CN105909252A - Vertical shaft wall temperature judgment method - Google Patents

Abstract

Disclosed is a vertical shaft wall temperature judgment method. The method includes the following steps that (1) all parameters of freezing pipes are measured or checked; (2) then the cold supply amount per day is determined; (3) a computational formula of freezing day number N which frozen earth needs to develop to the shaft wall is deduced; (4) a computational formula of the shaft wall temperature influenced by single ring hole is deduced; (5) a computational formula of the shaft wall temperature influenced by two or more freezing holes is deduced; (6) an n<th> day frozen earth development radius formula of a single freezing pipe is deduced; (7) the numerical value of a distance influence coefficient epsilon is determined; and (8) the all measured or checked parameters of the freezing pipes and the determined numerical value of the distance influence coefficient epsilon are substituted into the computational formula in the step (5). By means of the vertical shaft wall temperature judgment method, harsh conditions of an empirical method and an engineering analogy method are avoided, and data are obtained in advance through a scientific mode.

Description

A kind of vertical Care in method determination methods

Technical field

The present invention relates to shaft of vertical well field, particularly relate to a kind of vertical Care in method determination methods.

Background technology

Freezing technology oneself be widely applied in the underground engineering such as vertical and tunnel, freezing technology is to unknown and complexity Topsoil enters son to be freezed to process in advance.In vertical engineering, table soil section uses freezing technology construction to pass through.Over nearly 20 years, employing is freezed The vertical of method construction reaches hundreds of.Such as, when the depth of freezing is more than 400 meters, the design difficulty of various countries' freezing hole is relatively big, existing Technology is that full freeze section send cold the most simultaneously or stops freezing, and so easily causes the situation that Care in method is the most uneven, thus gives Self well digging construction brings huge difficulty and potential safety hazard, causes cost waste and construction delay.

Construction freezing method shaft of vertical well, freezing wall temperature field development prediction be very important, it was predicted that whether accurate Directly influence the speed of self well digging and the construction arrangement of next stage, along with the continuous increase of the depth of freezing, frozen construction In be difficult to accomplish precise controlling and prepare to hold, be under normal conditions super freeze or cross freeze, waste substantial amounts of electric power and material Material consumes, and digs safely block the most also to pit shaft simultaneously and brings a lot of uncertain potential safety hazard, causes and freezes shaft construction and often occur Disconnected pipe, the serious engineering accident such as permeable.While summing up lesson written in blood, vast technology scientific and technical personnel are making great efforts research more Shaft Freezing Temperature calculating and prediction theory accurately and reliably, it is desired to be able to grasp frost wall state of development more accurately.

If just carrying out prediction work before engineering design plan (EDP), can preferably instruct project of shaft freezing design work, The rapport that pick is built and freezed is done a good job of it from technology source.Ensure vertical pick build safety the most at all, be also most efficient method just It is to formulate a good project of shaft freezing, is also best " preventive injection " avoiding safety problem.Therefore, designed at project of shaft freezing First Cheng Houying is predicted according to the program, further according to the further prioritization scheme of result of prediction, could farthest protect Card pick build safely, be carried out continuously.

Although unit in charge of construction and R&D institution all freeze to calculate and analogue technique in actively research at present, the most just include Freezing prediction technology, but be mostly at improving and the experimental stage, have is using empirical method the most always, although these technology pair The prediction freezed has very great help, but has time error too big, still cannot function as reliable shaft construction foundation.Therefore, it is badly in need of A kind of method of the prediction obtaining situation of freezing exactly, first we need to solve the anticipation in advance of vertical Care in method, for Driving and masonry construction provides important guiding, takes the most suitably measure in time, creates optimum execution conditions.

Summary of the invention

The technical problem to be solved of the present invention is can not accurately judge the closure of freezing wall time, and the present invention uses The techniques below scheme above-mentioned technical problem of solution:

A kind of vertical Care in method determination methods, it is characterised in that comprise the following steps:

(1) measure or check each parameter of freezing pipe；

(2) it is then determined that every day send cold；

(3) release frozen soil develop into well side required for freeze natural law N computing formula；

(4) the Care in method computing formula affected by individual pen hole is released；

(5) computing formula of the Care in method affected by two or more freezing holes is released；

(6) n-th day frozen soil development radius formula of single freezing pipe is released；

(7) determine that distance affects the numerical value of coefficient ε；

(8) will measure or check each parameter of freezing pipe and determine in numerical value substitution (5th) step that distance affects coefficient ε In computing formula.

