Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall
Geothermal heat exchangers buried in diaphragm walls as an alternative of renewable energy sources can be quite competitive with shallow geothermal resources. The thermal response of a diaphragm wall embedded in the sand foundation under thermomechanical coupling conditions was followed in laborator...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2019
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irk-123456789-1883042023-02-23T01:27:24Z Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall You, S. Zhang, C.H. Cheng, X.H. Zhu, M. Научно-технический раздел Geothermal heat exchangers buried in diaphragm walls as an alternative of renewable energy sources can be quite competitive with shallow geothermal resources. The thermal response of a diaphragm wall embedded in the sand foundation under thermomechanical coupling conditions was followed in laboratory centrifuge tests. The model of exchanger tubes enclosed in the diaphragm wall embedded in the sand foundation accounts for lateral loading on the wall simulated by 1 and 50 g acceleration conditions in the centrifuge. Thermal loading, mechanical unloading, and thermomechanical coupling tests were carried out separately. The temperature, deformation, and soil pressure on the wall were monitored. The deformation and thermal stress along the cantilever wall were verified by numerical simulation. The thermal stress on the wall was revealed to be larger than the excavation-induced one. The maximum thermal stress was observed near the bottom of the wall. Though the wall was embedded in surrounding soil, heating caused accumulation of thermal stresses induced by temperature variations, which should be seriously considered in the heat exchanger design for cantilever walls of building structures. Геотермальные теплообменники, встроенные в стенку диафрагмы, являются альтернативным видом использования возобновляемой энергии, которая может быть получена из неглубоких геотермальных ресурсов. Исследован тепловой отклик стенки диафрагмы, вставленной в песочное основание, в условиях термомеханической связи путем лабораторных испытаний в центрифуге. Моделирование теплообменных трубок, встроенных в стенку диафрагмы, вставленную в песочное основание, включало поперечное нагружение стенки и осуществлялось в средах 1 и 50g в центрифуге. Испытания в условиях теплового нагружения, механической разгрузки и термомеханической связи проводились отдельно. Контролировались температура, деформация и давление грунта на стенку. Деформация и тепловое напряжение вдоль консольной стенки контролировались путем численного моделирования в каждом случае. Результаты испытаний показывают, что тепловое напряжение на стенке превышает напряжение, вызванное выемкой грунта. Максимальное тепловое напряжение наблюдалось вблизи основания стенки. Хотя стенка была связана окружающим грунтом, тепловое напряжение накапливалось в процессе нагрева в результате изменения температуры, что необходимо учитывать при конструировании теплообменника в консольной стене зданий. Геотермальні теплообмінники, вбудовані в стінку діафрагми, є альтернативним видом використання відновлюваної енергії, яка може бути отримана з неглибоких геотермальних ресурсів. Досліджено тепловий відгук стінки діафрагми, вставленої в пісочне підставу, в умовах термомеханічної зв'язку шляхом лабораторних випробувань в центрифузі. Моделювання теплообмінних трубок, вбудованих в стінку діафрагми, вставлену в пісочну основину, включало поперечне навантаження стінки і здійснювалося в середовищах 1 і 50g в центрифузі. Випробування в умовах теплового навантаження, механічного розвантаження і термомеханічного зв'язку проводились окремо. Контролювалися температура, деформація і тиск грунту на стінку. Деформація і теплову напругу вздовж консоль¬ной стінки контролювалися шляхом чисельного моделювання в кожному випадку. Результати випробувань показують, що теплове напруга на стінці перевищує напругу, викликану виїмкою грунту. Максимальна теплове напруга спостерігалося поблизу підстави стінки. Хоча стінка була пов'язана навколишнім грунтом, теплову напругу накопичувалося в процесі нагрівання в результаті зміни температури, що необхідно враховувати при конструюванні теплообмінника в консольної стіні будівель. 2019 Article Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall / S. You, C.H. Zhang, X.H. Cheng, M. Zhu // Проблеми міцності. — 2019. — № 1. — С. 72-79. — Бібліогр.: 10 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/188304 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел You, S. Zhang, C.H. Cheng, X.H. Zhu, M. Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall Проблемы прочности |
