Freezing design method for inclined shaft crossing strong permeable pebble layer

Abstract

The application discloses a freezing design method for a strong water-permeable pebble layer through a freezing process of an inclined shaft, and particularly relates to the technical field of freezing construction. The rock and soil parameters and the regional historical environment temperature of the pebble layer through which the target inclined shaft passes are obtained; a three-dimensional geometric model of the inclined shaft is established to determine the position, inclination and spacing of the freezing pipes arranged along the shaft axis; a spatial model of the freezing area coupled with the pebble layer is constructed; a freezing-heat-seepage multi-field coupling model is constructed according to the historical environment temperature and the freezing pipe arrangement information, the formation process of the freezing body is numerically simulated, and the evolution functions of the freezing boundary expansion range and the freezing thickness at different times are obtained; the freezing coverage is analyzed to determine whether each depth section meets the design freezing thickness and safety factor requirements. The method can realize multi-physical field coupling modeling of the freezing process and accurate control of the freezing body evolution, has the advantages of strong predictability, uniform freezing effect and the like, and is particularly suitable for the freezing design and construction of the inclined shaft under complex geological conditions.

Description

Technical Field

[0001] This invention relates to the field of freezing construction technology, specifically to a method for designing the freezing of inclined shafts through highly permeable pebble layers. Background Technology

[0002] In underground engineering, mine tunnels, and urban rail transit construction, inclined shafts are often used to traverse complex geological formations to achieve rapid excavation and structural connections. For complex geological conditions such as highly permeable pebble layers, due to their high porosity and high water flow velocity, traditional freezing methods struggle to form a continuous and stable freezing curtain in a short time. Furthermore, the freezing pipe layout angle is poorly adapted to the inclined shaft structure, easily causing problems such as frozen body displacement and uneven freezing, directly affecting tunneling safety and project quality.

[0003] Currently, the freezing method faces the following technical challenges when traversing water-bearing pebble layers: First, the freezing body takes a long time to form, and the freezing rate is greatly affected by groundwater disturbance; second, the traditional planar pipe layout method is difficult to adapt to the space and inclination angle requirements of inclined shafts; and third, the freezing calculation model often ignores the freezing thermal coupling effect and the heterogeneous distribution characteristics of the pebble layer, resulting in low design accuracy. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for freezing inclined shafts through highly permeable pebble layers to address the shortcomings of the prior art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for designing a method for freezing inclined shafts through highly permeable pebble layers, comprising: S1. Obtain the soil and rock parameters of the pebble layer in the target inclined shaft crossing section and the historical ambient temperature of the area; S2. Establish a three-dimensional geometric model of the inclined shaft, determine the position, inclination angle and spacing of the freezing pipes along the axis of the inclined shaft, and construct a spatial model of the frozen area coupled with the pebble layer; S3. Based on historical ambient temperature and freezing pipe layout information, a multi-field coupled model of freezing-heat transfer-seepage is constructed to numerically simulate the formation process of the frozen body and obtain the evolution functions of the freezing boundary expansion range R(t) and freezing thickness d(t) at different times t. S4. Based on the spatiotemporal development pattern of the frozen body, analyze the freezing coverage rate within different depth ranges of the inclined shaft, and determine whether the crossing safety conditions are met based on the minimum freezing thickness and the design safety factor. S5. If not satisfied, adjust the freezing pipe parameters according to the angle of the inclined well and the groundwater flow velocity, reconstruct the spatial model of the frozen area and return to S3; if satisfied, output the freezing design parameters, including freezing duration, freezing pipe spacing, freezing temperature control curve and freezing termination judgment conditions.

[0006] Preferably, obtaining the geotechnical parameters of the pebble layer traversed by the target inclined shaft and the historical ambient temperature of the area includes: The permeability coefficient distribution k(z) of the pebble layer at different depths was obtained by combining drilling sampling with in-situ permeability testing, where z is the depth coordinate along the axis of the inclined well. The specific heat capacity, thermal conductivity and initial water content of the undisturbed pebble layer samples were determined by thermophysical property testing methods. The functional relationship curves P(z) of thermophysical property parameters with depth were constructed by fitting the experimental data with the stratigraphic classification. We constructed the multi-year average evolution curve of the daily average surface temperature during typical seasons during the freezing period, and combined it with the geothermal gradient formula to inversely deduce the shallow geothermal field distribution T(z,t). The permeability coefficient k(z), thermophysical parameter P(z), and geothermal field T(z,t) are used as initial boundary conditions input into the spatial model of the frozen region.

[0007] Preferably, the step of establishing a three-dimensional inclined shaft geometric model and determining the position, inclination angle, and spacing of the freezing pipes along the inclined shaft axis includes: Obtain the spatial orientation, longitudinal profile parameters, and positional relationship between the target inclined shaft and the contact interface with the pebble layer. Construct a spatial interaction model between the inclined shaft and the pebble layer, and extract the path function L(x,y,z) of the inclined shaft axis in the three-dimensional coordinate system. Using the path function L(x,y,z) as a reference, the initial plan for laying out the freezing pipes in its normal profile is adopted by orthogonal projection. The angle between the inclination angle of the freezing pipes and the axis of the inclined well is controlled within a preset range. The coverage overlap rate of the freezing curtain at each depth is evaluated by combining the permeability coefficient distribution k(z) of the pebble layer. Based on the predicted results of coverage overlap rate and freezing body closure time, a freezing efficiency evaluation function is constructed to iteratively optimize the initial layout scheme of freezing tubes and output the final layout coordinates, tilt angle and spacing parameters of freezing tubes in three-dimensional space.

