CN104237301B - In-situ thermal response testing method for layered rock and soil thermophysical properties - Google Patents
In-situ thermal response testing method for layered rock and soil thermophysical properties Download PDFInfo
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- CN104237301B CN104237301B CN201410479673.XA CN201410479673A CN104237301B CN 104237301 B CN104237301 B CN 104237301B CN 201410479673 A CN201410479673 A CN 201410479673A CN 104237301 B CN104237301 B CN 104237301B
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Abstract
The invention provides an in-situ thermal response testing method for layered rock and soil thermophysical properties. According to the in-situ thermal response testing method for the layered rock and soil thermophysical properties, a thermal response test is performed on an assembled buried tube heat exchanger, the theoretical value of the average temperature of a group of circulating fluids is calculated through introduction of buried tube parameters and related test data in a formula, the actual value of the average temperature of the group of circulating fluids is measured through equipment, and the theoretical value and the actual value are calculated with a parameter estimation method, so that layered rock and soil thermal thermophysical property parameters can be determined. The in-situ thermal response testing method for the layered rock and soil thermophysical properties puts forwards a column heat source model and is applicable to tests of the layered thermophysical property parameters. The change of thermal resistance in drilled holes in the depth direction and the change of the heat exchange power in the drilled holes in the depth direction are considered, and the rock and soil thermophysical property parameters at a certain layer can be calculated accurately.
Description
Technical field
The present invention relates to technical field of ground source heat pump, a kind of geotechnical stratified hot physical property original position geo-thermal response test side is particularly related to
Method.
Background technology
In the prior art, to the method for testing of ground thermal property parameter it is the ground heat exchanger that will be shaped as U-shaped
Equivalent to regard a line source model as, overall by measuring correlation data calculation outlet source model thermal physical property parameter, this model
Method can only make overall judgement to the thermal physical property parameter of ground.In practice of construction, the depth of burying of ground heat exchanger
Relatively deep, often in more than 100m, this causes in the embedded scope of ground heat exchanger, and the distribution pattern of ground is uneven point
Cloth, and underground water content and seepage action of ground water speed are also different, the rock-soil layer caused in different depth has different heat
Physical parameter, line source model cannot accurately draw the thermal physical property parameter of the rock-soil layer in certain depth, to follow-up design nothing
Method provides useful data.
Existing post heat source model is proposed based on not stratified ground thermal property parameter test method, it is impossible to which directly set is used tricks
Point counting layer ground thermal property parameter.Must on the original basis be improved, propose a kind of new, it is adaptable to be layered hot physical property meter
The model and method of calculation.
The content of the invention
The present invention proposes a kind of hot physical property original position geo-thermal response test method of geotechnical stratified, solves hot physical property in the prior art
The problem that method of testing can not be measured to the thermal physical property parameter of specified rock-soil layer.
The technical proposal of the invention is realized in this way：
The invention provides a kind of hot physical property original position geo-thermal response test method of geotechnical stratified, comprise the following steps：
The first step, ground heat exchanger is connected with geo-thermal response test instrument, forms heat supplying loop, and by distribution type fiber-optic
Temp measuring system is measured ground heat exchanger, is carried out thermal response to ground heat exchanger by geo-thermal response test instrument and is tested and obtain
Data on flows in ground heat exchanger, from top to bottom many in ground heat exchanger are obtained by temperature-measuring system of distributed fibers
The temperature data of individual point for measuring temperature；
Second step, arranges to temperature data, and distance is entered from top to bottom to ground heat exchanger in units of at least 5m
Row layering, every layer of length is one or several unit distances, and the temperature data of all points for measuring temperature in every layer is summed up into shape
Into a data group；
3rd step, sets up plume source model, brings the data group data of kth layer into calculating formula：
By estimating λs、ρscsValue calculate Tf1kOne group of theoretical value, wherein,
Tf1kIt is the theoretical mean temperature of kth layer ground heat exchanger fluid circulating；
T0It is kth layer ground initial temperature；
QkIt is the heating power of kth layer, Qk=1163*G* Δs Tk, G is volume flow, Δ TkFor the import and export of kth layer are followed
The circulation body mean temperature temperature difference；
riIt is ground heat exchanger internal diameter；
rpIt is ground heat exchanger external diameter；
reIt is the outer radius when buret；
L is the length of unit distance；
Z is fourier coefficient, z=(asτ/(re 2)), as=(λs/(csρs)),asIt is the thermal diffusion coefficient of ground, λsIt is rock
Native mean coefficient of heat conductivity；csρsIt is ground specific heat per unit volume；
α1k=(2 π re2csρs)/(ccylinder), ccylinderIt is wellhole unit length thermal resistance；
kpIt is the thermal conductivity factor of tubing；
C=e0.5772=eγ, C is hot-fluid short circuit correction factor, and γ is Euler's constant；
H=2 π λsR’g, R 'gIt is unit length thermal contact resistance；
N is the pipe number quantity of ground heat exchanger.