Further, described step (1) needs measurement or the parameter checked are respectively as follows: and check salt water state and freezing pipe The brine temp of maximum heat radiation phase, so that it is determined that freezing pipe maximum coefficient of heat transfer Kt, measures at outside diameter d e of freezing pipe, vertical The kind of soil, determines the temperature diffusivity α of the rock stratum that soil specific heat capacity m and density p, this soil are formed accordingly and measures rock stratum Original temperature t₀, distance R helped away from well of freezing pipe_b；

Further, in described step (2), the cold that send of every day necessarily and is

24πd_eh_ek_t

Wherein de is the external diameter of freezing pipe, m；He is depth of stratum, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²· h)。

Further, in described step (3), frozen soil develops into the computing formula freezing natural law N required for well is helped and is:

$N=\frac{R_b^2}{{\mathrm{\&alpha;}}^2(\frac{24d_e{k}_t}{{\mathrm{m\&rho;t}}_0}+d_e^2)}$

Wherein R_bThe distance helped away from well for freezing pipe, m；α is the temperature diffusivity of rock stratum；De is the external diameter of freezing pipe, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²·h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀ For the original temperature of rock stratum, DEG C.

Further, in described step (4), the computing formula of the Care in method affected by individual pen hole is:

$t_b=t_0(1-\frac{\mathrm{\&alpha;}}{R_b}\sqrt{n(\frac{24d_e{k}_t}{{\mathrm{m\&rho;t}}_0}+d_e^2)})$

Wherein R_bThe distance helped away from well for freezing pipe, m；α is the temperature diffusivity of rock stratum；De is the external diameter of freezing pipe, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²·h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀ For the original temperature of rock stratum, DEG C；The n R for freezing natural law, in this formula_b> 500mm, this formula is applicable to be affected by individual pen hole The temperature of frost wall arbitrfary point.

Further, in described step (5), calculate the Care in method affected by two or more freezing holes, calculate Formula is as follows:

$t_b=t_0(1-\frac{\mathrm{\&alpha;}}{{\mathrm{\&epsiv;R}}_b}\sqrt{n(\frac{24d_e{k}_t}{{\mathrm{m\&rho;t}}_0}+d_e^2)})$

Wherein: R_bThe distance helped away from well for freezing pipe, m；α is the temperature diffusivity of rock stratum；De is the external diameter of freezing pipe, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²·h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀ For the original temperature of rock stratum, DEG C；N is for freezing natural law, and ε is that distance affects coefficient, the R in this formula_b>500mm。

Further, in described step (6), releasing n-th day frozen soil development radius of single freezing pipe, computing formula is such as Under:

$R_n=\mathrm{\&alpha;}\sqrt{n(\frac{24{\mathrm{dek}}_t}{{\mathrm{m\&rho;t}}_0}+{\mathrm{de}}^2)}$

Wherein α is the temperature diffusivity of rock stratum；De is the external diameter of freezing pipe, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/(m2·h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀For the original temperature of rock stratum, DEG C；N is for freezing Knot natural law.

Further, R_nIt is the frost wall development radius of n-th day, R_bmin、R_bmaxIt is that measuring point arrives freezing pipe nearest, farthest Distance.Single freezing pipe r_n≤R_bminTime, ε takes 1, and during double-row hole, ε minima takes 0.4, and maximum is 1.

Described step (4) is the most further comprising the steps of:

(1) assume that Virgin rock temperature is from t₀Dropping to 0 DEG C is a circulation, and saline and rock stratum thermal energy exchange can use equation below Represent:

Wherein he is depth of stratum, m；De is the external diameter of freezing pipe, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²· h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀For the original temperature of rock stratum, DEG C；

(2) formula of first day frozen soil development radius of single freezing pipe claim 1 is gone out from the above-mentioned derivation of equation:

$R_1=\sqrt{\frac{24{\mathrm{deK}}_t}{{\mathrm{m\&rho;t}}_0}+{\mathrm{de}}^2}$

(3) first day development radius R is assumed₁, within second day, develop into R₂Within n-th day, develop into R_n；

Freezing pipe send cold approximately equal every day, therefore has:

$Q=\underset{R_{n-1}}{\overset{R_n}{\&Integral;}}2{\mathrm{\&pi;m\&rho;h}}_e\mathrm{\&Delta;}trdr$

What in formula, Q represented freezing pipe every day send cold, △ t=t₀The temperature difference of-0 frost wall representing development every day is normal Number, can get according to above formula:

${\mathrm{\&pi;R}}_1^2=\mathrm{\&pi;}(R_2^2-R_1^2)=\mathrm{\&pi;}(R_3^2-R_2^2)=......=\mathrm{\&pi;}(R_n^2-R_{n-1}^2)$

N-th day frozen soil development radius of the most single freezing pipe:

Further, described step (4) is the most further comprising the steps of:

(1) in determining freezing range, certain point declines temperature, and n-th day temperature of this point have dropped

$\sqrt{\frac{n}{N}}{t}_0$

(2) the Care in method t after freezing n-th day is determined_b, formula is

$t_b=t_0(1-\sqrt{\frac{n}{N}})$

It is an advantage of the current invention that:

(1) only one or two subjective parameters in the freezing wall temperature field computing formula that the present invention is drawn, other are all Objective parameter obtained by frozen soil experiment, greatly reduces the artificial subjective error caused, calculated result and actual knot Fruit is closely.

(2) the most of project data needed for the present invention can meet Shaft Freezing construction.

(3) present invention can optimize project of shaft freezing, during project of shaft freezing is discussed, it is provided that prediction data reliably, enters And find defect and the deficiency of scheme according to prediction data, thus improve project of shaft freezing in advance.

Detailed description of the invention

Freeze to be by the liquefaction cooling of the material such as ammonia or carbon dioxide through electric energy, and brine circulation system carries out heat energy friendship Changing, hypothermic saline carries out thermal energy exchange again with rock stratum, thus reduces the purpose of ground temperature, eventually forms complete freezing Wall.

The step obtaining Care in method is as follows:

The first step: measure or check each parameter of freezing pipe:

Check salt water state and the brine temp of freezing pipe maximum heat radiation phase, so that it is determined that freezing pipe maximum coefficient of heat transfer Kt, measures outside diameter d e of freezing pipe, checks the native kind at vertical, determine corresponding this soil specific heat capacity M and density p, this soil The temperature diffusivity α and the original temperature t of measurement rock stratum of the rock stratum formed₀, distance R that freezing pipe is helped away from well_b；

Second step: obtain freezing pipe every day send cold

Assume that Virgin rock temperature is from t₀Dropping to 0 DEG C is a circulation, and saline and rock stratum thermal energy exchange can use equation below table Show:

$\mathrm{\&pi;}m\mathrm{\&rho;}({R_1}^2-d_e^2)h_e{t}_0=24{\mathrm{\&pi;d}}_e{h}_e{k}_t---\left(1\right)$

Wherein de is the external diameter of freezing pipe, m；He is depth of stratum, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²· h)。

Being understood freezing pipe by formula (1) send cold necessarily and to be 24 π d every day_eh_ek_t

3rd step: calculate frozen soil develop into well side required for freeze natural law N

By simulation, certain in freezing range is put temperature and is changed over curve approximation and be one and freeze natural law n The function of 1/2 power, within n-th day, temperature have dropped:

$\sqrt{\frac{n}{N}}{t}_0---\left(2\right)$

Wherein n represents and freezes natural law, N represent break ground develop into well side required for freeze natural law.

Therefore freeze the Care in method after n days:

$t_b=t_0(1-\sqrt{\frac{n}{N}})---\left(3\right)$

$N=\frac{R_b^2}{{\mathrm{\&alpha;}}^2(\frac{24d_e{k}_t}{{\mathrm{m\&rho;t}}_0}+d_e^2)}---\left(4\right)$

4th step, the Care in method computing formula that release is affected by individual pen hole:

$t_b=t_0(1-\frac{\mathrm{\&alpha;}}{R_b}\sqrt{n(\frac{24d_e{k}_t}{{\mathrm{m\&rho;t}}_0}+d_e^2)})---\left(5\right)$

Wherein: R_bThe distance helped away from well for freezing pipe, m；α is the temperature diffusivity of rock stratum；De is the external diameter of freezing pipe, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²·h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；

Formula (5) is along with R_bValue difference both can calculate Care in method can also calculate the temperature of any point in frost wall Degree, but it is not suitable for R_b≤ 500mm, because in the range of freezing pipe about 500mm, frozen soil has not continued to cooling, can To think that the frozen soil near freezing pipe is in temperature constant state, the heat that it absorbs all is diffused into the place beyond zone of constant temperature.Institute So that formula (5) to require R_b> 500mm, and this formula is applicable to the temperature of the frost wall arbitrfary point affected by individual pen hole.