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Geothermal heat exchangers buried in diaphragm walls as an alternative of renewable energy sources can be quite competitive with shallow geothermal resources. The thermal response of a diaphragm wall embedded in the sand foundation under thermomechanical coupling conditions was followed in laboratory centrifuge tests. The model of exchanger tubes enclosed in the diaphragm wall embedded in the sand foundation accounts for lateral loading on the wall simulated by 1 and 50 g acceleration conditions in the centrifuge. Thermal loading, mechanical unloading, and thermomechanical coupling tests were carried out separately. The temperature, deformation, and soil pressure on the wall were monitored. The deformation and thermal stress along the cantilever wall were verified by numerical simulation. The thermal stress on the wall was revealed to be larger than the excavation-induced one. The maximum thermal stress was observed near the bottom of the wall. Though the wall was embedded in surrounding soil, heating caused accumulation of thermal stresses induced by temperature variations, which should be seriously considered in the heat exchanger design for cantilever walls of building structures. |
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Article |
| author |
You, S. Zhang, C.H. Cheng, X.H. Zhu, M. |
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You, S. Zhang, C.H. Cheng, X.H. Zhu, M. |
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You, S. |
| title |
Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall |
| title_short |
Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall |
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Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall |
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Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall |
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Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall |
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centrifuge simulation of the thermal response of a dry sand-embedded diaphragm wall |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2019 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/188304 |
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Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded Diaphragm Wall / S. You, C.H. Zhang, X.H. Cheng, M. Zhu // Проблеми міцності. — 2019. — № 1. — С. 72-79. — Бібліогр.: 10 назв. — англ. |
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UDC 539.4
Centrifuge Simulation of the Thermal Response of a Dry Sand-Embedded
Diaphragm Wall
S. You,
a
C. H. Zhang,
a,1
X. H. Cheng,
b
and M. Zhu
b
a School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing,
China
b Department of Civil Engineering, Tsinghua University, Beijing, China
1 shuang_you@163.com
Geothermal heat exchangers buried in diaphragm walls as an alternative of renewable energy
sources can be quite competitive with shallow geothermal resources. The thermal response of a
diaphragm wall embedded in the sand foundation under thermomechanical coupling conditions was
followed in laboratory centrifuge tests. The model of exchanger tubes enclosed in the diaphragm wall
embedded in the sand foundation accounts for lateral loading on the wall simulated by 1 and 50 g
acceleration conditions in the centrifuge. Thermal loading, mechanical unloading, and thermo-
mechanical coupling tests were carried out separately. The temperature, deformation, and soil
pressure on the wall were monitored. The deformation and thermal stress along the cantilever wall
were verified by numerical simulation. The thermal stress on the wall was revealed to be larger than
the excavation-induced one. The maximum thermal stress was observed near the bottom of the wall.
Though the wall was embedded in surrounding soil, heating caused accumulation of thermal stresses
induced by temperature variations, which should be seriously considered in the heat exchanger
design for cantilever walls of building structures.
Keywords: cantilever diaphragm wall, thermal stress, centrifuge model, deformation, dry
sand.
Introduction. Shallow geothermal energy is an environmentally friendly form of
renewable energy that can provide an alternative source of energy for heating/cooling
buildings. The heat exchangers can be buried in piles, diaphragm walls and basement slabs.
