compared, for different signal-to-noise ratios, sampling frequencies, data sample lengths, and true phase differences. The results find that the phase difference estimation based on FFT is the best among all three methods and can effectively improve the precision of the experimental results. Simulation and measurement results further indicate that the attenuation measurement system achieves stable and reliable attenuation measurements in the range of 3–2000 Hz.

To address the technical challenges in dynamic monitoring of grout diffusion patterns under complex geological conditions, in this study, a distributed parallel grouting monitoring system based on electrical resistivity tomography was developed. The system achieves three-dimensional visualization of grout propagation through hardware architecture innovation and the integration of inversion algorithms. At the hardware level, a cascadable distributed data acquisition terminal was designed, employing a dynamic optimization strategy for electrode combinations. This breakthrough overcomes traditional serial acquisition limitations. Algorithmically, a Bayesian estimation-based geological unit merging inversion model was proposed; it dynamically calculates merging thresholds through the noise posterior probability, achieving an improvement of more than 30% in the inversion boundary resolution compared with traditional least squares methods. Numerical simulations and physical experiments demonstrated that dipole arrays with 0.5 m electrode spacing exhibit optimal sensitivity to variations in grout resistivity, accurately capturing electrical response characteristics during diffusion. In practical roadbed grouting applications, the system yielded a grout diffusion radius showing only a 0.3 m deviation from the core sampling verification results, with three-dimensional imaging clearly depicting the diffusion morphology. This system provides reliable technical support for the precise control and quality assessment of underground engineering grouting processes.