4th step, the actual average temperature of kth layer ground heat exchanger fluid circulating is calculated by the data group of kth group
Tf2k；
5th step, the one group of T drawn to the 3rd stepf1kThe T that value and the 4th step drawf2kValue carries out Parameter Estimation Method, calculates
Determine λs、ρscs。
Further, in the first step, geo-thermal response test instrument is to input constant heat flux or constant cold in ground heat exchanger
Stream.
Further, the temperature-measuring system of distributed fibers in the first step include a plurality of temperature-measuring optical fiber, on temperature-measuring optical fiber every
0.25m is provided with a temperature measurement node, and 4 temperature-measuring optical fibers are provided with every pipe of ground heat exchanger.
Further, also include carrying out ground heat exchanger equivalent treatment before the 3rd step, ground heat exchanger and work as
There is following relationship between buret：Wherein, D0It is the overall diameter of ground heat exchanger, DeIt is the equivalent when buret
Diameter.
Further, the arrangement in second step to data includes：Give up the data measured in preceding 10 hours, give up distance
The data measured in the 5m of ground.
Further, to the estimation in the 3rd step, further include：The data that will be measured in step 2 are brought into calculating formula
In obtain Tf1kOn λs、ρscsA function, by csρsIn 0 to 5*106Between travel through, λsTraveled through between 0 to 10, obtained
Tf1kOne group of theoretical value.
Further, the data in the 4th step by kth group calculate actual value Tf2kFurther include：By formula to Tf2k
Value is calculated：
Tf2k=(Tin+T2+T3+……+Tout)/N
Wherein, TinIt is recirculated water into entrance temperature at K layers,
ToutTemperature during for recirculated water outflow kth layer,
T2、T3... is followed successively by k layers of horizontal line on second average temperature data of temperature measurement node collection, K layers of horizontal line
Three average temperature datas ... of temperature measurement node collection；
N is the number of temperature measurement node collection in k layers.
Further, Parameter Estimation Method is least square method, and least square method is further included：
Step one, to each Tf1kValue and actual value Tf2kThe calculating of variance and F is carried out by equation below：
F=∑s (i=1, M) { Tf1ki- Tf2ki}2
Wherein M is the group number of test measurement data；
Step 2, relatively more each Tf1kThe size of the F that value is drawn, selects minimum F values, the corresponding T of minimum F valuesf1kIt is worth and is
Requirements；
Step 3, searches and the λ corresponding to requirementss、ρscsValue, the value is the corresponding λ of ground for calculating intervals、ρscsValue.
The hot physical property original position geo-thermal response test method of geotechnical stratified of the invention, is layered by depth to ground heat exchanger
Process and the data to each layer are recorded respectively, when needing that the thermal physical property parameter of certain depth rock-soil layer is measured
When, layering test data related to corresponding to certain depth rock-soil layer and underground pipe parameter can be brought into formula and carry out phase
The calculating answered, draws the thermal physical property parameter of certain depth rock-soil layer.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
The accompanying drawing to be used needed for having technology description is briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments of invention, for those of ordinary skill in the art, without having to pay creative labor, may be used also
Other accompanying drawings are obtained with according to these accompanying drawings.
Fig. 1 is the connection equipment schematic diagram of the embodiment of the hot physical property original position geo-thermal response test method of geotechnical stratified of the present invention；
Fig. 2 is the calculation procedure flow chart of the embodiment of the hot physical property original position geo-thermal response test method of the geotechnical stratified of Fig. 1；
Fig. 3 is the time-temperature curve schematic diagram of the hot physical property original position geo-thermal response test method of the geotechnical stratified of Fig. 1；And
Fig. 4 is the temperature survey schematic diagram of the kth layer of the hot physical property original position geo-thermal response test method of the geotechnical stratified of Fig. 1.
