Soil massif fracturing has a significant impact on change in engineering and geological conditions and, as a result, on stability of structures. Development of tectonic fracturing of local structures, taking into account the history of the process, its mechanism, resulting stresses in the massif and subsequent deformations of the rocks, led to a change in their structure, composition and strength characteristics, activation of hypergenesis and exogenous processes. The above circumstances require careful attention to identification of areas of increased fracturing, as the most dangerous in terms of risks during the construction of engineering structures. Field methods for assessing the fracturing of rock masses are laborious. It is not always possible to conduct instrumental surveys that allow solving the final problem - establishing patterns and sizes of damaged areas within local structures. The existing mathematical models for assessing fracturing, as a rule, are used to solve local problems: assessing the stability of developed pits, water content of rock masses, degree of fragmentation of individual blocks, etc. This information is not sufficient when assessing the areal distribution of weakened zones and clarifying their boundaries, since it does not take into account the history of the development of the structure, its parameters (dimensions, amplitude of the foundation block uplift, deformation properties of rocks). Aim. To develop a mathematical model of formation of the red -colored strata tectonic fracturing zones based on deformation criterion of destruction and mechanism of development of local structures. Results. The authors have developed a new mathematical model for predicting damage (fracturing) of terrigenous rocks of the red -colored strata that make up local structures, based on the mechanism of formation of local tectonic structures of the 3rd order and the deformation criterion of destruction. The paper introduces the mathematical dependencies that make it possible to predict the size (area) of taxa based on the data on the uplift amplitude of local structures. The results of the research can be used in assessing the fracturing of massifs composed of terrigenous rocks, and make it possible to judge the regularities in distribution of weakened zones within the entire massif being assessed.

In China's Chang'e 7 mission, a miniflyer will be carried for in-situ water ice measurement in permanently shadowed regions (PSRs) around the lunar south pole. The extreme cold environment within PSRs causes serious challenges for the safety of the miniflyer. Predication of temperatures in PSR is critical for designing the internal heating system and the heat source capacity. Conducting in-situ detection mission in relatively warm temperature can reduce the threat of the cold environment and save energy to maintain a suitable operation temperature for payloads. Since the polar-orbiting satellite lunar reconnaissance orbiter passes over the same location in the polar region with intervals of about a month, the temporally continuous observation is unavailable. Simulation is necessary to determine the temporally continuous temperatures of PSR during the mission. In this article, a numerical model of the temperatures in PSR is presented. The ray tracing approach is used to calculate the shadowing effect of terrain on scattered sunlight and thermal radiation. The PSR temperatures are simulated with the one-dimensional heat conduction equation. Simulated temperatures are compared with Diviner data for validation. The spatial and temporal temperature distributions of PSRs in crater Shackleton, which is the preferred landing site for the Chang'e 7 mission, are simulated from 2026 to 2028. The simulated temperature in high temporal resolution of one Earth hour can be applied to analyzing diurnal and seasonal temperatures in PSRs and is helpful for thermal management and design of the internal heating system. The time windows with relatively warm temperature in PSR at regions with slope angles less than 5(degrees) are recommended to save energy and reduce the hazards of the extremely cold environment.

The freezing front depth (z(ff)) of annual freeze-thaw cycles is critical for monitoring the dynamics of the cryosphere under climate change because z(ff) is a sensitive indicator of the heat balance over the atmosphere-cryosphere interface. Meanwhile, although it is very promising for acquiring global soil moisture distribution, the L-band microwave remote sensing products over seasonally frozen grounds and permafrost is much less than in wet soil. This study develops an algorithm, i.e., the brightness temperature inferred freezing front (BT-FF) model, for retrieving the interannual z(ff) with the diurnal amplitude variation of L-band brightness temperature (?T-B) during the freezing period. The new algorithm assumes first, the daily-scale solar radiation heating/cooling effect causes the daily surface thawing depth (z(tf)) variation, which leads further to ?T-B; second, ?T-B can be captured by an L-band radiometer; third, z(tf) and z(ff) are negatively linear correlated and their relation can be quantified using the Stefan equation. In this study, the modeled soil temperature profiles from the land surface model (STEMMUS-FT, i.e., simultaneous transfer of energy, mass, and momentum in unsaturated soil with freeze and thaw) and T-B observations from a tower-based L-band radiometer (ELBARA-III) at Maqu are used to validate the BT-FF model. It shows that, first, ?T-B can be precisely estimated from z(tf) during the daytime; second, the decreasing of z(tf) is linearly related to the increase of z(ff) with the Stefan equation; third, the accuracy of retrieved z(ff) is about 5-25 cm; fourth, the proposed model is applicable during the freezing period. The study is expected to extend the application of L-band T-B data in cryosphere/meteorology and construct global freezing depth dataset in the future.