[0008] Preferably, the construction of the frozen region spatial model coupled with the pebble layer includes: Based on the three-dimensional geological structure model, the range, thickness, permeability coefficient zoning of the pebble layer and its relative position to the axis of the inclined well are imported. The frozen-affected zone and the unaffected zone within the pebble layer are identified, and the initial frozen simulation envelope is delineated with the freezing pipe layout area as the center. Based on the geothermal field T(z,t), freezing initiation temperature, soil moisture content, and latent heat of freezing parameters, a model for the changes in thermal conductivity and water migration coefficient before and after freezing is constructed, a dynamic heat-water coupling coefficient field is established, and the coupling coefficient field is embedded into the spatial grid model of the frozen area. By using adaptive mesh generation technology, the frozen boundary region is refined, and the coupled modeling of the frozen region spatial model and the spatial interaction model is completed.

[0009] Preferably, the step of constructing a multi-field coupled model of freezing-heat transfer-seepage based on historical ambient temperature and freezing pipe layout information includes: The multi-year average surface temperature curve during the freezing period is used as the upper boundary condition. Combined with the geothermal gradient model, the time temperature field T(z,t) at different depths is calculated. Then, the freezing pipe layout coordinates, freezing temperature control curve and circulation flow parameters are used as internal boundary conditions to form a time-space distributed freezing source term field. The heat conduction equation and water seepage equation of the soil in the frozen area are established. Considering the release of latent heat of freezing, phase change of pore water and phase change degradation effect of permeability coefficient, a set of multi-physical response functions of heat transfer-seepage-phase change is constructed, in which the coefficient parameters of each physical field are dynamically updated with temperature and saturation. Based on the finite difference method, loose coupling is used to iteratively solve the heat conduction equation and the seepage equation in the same simulation step.

[0010] Preferably, the numerical simulation of the formation process of the frozen body to obtain the evolution functions of the frozen boundary expansion range R(t) and the frozen thickness d(t) at different time t includes: Based on the constructed freezing-heat transfer-seepage coupling model, the initial freezing temperature field, freezing pipe boundary temperature, and soil thermal-hydraulic physical parameters are input to carry out multi-time freezing simulation and obtain the response data of temperature and moisture content at each node during the freezing process. Within each freezing simulation period, the boundary position of the frozen body is identified based on the freezing criterion temperature. An isothermal surface extraction algorithm is used to generate the three-dimensional boundary envelope surface of the frozen area. The maximum lateral expansion radius R(t) of the frozen body and the thickness d(t) of the freezing curtain are calculated to form a freezing boundary time series dataset. Regression analysis and fitting were performed on the dataset of frozen boundary parameters changing over time to construct the frozen extension boundary evolution function R(t) and the frozen thickness evolution function d(t).

[0011] Preferably, the step of analyzing the freeze coverage rate at different depths of the inclined shaft based on the spatiotemporal development pattern of the frozen body includes: The freezing boundary evolution function R(t) and the freezing thickness function d(t) are mapped to the three-dimensional freezing region spatial grid, and multiple depth segments are divided along the inclined shaft axis. The cross-sectional profile data of the freezing curtain of each segment at different times are extracted. Based on the cross-sectional geometry of the frozen curtain in each depth segment, the cross-sectional area Af of the frozen area and the theoretical frozen control area At are calculated. The ratio of these values ​​is used to define the frozen coverage index, and a distribution function for the frozen coverage as a bivariate of depth and time is established. Gradient analysis was performed on the frozen coverage distribution function to identify weak areas where the coverage was below the safety threshold, and a spatial distribution map of the freezing effect of the inclined well was generated.

[0012] Preferably, the step of determining whether the crossing safety conditions are met based on the minimum freezing thickness and the design safety factor includes: Set the minimum freezing thickness for design Based on the construction load level and groundwater pressure of penetrating the pebble layer, the appropriate design safety factor K is selected, and the lower limit of the required theoretical freezing thickness is calculated. ; The frozen thickness evolution function d(t) is compared with the frozen thickness d(z,t) of each depth segment in the frozen spatial model to determine the freezing stability at the moment. Does it satisfy the following? This forms a safety determination matrix for the frozen thickness. Depth sections that do not meet the safety criterion for freezing thickness are marked and output as areas where crossing conditions are not met.

[0013] The technical effects and advantages provided by the present invention in the above technical solution are as follows: 1. This invention establishes a freezing design method that integrates the geometric characteristics of inclined shafts, freezing evolution patterns, and permeability characteristics of pebble layers. This method achieves system integration of key aspects such as freezing pipe layout, freezing zone modeling, multi-field coupled simulation, freezing boundary prediction, and safety verification. By introducing freezing coverage indicators and a freezing thickness safety matrix, it can accurately identify weak freezing zones and dynamically adjust design parameters.