Specific embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
The hot physical property original position geo-thermal response test method of geotechnical stratified of the present embodiment comprises the following steps：
The first step, as shown in figure 1, ground heat exchanger 1 is connected with geo-thermal response test instrument 2, forms heat supplying loop, and lead to
Cross temperature-measuring system of distributed fibers 3 to measure ground heat exchanger 1, ground heat exchanger 1 is carried out by geo-thermal response test instrument 2
Thermal response is tested and obtains the data on flows in ground heat exchanger, and obtaining underground pipe by temperature-measuring system of distributed fibers 3 changes
The temperature data of the multiple points for measuring temperature in hot device 1 from top to bottom；
Second step, arranges to temperature data, and distance is entered from top to bottom to ground heat exchanger 1 in units of at least 5m
Row layering, every layer of length is one or several unit distances, and the temperature data of all points for measuring temperature in every layer is summed up into shape
Into a data group；
3rd step, sets up plume source model, brings the data of kth group data group into calculating formula：
By estimating λs、ρscsValue calculate Tf1kOne group of theoretical value；
4th step, the actual average temperature of kth layer ground heat exchanger fluid circulating is calculated by the data group of kth layer
Tf2k；
5th step, the one group of T drawn to the 3rd stepf1kThe T that value and the 4th step drawf2kValue carries out Parameter Estimation Method, calculates
Determine λs、ρscs。
The hot physical property original position geo-thermal response test method of geotechnical stratified of the present embodiment, regards ground heat exchanger 1 as equivalent
, there is relational expression between ground heat exchanger 1 and Equivalent Column pipe in Equivalent Column pipeWherein, D0For underground pipe is changed
The overall diameter of hot device 1, DeIt is the equivalent diameter when buret.For Equivalent Column pipe, the model proposed using Carslaw is met
Expression formula one：
Tp- T0=(Q/ λsL) * G (z, p),
In order to correct in ground heat exchanger 1 image and the quantity of ground heat exchanger 1 of two pipe fitting hot-fluid short circuits
Problem, has expression formula two after hot-fluid short circuit correction factor C and U-tube number n is with the addition of on the basis of temperature difference formula：
ΔTP=Tf- TP={ Q (RC+RP)}/(2πre*L*C*n),
Expression formula one and expression formula two are combined and can obtain expression formula three：
Tf=T0+{(Q/λsL) * G (z, p) }+{ [Q (RC+RP)]/(2πre*L*C*n)}。
For the thermal resistance R of Equivalent Column pipebThere is expression formula four：
Meanwhile, when the z values in expression formula one are more than 0.5, expression formula one is also denoted as expression formula five：
Tp- T0=(Q/ (4 π λsL)) { 2h+ln (4z/C)-[(4h- α1)/(2*α1*z)]+[(α1-2)/(2*α1*z)]*
ln(4z/C)}。
Expression formula four and expression formula five are brought into the calculating formula that expression formula three i.e. cocoa draws individual layer mean flow：
In calculating formula, the meaning of each symbol is as follows：
Tf1kIt is the theoretical mean temperature of kth layer ground heat exchanger fluid circulating；
T0It is kth layer ground initial temperature；
QkIt is the heating power of kth layer, Qk=1163*G* Δs Tk, G is volume flow, Δ TkFor the import and export of kth layer are followed
The circulation body mean temperature temperature difference；
riIt is ground heat exchanger internal diameter；
rpIt is ground heat exchanger external diameter；、
reIt is the outer radius when buret；
L is the length of unit distance；
Z is fourier coefficient, z=(asτ/(re 2)), as=(λs/(csρs)),asIt is the thermal diffusion coefficient of ground, λsIt is rock
Native mean coefficient of heat conductivity；csρsIt is ground specific heat per unit volume；
α1k=(2 π re2csρs)/(ccylinder), ccyLinder is wellhole unit length thermal resistance；
kpIt is the thermal conductivity factor of tubing；
C=e0.5772=eγ, C is hot-fluid short circuit correction factor, and γ is Euler's constant；
H=2 π λsR’g, R 'gIt is unit length thermal contact resistance；
N is the pipe number quantity of ground heat exchanger.