5th step: release the computing formula of the Care in method affected by two or more freezing holes

By field measurement date comprision, the frost wall any point temperature that formula (5) is affected by individual pen hole in calculating It is accurately when spending, and calculates the temperature between two row's freezing holes and have larger difference, such as the measuring point between main round and via hole. Reason is between double-row hole, and measuring point is affected by two or more freezing holes simultaneously, affects size by single freezing pipe frozen soil development half Footpath controls with the distance ratio of measuring point to nearest freezing hole, and being defined as distance affects coefficient ε, and formula (5) is revised as accordingly:

$t_b=t_0(1-\frac{\mathrm{\&alpha;}}{{\mathrm{\&epsiv;R}}_b}\sqrt{n(\frac{24d_e{k}_t}{{\mathrm{m\&rho;t}}_0}+d_e^2)})---\left(6\right)$

6th step: release n-th day frozen soil development radius formula of single freezing pipe

Assume that Virgin rock temperature is from t₀Dropping to 0 DEG C is a circulation, and saline and rock stratum thermal energy exchange can use equation below table Show:

$\mathrm{\&pi;}m\mathrm{\&rho;}({R_1}^2-d_e^2)h_e{t}_0=24{\mathrm{\&pi;d}}_e{h}_e{k}_t---\left(7\right)$

Wherein he is depth of stratum, m；De is the external diameter of freezing pipe, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²· h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀For the original temperature of rock stratum, DEG C；

The formula of first day frozen soil development radius of single freezing pipe claim 1 is gone out from the above-mentioned derivation of equation:

$R_1=\sqrt{\frac{24{\mathrm{deK}}_t}{{\mathrm{m\&rho;t}}_0}+{\mathrm{de}}^2}---\left(8\right)$

Assume first day development radius R₁, within second day, develop into R₂Within n-th day, develop into R_n；

Freezing pipe send cold approximately equal every day, therefore has:

$Q=\underset{R_{n-1}}{\overset{R_n}{\&Integral;}}2{\mathrm{\&pi;m\&rho;h}}_e\mathrm{\&Delta;}trdr---\left(9\right)$

What in formula (9), Q represented freezing pipe every day send cold, △ t=t₀The temperature difference of-0 frost wall representing development every day For constant, can get according to above formula:

${\mathrm{\&pi;R}}_1^2=\mathrm{\&pi;}(R_2^2-R_1^2)=\mathrm{\&pi;}(R_3^2-R_2^2)=......=\mathrm{\&pi;}(R_n^2-R_{n-1}^2)---\left(10\right)$

N-th day frozen soil of single freezing pipe development radius can be obtained by formula (10):

$R_n=\sqrt{n}{R}_1---\left(11\right)$

Formula (8) is substituted into formula (11) computing formula as follows:

$R_n=\mathrm{\&alpha;}\sqrt{n(\frac{24{\mathrm{dek}}_t}{{\mathrm{m\&rho;t}}_0}+{\mathrm{de}}^2)}---\left(12\right)$

7th step: determine that distance affects the numerical value of coefficient ε

RbmaxRbmin(single row of holesn>Rbmin)	1.6	1.5	1.4	1.3	1.2	1.1	1
								ε	1	1	1	0.95	0.9	0.85	0.8
rn/Rbmin(double-row hole)	1.1	1	0.9	0.8	0.7	0.6	0.4
								ε	0.4	0.45	0.5	0.6	0.65	0.8	1

Table 1: distance affects coefficient table

R in upper table_nIt is the frost wall development radius of n-th day, R_bmin、R_bmaxBe measuring point arrive freezing pipe nearest, farthest away from From.Single freezing pipe R_n≤R_bminTime, ε takes 1, and during double-row hole, ε minima takes 0.4, and maximum is 1.

8th step: will measure or check that each parameter of freezing pipe substitutes into the computing formula in formula (6) with the value of the ε determined In.