[0014] 2. The multi-field coupling and adaptive optimization strategy proposed in this invention effectively solves the problems of uneven freezing expansion, unbalanced freezing body formation, and difficulty in identifying freezing failure zones in highly permeable pebble layers. It has significant advantages such as more comprehensive structural response, more intelligent parameter control, and more refined model prediction. It is particularly suitable for inclined well freezing projects with complex geological conditions and large structural morphological changes. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0016] Figure 1 This is a schematic diagram of the method of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] For examples, please refer to Figure 1 As shown in this embodiment, the method for designing the freezing of inclined shafts through highly permeable pebble layers includes: S1. Obtain the soil and rock parameters of the pebble layer in the target inclined shaft crossing section and the historical ambient temperature of the area; S2. Establish a three-dimensional geometric model of the inclined shaft, determine the position, inclination angle and spacing of the freezing pipes along the axis of the inclined shaft, and construct a spatial model of the frozen area coupled with the pebble layer; S3. Based on historical ambient temperature and freezing pipe layout information, a multi-field coupled model of freezing-heat transfer-seepage is constructed to numerically simulate the formation process of the frozen body and obtain the evolution functions of the freezing boundary expansion range R(t) and freezing thickness d(t) at different times t. S4. Based on the spatiotemporal development pattern of the frozen body, analyze the freezing coverage rate within different depth ranges of the inclined shaft, and determine whether the crossing safety conditions are met based on the minimum freezing thickness and the design safety factor. S5. If not satisfied, adjust the freezing pipe parameters according to the angle of the inclined well and the groundwater flow velocity, reconstruct the spatial model of the frozen area and return to S3; if satisfied, output the freezing design parameters, including freezing duration, freezing pipe spacing, freezing temperature control curve and freezing termination judgment conditions.

[0019] In this invention, in order to accurately simulate and predict the freezing expansion characteristics of the area where the inclined shaft passes through a highly permeable pebble layer, it is necessary to first obtain the key soil and rock parameters of the pebble layer in the crossing section and the historical environmental temperature data of the area, and use them as the initial boundary conditions input of the freezing model to ensure that the simulation process has geological adaptability and thermal-water coupling response capability.

[0020] First, data was collected at multiple points and depths in the pebble layer area traversed by the target deviated well through a combination of drilling sampling and in-situ permeability testing. Specifically, several representative boreholes were selected, and test points were set up at certain depth intervals (e.g., every 1 meter) in each borehole. The permeability coefficient at each point was determined using a double-ring permeability test or a pressure water test. To reflect the heterogeneity of the pebble layer's permeability characteristics, the depth value corresponding to each test point was labeled z, and a distribution function k(z) of the permeability coefficient as a function of depth was constructed. This function can be fitted using spline interpolation, polynomial fitting, or other least squares methods to reflect the longitudinal hydraulic characteristics of the pebble layer along the axis of the deviated well.

[0021] Secondly, to establish the thermal field evolution boundary during the freezing process of the deviated well, it is necessary to determine the thermophysical parameters of undisturbed gravel layer samples. Specifically, representative undisturbed gravel layer samples are obtained simultaneously during drilling, and their specific heat capacity, thermal conductivity, and initial water cut are measured using laboratory thermophysical property testing equipment (such as thermal conductivity meters and specific heat meters). To avoid errors caused by changes in particle composition and water content, the samples are classified according to stratigraphic position, and statistical analysis is performed on the data of each type. Based on this, a function P(z) is constructed to represent the variation of thermophysical parameters with depth, where P(z) is a set of multiple parameters including specific heat capacity, thermal conductivity, and water cut, and z is the depth. This function can be established using a regression analysis model to reflect the changing trend of thermal conductivity along the depth direction of the deviated well.

[0022] Third, regarding the boundary heat source situation during the freezing period, by analyzing historical meteorological data of the target area over the past ten years or longer, and selecting daily average surface temperature data of typical cold seasons (such as January to February), we can plot and construct the multi-year average evolution curve of daily average surface temperature in the region. Where t is the time variable within the freezing period. To extend surface temperature into the underground space, a geothermal gradient formula is further adopted, which assumes that the geothermal temperature increases linearly or nonlinearly with depth z. This is combined with measured geothermal data to infer the shallow geothermal field T(z,t) within the freezing area. T(z,t) can be expressed as the surface temperature... Adding the product of the temperature gradient term and depth z results in a two-dimensional distribution function that reflects the co-variance of geothermal temperature with both time and depth. For areas affected by local groundwater disturbance, a correction term can be introduced to improve the accuracy of geothermal predictions.

[0023] Finally, the permeability coefficient distribution k(z), the thermophysical parameter function P(z), and the shallow geothermal field T(z,t) obtained above are used as the initial boundary conditions input for the freezing simulation model. k(z) controls the convection effect and seepage field evolution of groundwater during the freezing expansion process; P(z) describes the thermal conductivity and freezing delay of the frozen body in the heterogeneous pebble layer; and T(z,t) directly determines the freezing initiation conditions and the dynamic changes in boundary heat flux during the freezing forward simulation. In specific numerical simulation software (such as FLAC3D or COMSOL Multiphysics), the above functions can be defined through table input or boundary function interface, and together with the freezing pipe layout model and the freezing cycle temperature control curve, they constitute a complete spatial model of the frozen region.

[0024] In this invention, to improve the design accuracy and freezing effect of the freezing method in inclined shafts traversing highly permeable pebble layers, a complete process from frozen geometric modeling to coupled modeling of the frozen area and geological model is proposed. This process comprehensively considers the three-dimensional orientation characteristics of the inclined shaft, the arrangement of freezing pipes, and the water-thermal properties of the pebble layer. In the initial stage of freezing, a high-precision, responsive frozen simulation area is constructed, providing boundary conditions and computational basis for subsequent thermal-water coupled numerical simulation.