In the first step of the present embodiment, temperature-measuring system of distributed fibers 3 is by temperature-measuring optical fiber in ground heat exchanger 1
Temperature measure.Wherein, geo-thermal response test instrument 2 is distributed to constant heat flux or constant cold flow is input into ground heat exchanger
Formula optical fiber temperature measurement system includes a plurality of temperature-measuring optical fiber, and 0.25m is provided with a temperature measurement node on temperature-measuring optical fiber, that is, set
Temperature-measuring optical fiber in every pipe of ground heat exchanger is surveyed by spacing of 0.25m to the temperature in ground heat exchanger 1
Amount.Preferably, 4 optical fiber are provided with every pipe of ground heat exchanger.Meanwhile, the heat supply being connected with ground heat exchanger 1
The flow of corresponding recirculated water in the record ground heat exchanger 1 of loop.The temperature data measured by temperature-measuring optical fiber and heat supply are returned
The data on flows of road record can calculate corresponding T0、ΔTkAnd Qk.In whole test process, the temperature of ground heat exchanger
As shown in Figure 3, in figure 3, each layer slope of curve is very close for degree-time graph, the ground point around this explanation underground pipe
Cloth is uniform, and each layer of the irregular of curve is mainly changed by heating power and caused in addition.
In use, for the requirement to precision, it is necessary to give up the unstable data measured by preceding 10 hours, together
When, due to surface temperature by temperature, environment etc. objective factor influenceed, in order to obtain more accurate data, preferably point
The hot physical property of ground is analysed, should at least give up 5 meters before underground of measurement data.
For the qualified data that can be used, in addition it is also necessary to carry out packet transaction, i.e., ground heat exchanger 1 is carried out at layering
Reason.In the present embodiment, to ground heat exchanger 1 layered shaping is it needs to be determined that unit distance, ground heat exchanger 1 is in unit
Should occur obvious temperature change in distance and be beneficial to follow-up calculating.Preferably, the length of unit distance should be more than or
Equal to 5m.When it is determined that after unit distance, ground heat exchanger 1 is from top to bottom divided into M layers, every layer of length is one or several
Unit distance, when the temperature in ground heat exchanger 1 is measured, the data of each point for measuring temperature in each layer is summed up
In one group and form this layer of corresponding temperature data group.
In the hot physical property for calculating the rock-soil layer corresponding to kth layer, it is necessary to the corresponding data group of kth layer is brought into calculating
In formula, T is obtainedf1kOn λs、ρscsA function, by setting λs、ρscsSpan and carry out exhaustion and can obtain many
Individual Tf1kValue, formed Tf1kOne group of theoretical value.Meanwhile, as shown in figure 4, the kth layer measured according to optical fiber temperature measurement system
Temperature data group, can be by expression formula six：Tf2k=(Tin+T2+T3+……+Tout)/N calculates the actual cycle fluid of kth layer
Mean temperature.
In exhaustion, λsValue traveled through between 0 to 10, ρscsSpan in 0 to 5*106Between travel through.
Wherein, TinIt is recirculated water into entrance temperature at K layers,
ToutTemperature during for recirculated water outflow kth layer,
T2、T3... is followed successively by k layers of horizontal line on second average temperature data of temperature measurement node collection, K layers of horizontal line
Three average temperature datas ... of temperature measurement node collection；
N is the number of temperature measurement node collection in k layers.
As shown in figure 4, when actually calculating, TinIt is first average temperature data of temperature measurement node collection on k layers of horizontal line,
ToutIt is the average temperature data of last temperature measurement node collection on k layers of horizontal line.Due in each pipe of ground heat exchanger
Be provided with a plurality of temperature-measuring optical fiber, calculate certain level line on temperature when should be by the temperature-measuring optical fiber on the horizontal line
Temperature measured by temperature measurement node be added together after divided by the radical of optical fiber to obtain the mean temperature on the horizontal line, improve
The precision of data.