Specific embodiment is as follows:

Freezing hole helps distance R to well_bIt is 1.5m, below 200m 2.1m at more than 200m.Number is surveyed according to slanting of freezing hole According to and combine table 1 below and can obtain the distance of corresponding frozen crust position and affect the value of coefficient ε.

Recording S1 hole salt water state is laminar flow, subzero 26/ DEG C of the brine temp of freezing pipe maximum heat radiation phase；

Recording S2 hole salt water state is laminar flow, subzero 28/ DEG C of the brine temp of freezing pipe maximum heat radiation phase；

Recording S3 hole salt water state is laminar flow, subzero 30/ DEG C of the brine temp of freezing pipe maximum heat radiation phase；

According to table 1, Kt span is k_t=(882000～1080000) J/ (m²·h)；

Table 2 freezing pipe maximum coefficient of heat transfer (unit heat flow) Kt reference value

Parameter determination last string Care in method in summary data and table 3.

Care in method correspondence table predicted by table 3

Care in method reply table surveyed by table 4

According to table 3 and the contrast of table 4, it was predicted that Care in method and the actual Care in method error measured less than 1 DEG C, produce Source of error be due to measuring point cannot be accurately positioned with the impact of ambient temperature caused by.

The foregoing is only the preferred embodiment of the invention, not in order to limit the invention, all at this Any amendment, equivalent and the improvement etc. made within the spirit of innovation and creation and principle, should be included in the invention Protection domain within.

Claims (10)

1. a vertical Care in method determination methods, it is characterised in that comprise the following steps:

(1) measure or check each parameter of freezing pipe；

(2) it is then determined that every day send cold；

(3) release frozen soil develop into well side required for freeze natural law N computing formula；

(4) the Care in method computing formula affected by individual pen hole is released；

(5) computing formula of the Care in method affected by two or more freezing holes is released；

(6) n-th day frozen soil development radius formula of single freezing pipe is released；

(7) determine that distance affects the numerical value of coefficient ε；

(8) will measure or check each parameter of freezing pipe and determine that distance affects the calculating in numerical value substitution (5th) step of coefficient ε In formula.

A kind of vertical Care in method determination methods the most according to claim 1, it is characterised in that described step (1) needs The parameter measured or check is respectively as follows: checks salt water state and the brine temp of freezing pipe maximum heat radiation phase, so that it is determined that freeze Knot pipe maximum coefficient of heat transfer Kt, measures the kind of soil at outside diameter d e of freezing pipe, vertical, determine corresponding soil specific heat capacity m and The temperature diffusivity α and the original temperature t of measurement rock stratum of the rock stratum that density p, this soil are formed₀, the distance helped away from well of freezing pipe R_b。

A kind of vertical Care in method determination methods the most according to claim 1, it is characterised in that in described step (2), The cold that send of every day necessarily and is

24πd_eh_ek_t

Wherein de is the external diameter of freezing pipe, m；He is depth of stratum, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²·h)。

A kind of vertical Care in method determination methods the most according to claim 1, it is characterised in that in described step (3), Frozen soil develops into the computing formula freezing natural law N required for well is helped:

$N=\frac{R_b^2}{{\mathrm{\&alpha;}}^2(\frac{24d_e{k}_t}{{\mathrm{m\&rho;t}}_0}+d_e^2)}$

Wherein R_bThe distance helped away from well for freezing pipe, m；α is the temperature diffusivity of rock stratum；De is the external diameter of freezing pipe, m；k_tFor Freezing pipe maximum coefficient of heat transfer, J/ (m²·h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀For rock stratum Original temperature, DEG C.

A kind of vertical Care in method determination methods the most according to claim 1, it is characterised in that in described step (4), The computing formula of the Care in method affected by individual pen hole is:

$t_b=t_0(1-\frac{\mathrm{\&alpha;}}{R_b}\sqrt{n(\frac{24d_e{k}_t}{{\mathrm{m\&rho;t}}_0}+d_e^2)})$

Wherein R_bThe distance helped away from well for freezing pipe, m；α is the temperature diffusivity of rock stratum；De is the external diameter of freezing pipe, m；k_tFor Freezing pipe maximum coefficient of heat transfer, J/ (m²·h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀For rock stratum Original temperature, DEG C；The n R for freezing natural law, in this formula_b> 500mm, this formula is applicable to the frost wall affected by individual pen hole The temperature of arbitrfary point.