[0025] First, acquire the spatial orientation information of the target inclined shaft, including the three-dimensional coordinates of the starting and ending points, elevation changes, dip angle, curve segment radius, vertical projection length, and longitudinal profile parameters along the axis. Simultaneously, acquire the contact interface data between the inclined shaft and the pebble layer it traverses, such as the entry point, exit point, elevation difference, and intersection angle. Then, using three-dimensional geological modeling software (such as Surfer, GOCAD, or a custom CAD-BIM interface), construct a three-dimensional interactive model of the spatial structure of the inclined shaft's central axis and the pebble layer.

[0026] Based on this, the path function L(x,y,z) of the inclined shaft axis in the three-dimensional coordinate system is extracted. This function is obtained by spatial interpolation fitting of the inclined shaft direction data. L(x,y,z) can be represented as a set of parametric functions with arc length s as independent variable, for example, L(s) = [x(s), y(s), z(s)], which is used to describe the spatial reference line on which the freezing pipe layout is based.

[0027] Subsequently, using the path function L(x,y,z) as a reference, the orthogonal projection pipe laying method was adopted to initially lay the freezing pipes in the local normal profile of the inclined shaft axis. The freezing pipe array was arranged in a ring or fan shape, and the angle between each freezing pipe and the inclined shaft axis was controlled within the range of 10° to 30° to balance the freezing coverage and construction convenience.

[0028] To improve the uniformity of the freezing effect and the degree of curtain closure, the arrangement of freezing pipes was further coupled with the permeability coefficient distribution k(z) of the pebble layer. By analyzing the response relationship between the spacing of freezing pipes and the hydraulic conductivity of the pebble layer at various depths, the coverage overlap rate of the frozen curtain at different depths was calculated. This index is defined as the ratio of the overlapping area of ​​the frozen zone to the area of ​​the theoretical frozen zone, reflecting the closure integrity of the frozen body.

[0029] Based on this, the predicted closure time of the frozen body is introduced, and a freezing efficiency evaluation function is constructed by combining the freezing coverage overlap rate. This function can be expressed as freezing efficiency E = f(freezing time tclosure, coverage overlap rate Roverlap). Through objective function optimization, the freezing pipe layout parameters are iteratively adjusted, including freezing pipe spacing d, layout density n, and layout angle α. Finally, the layout coordinate set, inclination parameters, and spatial spacing of the freezing pipes in three-dimensional space are output to ensure that the frozen body can be stably formed and effectively closed throughout the entire inclined well section.

[0030] After the freezing pipes are laid out, the next step is to carry out spatial modeling of the frozen area. The core objective of this step is to construct a spatial model of the frozen area that can be used for thermal-hydraulic coupled numerical simulations. This model must maintain a high degree of accuracy in matching the geological structure of the pebble layer to ensure that the simulation results truly reflect the engineering environment.

[0031] First, the geometric extent, thickness distribution, and permeability coefficient zoning of the pebble layer were imported based on geological modeling data. The pebble layer traversed by the inclined well axis was divided into several regions with different permeability characteristics, and the freezing-affected zone and non-affected zone within the effective range of the freezing method were identified. The freezing-affected zone was defined as the thermal conduction radius R of the freezing pipe. t The boundary of the region within the range can be estimated using the initial thermal conductivity radius.

[0032] A freezing simulation envelope is established around the freezing pipe layout area. This envelope serves as the outer boundary for spatial modeling of the freezing area. Its three-dimensional structure is an irregular long cylinder or an approximate ellipsoid that extends along the axis of the inclined shaft. Its cross-sectional dimensions are set based on empirical values ​​of the freezing heat diffusion theory, and are usually 1.5 to 2 times the radius of the freezing pipe.

[0033] Secondly, based on the obtained geothermal field T(z,t), freezing initiation temperature Tf, and initial soil moisture content... Based on parameters such as latent heat of freezing (Lf), a model was constructed to demonstrate the variation of thermal conductivity λ(T) and moisture transport coefficient D(W) during the freezing process. The model showed that thermal conductivity λ increases with decreasing temperature, while moisture transport coefficient D drops sharply at the freezing initiation point, exhibiting a significant nonlinear change.

[0034] The aforementioned model is used to construct a dynamic heat-water coupled parameter field, which reflects the dynamic changes in the heat transfer capacity and moisture migration capacity of the soil surrounding the inclined well during the freezing process. This coupled parameter field is embedded into the spatial grid model of the frozen area to realize the physical behavior response mechanism of the freezing model.

[0035] Finally, an adaptive mesh generation technique was employed to discretize and model the frozen region, with a particularly refined meshing strategy used in the frozen boundary region to improve the accuracy of boundary capture. To accommodate the dynamic expansion process of the frozen body, a triggering mechanism for changes in state parameters before and after freezing was introduced. By comparing the changes in the temperature and moisture fields of the elements, the direction and rate of frozen boundary advancement were identified, enabling dynamic migration identification and updating of the frozen body boundary.

[0036] The spatial model of the frozen region is integrated with the aforementioned three-dimensional inclined well-pebble layer interaction model through coordinate mapping and boundary coupling, achieving a unified representation of the frozen simulation area and geological structure. This model can be imported into multiphysics coupling analysis software platforms (such as COMSOL, FLAC3D, etc.) as a foundational platform for subsequent analysis of heat conduction, seepage, and deformation during the freezing process.

[0037] To achieve high-precision prediction of the freezing process of inclined wells in highly permeable gravel layers, this invention provides a multi-field coupled modeling method for freezing-heat transfer-seepage that integrates historical ambient temperature information, freezing pipe layout parameters, and soil physical properties. Based on this method, numerical simulation of the frozen body expansion process is carried out, the evolution characteristic function of the frozen boundary is extracted, and a time response prediction mechanism for freezing thickness and freezing radius is formed.