Obtaining Tf1kOne group of theoretical value and actual average temperature after, can be by the least square method in Parameter Estimation Method
Calculate the λ for determining the rock-soil layer corresponding to k layerss、ρscs.Least square method is specially relative to each theoretical value flat with actual
Equal temperature value asks calculation variance and F by expression formula seven,
F=∑s (i=1, M) { Tf1ki- Tf2ki}2
Wherein M is the group number of test measurement data.
Obtain the corresponding variance of each theoretical value and after to each variance and being compared, select the minimum variance of numerical value
With the minimum variance and corresponding theoretical value are requirements, the corresponding λ of the requirementss、ρscsGround corresponding to as k layers
λs、ρscs。
Because the data volume that this portion calculates design is big, very complicated is calculated, can be complete by computer in practical operation
Into the calculating of this part, calculation procedure flow chart is as shown in Figure 2.
The hot physical property original position geo-thermal response test method of the geotechnical stratified of the present embodiment due to carrying out layered shaping to Mathematical Modeling,
Cause the blade diameter length ratio of model to be greatly increased relative to the blade diameter length ratio of line source model, it is impossible to directly to apply mechanically original line source model, need
To use new calculation.The hot physical property original position geo-thermal response test method of geotechnical stratified in the present embodiment, changes to underground pipe
During hot device 1 is layered, it is contemplated that along depth direction drilling internal thermal resistance RbChange, along depth direction drilling in heat exchange
The change of power Q so that the final λ for calculatings、ρs、cs.The actual thermal physical property parameter of ground is more nearly, calculating is improve
The computational accuracy of formula.Meanwhile, calculating formula in the present embodiment empirical equation different from the past, without carry out substantial amounts of hypothesis and
Cumbersome derivation, the intrinsic parameter of underground pipe and relevant test data need to be only brought into direct by being calculated in calculating formula obtaining
Go out the theoretical value of key parameter in least square method, with a wide range of applications and convenience is convenient for promotion and application.
Presently preferred embodiments of the present invention is the foregoing is only, is not intended to limit the invention, it is all in essence of the invention
Within god and principle, any modification, equivalent substitution and improvements made etc. should be included within the scope of the present invention.
Claims (8)
1. a kind of geotechnical stratified hot physical property original position geo-thermal response test method, it is characterised in that comprise the following steps：
The first step, ground heat exchanger (1) is connected with geo-thermal response test instrument (2), forms heat supplying loop, and by distributed light
Fine temp measuring system (3) is measured ground heat exchanger (1), and ground heat exchanger (1) is entered by the geo-thermal response test instrument (2)
Row thermal response is tested and obtains the data on flows in the ground heat exchanger (1), by the temperature-measuring system of distributed fibers
(3) temperature data of the multiple points for measuring temperature in the ground heat exchanger (1) from top to bottom is obtained；
Second step, arranges to the temperature data, in units of at least 5m distance to ground heat exchanger (1) from top to bottom
It is layered, every layer of length is one or several unit distances, and by the temperature data of all described point for measuring temperature in every layer
Sum up and form a data group；
3rd step, sets up plume source model, brings the data group data of kth layer into calculating formula：
By estimating λs、ρscsValue calculate Tf1kOne group of theoretical value, wherein,
Tf1kIt is the theoretical mean temperature of kth layer ground heat exchanger fluid circulating；
T0It is kth layer ground initial temperature；
QkIt is the heating power of kth layer, Qk=1163*G* Δs Tk, G is volume flow, Δ TkIt is the import and export circulation of fluid of kth layer
The mean temperature temperature difference；
riIt is ground heat exchanger internal diameter；
rpIt is ground heat exchanger external diameter；
reIt is the outer radius when buret；
L is the length of unit distance；
Z is fourier coefficient, z=(asτ/(re 2)), as=(λs/(csρs)),asIt is the thermal diffusion coefficient of ground, λsFor ground is flat
Equal thermal conductivity factor；csρsIt is ground specific heat per unit volume；
α1k=(2 π re2csρs)/(ccylinder), ccylinderIt is wellhole unit length thermal resistance；
kpIt is the thermal conductivity factor of tubing；
C=e0.5772=eγ, C is hot-fluid short circuit correction factor, and γ is Euler's constant；
H=2 π λsR’g, R 'gIt is unit length thermal contact resistance；
N is the pipe number quantity of ground heat exchanger；
4th step, the actual average temperature T of kth layer ground heat exchanger fluid circulating is calculated by the data group of kth layerf2k；
5th step, the one group of T drawn to the 3rd stepf1kThe T that value and the 4th step drawf2kValue carries out Parameter Estimation Method, calculates and determines
Go out λs、ρscs。
2. a kind of geotechnical stratified according to claim 1 hot physical property original position geo-thermal response test method, it is characterised in that the
In one step, the geo-thermal response test instrument (2) is to input constant heat flux or constant cold flow in the ground heat exchanger (1).