A kind of vertical Care in method determination methods the most according to claim 1, it is characterised in that in described step (5), Calculating the Care in method affected by two or more freezing holes, computing formula is as follows:

$t_b=t_0(1-\frac{\mathrm{\&alpha;}}{{\mathrm{\&epsiv;R}}_b}\sqrt{n(\frac{24d_e{k}_t}{{\mathrm{m\&rho;t}}_0}+d_e^2)})$

Wherein: R_bThe distance helped away from well for freezing pipe, m；α is the temperature diffusivity of rock stratum；De is the external diameter of freezing pipe, m；k_t For freezing pipe maximum coefficient of heat transfer, J/ (m²·h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀For rock The original temperature of layer, DEG C；N is for freezing natural law, and ε is that distance affects coefficient, the R in this formula_b>500mm。

A kind of vertical Care in method determination methods the most according to claim 1, it is characterised in that in described step (6), Releasing n-th day frozen soil development radius of single freezing pipe, computing formula is as follows:

$R_n=\mathrm{\&alpha;}\sqrt{n(\frac{24{\mathrm{dek}}_t}{{\mathrm{m\&rho;t}}_0}+{\mathrm{de}}^2)}$

Wherein α is the temperature diffusivity of rock stratum；De is the external diameter of freezing pipe, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²·h)；M is the specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀For the original temperature of rock stratum, DEG C；N is for freezing Natural law.

A kind of vertical Care in method determination methods the most according to claim 7, it is characterised in that R_nIt it is the frost wall of n-th day Development radius, R_bmin、R_bmaxIt it is the measuring point distance that arrives freezing pipe nearest, farthest.Single freezing pipe r_n≤R_bminTime, ε takes 1, double During hole, ε minima takes 0.4, and maximum is 1.

A kind of vertical Care in method determination methods the most according to claim 7, it is characterised in that described step (4) it Front further comprising the steps of:

(1) assume that Virgin rock temperature is from t₀Dropping to 0 DEG C is a circulation, and saline and rock stratum thermal energy exchange can represent by equation below:

$\mathrm{\&pi;}m\mathrm{\&rho;}({R_1}^2-d_e^2)h_e{t}_0=24{\mathrm{\&pi;d}}_e{h}_e{k}_t$

Wherein he is depth of stratum, m；De is the external diameter of freezing pipe, m；k_tFor freezing pipe maximum coefficient of heat transfer, J/ (m²·h)；M is The specific heat capacity of soil, J/kg DEG C；ρ is the density of soil, kg/m³；t₀For the original temperature of rock stratum, DEG C；

(2) formula of first day frozen soil development radius of single freezing pipe claim 1 is gone out from the above-mentioned derivation of equation:

$R_1=\sqrt{\frac{24{\mathrm{deK}}_t}{{\mathrm{m\&rho;t}}_0}+{\mathrm{de}}^2}$

(3) first day development radius R is assumed₁, within second day, develop into R₂Within n-th day, develop into R_n；

Freezing pipe send cold approximately equal every day, therefore has:

$Q=\underset{R_{n-1}}{\overset{R_n}{\&Integral;}}2{\mathrm{\&pi;m\&rho;h}}_e\mathrm{\&Delta;}trdr$

What in formula, Q represented freezing pipe every day send cold, △ t=t₀The temperature difference of-0 frost wall representing development every day is constant, root Can get according to above formula:

${\mathrm{\&pi;R}}_1^2=\mathrm{\&pi;}(R_2^2-R_1^2)=\mathrm{\&pi;}(R_3^2-R_2^2)=......=\mathrm{\&pi;}(R_n^2-R_{n-1}^2)$

N-th day frozen soil development radius of the most single freezing pipe:

$R_n=\sqrt{n}{R}_1$

A kind of vertical Care in method determination methods the most according to claim 4, it is characterised in that described step (4) it Front further comprising the steps of:

(1) in determining freezing range, certain point declines temperature, and n-th day temperature of this point have dropped

$\sqrt{\frac{n}{N}}{t}_0$

(2) the Care in method t after freezing n-th day is determined_b, formula is

$t_b=t_0(1-\sqrt{\frac{n}{N}})$