[0038] This invention first uses the multi-year historical surface temperature curve within the freezing period as the basis for external boundary conditions to construct a model of the freezing heat source and environmental field input. By retrieving nearly ten years of winter meteorological observation data for the target project area, the daily average surface temperature during the freezing period is calculated. The original data is smoothed using a moving average method or a Fourier periodic function to obtain a temperature change function that combines periodic and random disturbances. This function serves as the input to the upper boundary temperature field of the frozen model.

[0039] To simulate the heat transfer effect from the surface to the deeper layers of the frozen region, a vertical temperature field T(z,t) is further constructed based on a geothermal gradient model. Considering the linear geothermal gradient G (in °C / m) under steady-state heat transfer conditions, the initial temperature at a certain depth z of the stratum can be expressed as: , where z is the vertical depth from the Earth's surface. For areas with groundwater disturbance or thermal convection coupling, a formation thermal conductivity adjustment coefficient can be introduced to correct for temperature decay.

[0040] Subsequently, by combining the three-dimensional coordinates of the freezing tube arrangement, the freezing liquid temperature control curve Tc(t), and the circulation flow rate Q(t) in the freezing design scheme, a heat source distribution model of the freezing tube is constructed. The freezing tube is discretized into several heat source units, and their temperature control strategies at each time step are defined. These units are then mapped to corresponding nodes in the simulation region according to their spatial locations, forming a freezing source term field with spatiotemporal distribution characteristics, which serves as the internal boundary input of the model.

[0041] After setting the boundary conditions, the following set of governing equations are established for the multi-physical response behavior of the pebble layer region where the frozen body is located: Heat conduction equation: used to describe the temperature change with time and space during freezing, considering the influence of the latent heat of freezing of soil, and adopting the unsteady-state heat conduction differential form; Water seepage equation: Based on the theory of saturated / unsaturated porous media, a groundwater migration control model is constructed to reflect the redistribution mechanism of water during the freezing expansion process; Phase change response mechanism: Considering the energy release brought about by the phase change of water in the soil from liquid to solid during freezing, and the dynamic influence of this process on permeability and thermal properties, the permeability coefficient k decreases exponentially with the increase of ice fraction, and the thermal conductivity λ also shows segmented changes before and after freezing.

[0042] The aforementioned governing equations are transformed into a numerically solvable form. Spatial and temporal discretization is performed using the finite difference method, and a loosely coupled computational strategy is employed to iteratively solve the heat conduction and moisture seepage equations simultaneously. Within each computational time step, the temperature field distribution is first iteratively solved, then the water content and permeability of each node are updated based on the temperature, and this information is fed back to the next round of temperature calculation until convergence. This method enables the simultaneous simulation of freezing temperature gradients, moisture migration paths, and the formation process of frozen regions.

[0043] Based on the established freezing-heat transfer-seepage coupled model, a multi-time-period freezing simulation experiment was conducted. The initial temperature field T0(z), the working temperature of the freezing pipe Tc, and the soil thermophysical parameters P(z) were input. The freezing time span (e.g., simulating a 90-day cycle) and the calculation time step (e.g., every 12 hours) were set, and a multi-step iterative simulation was run to obtain the response data of temperature T(x,y,z,t) and moisture content S(x,y,z,t) of each grid node in the frozen region as a function of time.

[0044] In each freezing simulation time step, the current freezing region boundary is identified based on freezing criteria (e.g., temperature below -1℃, water content below critical saturation, etc.). An isothermal surface extraction algorithm is used to extract the temperature field isosurface from the 3D mesh, and this surface is defined as the freezing boundary surface. This freezing boundary constitutes the 3D spatial envelope of the frozen body, recording the geometric characteristics of the frozen region at each time t.

[0045] Furthermore, based on the extraction of the frozen boundary, the maximum expansion radius R(t) of the frozen body in the orthogonal direction of the inclined shaft axis is calculated, i.e., the farthest distance from the outer boundary of the frozen body to the axis, and the thickness d(t) of the closed region of the frozen body opposite the center of the freezing pipe. The corresponding distance data are obtained using geometric analysis or discrete node fitting methods, and a frozen boundary time series dataset is generated. , where n is the total number of time series data.

[0046] The frozen boundary dataset is input into the regression analysis module, and a suitable nonlinear function (such as a logarithmic growth function, a hyperbolic function, or a piecewise power function) is selected for fitting. Finally, the evolution function of the frozen expansion radius R(t) and the evolution function of the frozen thickness d(t) are constructed. Taking a common piecewise power function as an example, the frozen thickness d(t) can be expressed as: Where a and b are the fitting coefficients. dmax represents the stable time point at which the frozen curtain tends to close, and dmax represents the maximum thickness of the frozen body. The frozen expansion radius R(t) can also be expressed in a similar way.

[0047] To address the presence of groundwater disturbance, a disturbance correction term is introduced into the fitting results. For example, the linear negative influence of groundwater flow velocity v on freezing rate is considered to construct a freezing prediction model that more closely reflects the actual environment. Where α and β are disturbance influence coefficients, v is groundwater flow velocity, and d'(t) and R'(t) are the corrected freezing boundary functions.