3. a kind of geotechnical stratified according to claim 2 hot physical property original position geo-thermal response test method, it is characterised in that described
The temperature-measuring system of distributed fibers (3) in the first step includes a plurality of temperature-measuring optical fiber, is set every 0.25m on the temperature-measuring optical fiber
A temperature measurement node is equipped with, 4 temperature-measuring optical fibers are provided with every pipe of the ground heat exchanger.
4. a kind of geotechnical stratified according to claim 1 hot physical property original position geo-thermal response test method, it is characterised in that the
Also include carrying out the ground heat exchanger (1) equivalent treatment before three steps, the ground heat exchanger (1) and described work as buret
Between there is following relationship：Wherein, D0It is the overall diameter of ground heat exchanger (1), DeIt is the equivalent when buret
Diameter.
5. a kind of geotechnical stratified according to claim 1 hot physical property original position geo-thermal response test method, it is characterised in that described
Arrangement in second step to the data includes：Give up the data measured in preceding 10 hours, give up and measured in the 5m of ground
Data.
6. a kind of geotechnical stratified according to claim 5 hot physical property original position geo-thermal response test method, it is characterised in that to institute
The estimation in the 3rd step is stated, is further included：The data that will be measured in step 2 obtain T in being brought into calculating formulaf1kOn λs、ρscsA function, by csρsIn 0 to 5*106Between travel through, λsTraveled through between 0 to 10, obtain Tf1kOne group of theoretical value.
7. a kind of geotechnical stratified according to claim 1 hot physical property original position geo-thermal response test method, it is characterised in that described
Data in 4th step by kth group calculate actual value Tf2kFurther include：By formula to Tf2kValue is calculated：
Tf2k=(Tin+T2+T3+……+Tout)/N
Wherein, TinIt is recirculated water into entrance temperature at K layers,
ToutTemperature during for recirculated water outflow kth layer,
T2、T3... it is followed successively by k layers of horizontal line the 3rd on second average temperature data of temperature measurement node collection, K layers of horizontal line
The average temperature data ... of temperature measurement node collection；
N is the number of temperature measurement node collection in k layers.
8. a kind of geotechnical stratified according to claim 1 hot physical property original position geo-thermal response test method, it is characterised in that described
Parameter Estimation Method is least square method, and the least square method is further included：
Step one, to each Tf1kValue and actual value Tf2kThe calculating of variance and F is carried out by equation below：
F=∑s (i=1, M) { Tf1ki- Tf2ki}2
Wherein M is the group number of test measurement data；
Step 2, relatively more each Tf1kThe size of the F that value is drawn, selects minimum F values, the corresponding T of minimum F valuesf1kIt is demand to be worth
Value；
Step 3, searches and the λ corresponding to requirementss、ρscsValue, the value is the corresponding λ of ground for calculating intervals、ρscsValue.
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| CN105136846B (en) * | 2015-08-14 | 2017-11-24 | 东南大学 | Rock And Soil thermal physical property parameter in-situ test instrument |
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| CN106908475A (en) * | 2017-04-07 | 2017-06-30 | 中国能源建设集团科技发展有限公司 | Ground rock heat transduction assay system and method |
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| CN109632872A (en) * | 2018-12-05 | 2019-04-16 | 新奥数能科技有限公司 | A kind of geo-thermal response test system and method based on thermoelectric cooling unit |
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| CN112613152B (en) * | 2020-11-26 | 2023-11-10 | 安徽工业大学 | Sleeve type buried pipe rock-soil thermophysical parameter estimation method |
| CN112632788B (en) * | 2020-12-28 | 2022-09-06 | 中国科学技术大学 | Thermal response test method for rock-soil thermal conductivity distribution |
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