[0048] In this invention, in order to achieve quantitative assessment of the formation quality of frozen bodies and accurate determination of the safety of freezing construction, a freezing coverage analysis mechanism based on the spatiotemporal evolution law of frozen bodies is further constructed, and combined with structural design standards, the safety judgment of crossing is achieved through the freezing thickness verification method.

[0049] Under the cooling effect of the freezing pipes, the frozen body gradually expands into the surrounding soil, and its spatial geometry exhibits non-uniformity over time. Particularly in inclined shaft structures, due to the spatial tilt angle between the shaft axis and the arrangement of the freezing pipe array, the expansion of the frozen body is influenced by factors such as differences in soil thermal properties, the density of the freezing pipes, and groundwater disturbance, resulting in significant differences in the cross-sectional morphology of the frozen body at different depths. Therefore, this invention proposes using the frozen body coverage rate as the core indicator to conduct a stratified evaluation of the formation effect of the frozen body at each depth level.

[0050] First, the constructed frozen boundary extension function R(t) and frozen thickness function d(t) are mapped onto the three-dimensional spatial mesh of the frozen region. The spatial mesh W(x,y,z) of the frozen region has been established in the previous steps. Based on the inclined shaft axis L(x,y,z), the frozen model is divided into multiple depth segments Δz along the axis direction. Each segment represents a frozen sub-region with independent freezing characteristics.

[0051] At each time t in the freezing simulation, the cross-sectional profile of the frozen curtain within each depth segment Δzᵢ is extracted. The profile extraction method is based on the isothermal surface defined by the freezing criterion in the temperature field (e.g., temperature below -1℃), forming a closed freezing boundary curve on each profile. The actual frozen cross-sectional area Af(z,t) enclosed by this profile is calculated using a geometric algorithm.

[0052] Meanwhile, during the freezing design phase, the theoretical freezing cross-sectional area At(z) within the freezing design control range has been set, which is determined based on engineering parameters such as the freezing pipe layout boundary or the required surrounding rock support width.

[0053] The frozen coverage C(z,t) is defined as: This indicator reflects the completeness of the frozen curtain formation at various depths, and its value ranges from 0 to 1. When C is close to 1, it indicates that the freeze is fully closed; when C is low, it indicates that there are weak or unfrozen areas in the section.

[0054] The data on the change of frozen coverage over time for all layers are organized into a frozen coverage distribution function C(z,t), which is a depth-time bivariate response matrix. By visualizing C(z,t), isopleth maps and heat maps of frozen coverage can be drawn to show the formation pattern of frozen bodies at different depths and freezing periods.

[0055] To identify vulnerable areas affecting traversal safety, this invention further introduces a freeze coverage safety threshold. This threshold is set based on construction experience or structural safety specifications (e.g., 0.8~0.9), when the coverage of a certain floor section... During the frozen stable moment Less than This refers to sections marked as insufficiently covered by freezing, which can serve as key control objects for subsequent optimization design or local reinforcement.

[0056] Finally, all depth segments with freezing coverage less than the threshold are integrated to form a spatial distribution map of the freezing effect of the inclined shaft, which is used to guide the local adjustment of freezing parameters and the identification of crossing risks.

[0057] To ensure the safe passage of inclined shaft excavation through areas with highly permeable gravel layers, this invention, based on the assessment of frozen coverage rate, further uses frozen thickness as a criterion to verify structural safety, and proposes a safety judgment method based on minimum frozen thickness and design safety factor.

[0058] First, based on the engineering design requirements and the formation hydraulic conditions, the minimum freezing thickness is set. The thickness is typically selected between 0.8 and 1.5 meters. The freezing thickness is the minimum distance between the closed areas on both sides of the frozen body, which determines its comprehensive protection against groundwater infiltration, surrounding rock pressure, and temperature stability.

[0059] Considering the complex structural stress conditions during the inclined shaft crossing process, a design safety factor K (generally ranging from 1.3 to 1.8) needs to be introduced to ensure sufficient safety redundancy in the frozen thickness. The theoretically required lower limit of the frozen thickness. The calculation formula is: ;in, This represents the lower limit of the required freezing thickness for each depth segment.

[0060] The frozen thickness d(z,t) of each depth segment extracted from the freezing simulation is compared with the freezing stabilization time. The following is the frozen thickness value By comparison, a safety judgment matrix S(z) for the frozen thickness is established, which is expressed as: If If, then S(zᵢ) = 1 (safe); if If the condition is not met, then S(zᵢ) = 0 (unsafe). This matrix reflects the safety status of each depth segment, and the frozen weak segments that do not meet the crossing conditions can be quickly identified through intuitive layout.

[0061] In this invention, the aforementioned steps have completed multi-field simulation of the frozen body formation process, construction of the frozen boundary evolution function, coverage analysis, and crossing safety verification. To achieve closed-loop control in engineering design, this step further proposes a feedback adjustment and finalization mechanism for frozen design parameters. Analysis using the frozen thickness determination matrix S(z) and the frozen coverage function C(z,t) revealed that the frozen coverage rate in certain depth sections of deviated wells did not reach the safe threshold. or frozen thickness Less than design requirements If the current parameter combination fails to meet the crossing safety conditions, the freezing scheme is considered to be ineffective. In this case, the system will trigger a freezing scheme optimization feedback mechanism, primarily involving the following two parameter adjustment directions: Inclined shaft structures typically have a certain inclination angle θ (the angle between the inclination and the horizontal plane). If the freezing pipes are arranged strictly vertically, it may cause uneven cooling coverage of the frozen body along the axis of the inclined shaft. Therefore, when freezing conditions are not met, the angle α between the freezing pipes and the axis is adjusted according to the current inclination angle θ of the inclined shaft, so that it fits the inclined shaft structure more closely in space, thereby improving the forming effect of the frozen curtain in local areas. The adjustment strategy generally follows: For inclined wells with a large inclination angle (θ ≥ 30°), the included angle α of the freezing pipe should be appropriately reduced; For inclined shafts with a small inclination angle, a dense layout at equal angles can be used to increase the freezing overlap rate.

[0062] Groundwater in highly permeable pebble layers exhibits a significant cold-carrying effect; the higher the horizontal flow velocity (v), the stronger the disturbance to the frozen body. To compensate for the insufficient frozen thickness and boundary distortion caused by this disturbance, the following two strategies can be adopted: Reduce the spacing between freezing pipes (dfg): Increase the cold density by locally densifying the pipes, so that the freezing expansion rate is faster than the water flow disturbance rate; Optimize the freezing temperature control curve Tc(t): enhance freezing potential by extending the minimum freezing time, reducing the average freezing temperature, and using a stepped cooling curve.

[0063] Based on the above parameter adjustment results, reconstruct the frozen area spatial model WR′, and return to the aforementioned steps S3 to S6 (including freezing simulation, boundary identification, coverage analysis, and security assessment) until the freezing coverage is achieved. and freezing thickness All meet the design requirements.

[0064] When the freezing plan is verified and determined to meet the crossing safety conditions, that is, the freezing coverage in all key depth sections is not less than And the frozen thickness meets the requirements. If the freezing scheme is successful, it is considered a valid frozen design, and the following design parameters are output: The freezing duration is the shortest time required for the frozen body to reach a closed state and meet the safety margin. The stabilization time of the frozen body is calculated based on the freezing thickness evolution function d(t) and the freezing boundary function R(t). Based on the heat exchange stability check in the later stage of freezing, the final freezing control time Tf is set, which is usually taken as... to The interval is Δt, where Δt is the freeze margin buffer duration (e.g., 3 to 7 days).

[0065] The output freezing pipe layout parameters include the average spacing between freezing pipes, the number of pipe groups, and the arrangement method within each depth segment. If there are localized areas requiring additional freezing, the corresponding spatial coordinate segments and pipe spacing variation information are marked.

[0066] Freezing fluid temperature control schemes typically include a pre-cooling stage, a constant-temperature freezing stage, and a stabilization stage. The output temperature control curve Tc(t) is a piecewise time-temperature function, expressed as follows: (Pre-cooling stage); (Constant temperature freezing stage); (During the stability maintenance phase, a slight increase). in Let be the initial temperature, and 'a' be the cooling rate. ΔT represents the target freezing liquid temperature, and ΔT represents the temperature difference for maintaining stability.

[0067] Freezing termination typically employs a multi-criteria triggering mechanism, including: The freezing temperature at all monitoring points remained stable at T ≤ -5℃; All critical depths of frozen thickness ; The frozen curtain must remain continuously closed for at least Δt days; The groundwater flow velocity did not cause the frozen boundary to retreat.

[0068] Once the above criteria are met, the system will automatically output a freeze termination suggestion and can coordinate with construction to begin preparations for crossing.

[0069] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for designing the freezing of inclined shafts through highly permeable pebble layers, characterized by: include: S1. Obtain the soil and rock parameters of the pebble layer in the target inclined shaft crossing section and the historical ambient temperature of the area; S2. Establish a three-dimensional geometric model of the inclined shaft, determine the position, inclination angle and spacing of the freezing pipes along the axis of the inclined shaft, and construct a spatial model of the frozen area coupled with the pebble layer; The establishment of a three-dimensional inclined shaft geometric model, and the determination of the position, inclination angle, and spacing of the freezing pipes along the inclined shaft axis, includes: Obtain the spatial orientation, longitudinal profile parameters, and positional relationship between the target inclined shaft and the contact interface with the pebble layer. Construct a spatial interaction model between the inclined shaft and the pebble layer, and extract the path function L(x,y,z) of the inclined shaft axis in the three-dimensional coordinate system. Using the path function L(x,y,z) as a reference, the initial plan for laying out the freezing pipes in its normal profile is adopted by orthogonal projection. The angle between the inclination angle of the freezing pipes and the axis of the inclined well is controlled within a preset range. The coverage overlap rate of the freezing curtain at each depth is evaluated by combining the permeability coefficient distribution k(z) of the pebble layer. Based on the predicted results of coverage overlap rate and freezing body closure time, a freezing efficiency evaluation function is constructed to iteratively optimize the initial layout scheme of freezing tubes and output the final layout coordinates, tilt angle and spacing parameters of freezing tubes in three-dimensional space. S3. Based on historical ambient temperature and freezing pipe layout information, a multi-field coupled model of freezing-heat transfer-seepage is constructed to numerically simulate the formation process of the frozen body, obtaining the evolution functions of the freezing boundary expansion range R(t) and freezing thickness d(t) at different times t, including: Based on the constructed freezing-heat transfer-seepage coupling model, the initial freezing temperature field, freezing pipe boundary temperature, and soil thermal-hydraulic physical parameters are input to carry out multi-time freezing simulation and obtain the response data of temperature and moisture content at each node during the freezing process. Within each freezing simulation period, the location of the frozen body boundary is identified based on the freezing criterion temperature. An isothermal surface extraction algorithm is used to generate the three-dimensional boundary envelope of the frozen region. The freezing boundary extension range R(t) and freezing thickness d(t) are calculated to form a freezing boundary time series dataset. Regression analysis and fitting were performed on the dataset of frozen boundary parameters changing over time to construct the evolution function of frozen expansion boundary and the evolution function of frozen thickness. S4. Based on the spatiotemporal development pattern of the frozen body, analyze the freezing coverage rate within different depth ranges of the inclined shaft, and determine whether the crossing safety conditions are met based on the minimum freezing thickness and the design safety factor. The analysis of the freezing coverage rate at different depths of the inclined shaft based on the spatiotemporal development pattern of the frozen body includes: The evolution function of the frozen extension boundary and the evolution function of the frozen thickness are mapped to the three-dimensional frozen region spatial grid. Multiple depth segments are divided along the direction of the inclined shaft axis, and the cross-sectional profile data of the frozen curtain of each segment at different times are extracted. Based on the cross-sectional geometry of the frozen curtain in each depth segment, the cross-sectional area Af of the frozen area and the theoretical frozen control area At are calculated. The ratio of these values ​​is used to define the frozen coverage index, and a distribution function for the frozen coverage as a bivariate of depth and time is established. Gradient analysis was performed on the frozen coverage distribution function to identify weak areas where the coverage was below the safety threshold, and a spatial distribution map of the freezing effect of the inclined well was generated. S5. If not satisfied, adjust the freezing pipe parameters according to the angle of the inclined well and the groundwater flow velocity, reconstruct the spatial model of the frozen area and return to S3; if satisfied, output the freezing design parameters, including freezing duration, freezing pipe spacing, freezing temperature control curve and freezing termination judgment conditions.

2. The method for designing the freezing of inclined shafts through highly permeable pebble layers according to claim 1, characterized in that: The acquisition of the geotechnical parameters of the pebble layer traversed by the target inclined shaft and the historical environmental temperature of the area includes: The permeability coefficient distribution k(z) of the pebble layer at different depths was obtained by combining drilling sampling with in-situ permeability testing, where z is the depth coordinate along the axis of the inclined well. The specific heat capacity, thermal conductivity and initial water content of the undisturbed pebble layer samples were determined by thermophysical property testing methods. The functional relationship curves P(z) of thermophysical property parameters with depth were constructed by fitting the experimental data with the stratigraphic classification. We constructed the multi-year average evolution curve of the daily average surface temperature during typical seasons during the freezing period, and combined it with the geothermal gradient formula to inversely deduce the shallow geothermal field distribution T(z,t). The permeability coefficient distribution k(z), the functional relationship curve of the thermophysical parameters with depth P(z), and the shallow geothermal field distribution T(z,t) are used as initial boundary conditions input into the spatial model of the frozen area.

3. The method for designing the freezing of inclined shafts through highly permeable pebble layers according to claim 1, characterized in that: The construction of the frozen region spatial model coupled with the pebble layer includes: Based on the three-dimensional geological structure model, the range, thickness, permeability coefficient zoning of the pebble layer and its relative position to the axis of the inclined well are imported. The frozen-affected zone and the unaffected zone within the pebble layer are identified, and the initial frozen simulation envelope is delineated with the freezing pipe layout area as the center. Based on the shallow geothermal field distribution T(z,t), freezing initiation temperature, soil moisture content, and latent heat of freezing parameters, a model for the changes in thermal conductivity and water migration coefficient before and after freezing is constructed, a dynamic heat-water coupling coefficient field is established, and the coupling coefficient field is embedded into the spatial grid model of the frozen area. By using adaptive mesh generation technology, the frozen boundary region is refined, and the coupled modeling of the frozen region spatial model and the spatial interaction model is completed.

4. The method for designing the freezing of inclined shafts through highly permeable pebble layers according to claim 3, characterized in that: Based on historical ambient temperature and freezing pipe layout information, a multi-field coupled model of freezing-heat transfer-seepage is constructed, including: The multi-year average surface temperature curve during the freezing period is used as the upper boundary condition. Combined with the geothermal gradient model, the shallow geothermal field distribution T(z,t) at different depths is calculated. Then, the coordinates of the freezing pipe layout, the freezing temperature control curve, and the circulation flow parameters are used as the internal boundary conditions to form a time-space distributed freezing source term field. The heat conduction equation and water seepage equation of the soil in the frozen area are established. Considering the release of latent heat of freezing, phase change of pore water and phase change degradation effect of permeability coefficient, a set of multi-physical response functions of heat transfer-seepage-phase change is constructed, in which the coefficient parameters of each physical field are dynamically updated with temperature and saturation. Based on the finite difference method, loose coupling is used to iteratively solve the heat conduction equation and the seepage equation in the same simulation step.

5. The method for designing the freezing of inclined shafts through highly permeable pebble layers according to claim 1, characterized in that: The process of determining whether the crossing safety conditions are met based on the minimum freezing thickness and the design safety factor includes: Set the minimum freezing thickness for design Based on the construction load level and groundwater pressure of penetrating the pebble layer, the appropriate design safety factor K is selected, and the lower limit of the required theoretical freezing thickness is calculated. ; The frozen thickness evolution function is compared with the frozen thickness d(t) of each depth segment in the frozen space model to determine the freezing stability at the moment. Does it satisfy the following? This forms a safety determination matrix for the frozen thickness. Depth sections that do not meet the safety criterion for freezing thickness are marked and output as areas where crossing conditions are not met.

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