A fluid is circulated within the buried closed tubes to transport the heat stored in the soil to
the heating/cooling system in the building above [1]. Xia et al. [2] investigated the heat
transfer performance of geothermal heat exchangers installed in diaphragm walls in the
Shanghai Museum of Natural History. Hamada et al. [3] embedded heat exchange pipes in
friction piles for use in air-conditioning systems in offices and other civil buildings in
Japan. Laloui et al. [4] conducted an in situ test of a heat exchanger pile under actual
conditions at the Swiss Federal Institute of Technology in Lausanne. Stewart and
McCartney [5] used a centrifuge model to investigate the mechanical behavior of an
end-bearing pile subjected to cyclic heating. Goode et al. [6] used centrifuge models to
investigate how thermal influenced the ultimate capacity of piles embedded in dry medium
dense sand. Centrifuge models were also used to assess energy piles subjected to heating
and cooling cycles in clay [7] and the heating effects of piles embedded in saturated sand
[8], they found that shaft resistance of a pile increased as the temperature increasing, and
toe resistance increased more rapidly than shaft resistance due to a larger downward
expansion of the pile at higher temperature increment. The current understanding of
thermomechanical (TM) interaction between wall and soil under elevated temperatures is
still quite limited. Due to field studies are expensive and complicate, centrifuge modeling
was used to study the TM coupling process. This approach provides a better understanding
of the geotechnical design for safety control. In this study, the exchanger tubes enclosed in
a diaphragm wall (Fig. 1) are designed and carried out in a dry sand foundation. The major
© S. YOU, C. H. ZHANG, X. H. CHENG, M. ZHU, 2019
72 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
objectives are to investigate thermal response of cantilevered diagram wall in TM coupling
conditions. Moreover, related TM interaction between wall and soil under heating condition
was also studied.
1. Test Models and Procedure.
1.1. Centrifuge Modeling. To physically model the heat exchange in the diaphragm
wall embedded in sand, a 1/ N sized model of the prototype diaphragm wall was placed in
a centrifuge and the heat diffusion processes were accelerated N 2 times compared with
those in the field because the heat transfer rates were N times faster under N g�
conditions. The other relevant scaling laws are summarized in Table 1.
1.2. Model Box Setup. The geo-centrifuge at Tsinghua University has a maximum
acceleration of 250g, a maximum load of 50g-ton, an effective radius of 2 m, a
0.8�0.7�0.6 m nacelle, and a 0.6�0.2�0.55 m model casing (Fig. 2). To simulate the
thermal response of the diaphragm wall in the sand foundation in TM coupling conditions,
all of the tests were performed under 50g. The cantilevered diaphragm wall was made of
copper, and was 30 cm high, 20 cm wide, and 1.4 cm thick (the prototype was
15�10�0.7 m). The excavation depth was 10 cm, which corresponded to a 5 m deep
prototype excavation. A semiconductor chilling plate (40�40�3.9 mm) was used to heat
the wall from the ambient temperature to around 50�C. The model was wrapped in foam
plastic for thermal insulation.
Centrifuge Simulation of the Thermal Response ...
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 73
Fig. 1. Skeleton of the geothermal heat exchanger embedded in a cantilevered diaphragm wall.
T a b l e 1
Relevant Scaling Ratio ([9, 10])
Parameter Model–prototype ratio Parameter Model–prototype ratio
Length 1/ N Strain 1
Temperature 1 Energy density 1
Density 1 Energy 1 3/ N
Mass 1/ N 3 Stress 1
Acceleration N Force 1/ N 2
Velocity 1 Heat diffusion 1 2/ N
Displacement 1/ N
1.3. Measurements. Six strain foils were affixed to the middle of the wall at depths of
10, 15, and 20 cm to monitor the vertical deformation of the wall. Soil pressure sensors
were situated on both sides of the wall at depths of 10 and 20 cm to monitor the soil
pressure. Twelve thermocouple temperature sensors were used to monitor the temperature
distribution in the model, and one was used to monitor the ambient temperature. Six
sensors were installed on each side of the wall (Fig. 3). A camera was used to monitor the
movement of the soil.
S. You, C. H. Zhang, X. H. Cheng, and M. Zhu
74 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
Fig. 2. Geotechnical centrifuge and model casing.
Fig. 3. Arrangement of the gauges in the testing model: (a) strain foil, (b) temperature sensor.
a b
1.4. Testing Program. Copper model energy cantilever tests with different
temperatures and loading sequences were carried out in dry medium sand. The test program
is summarized in Table 2. (i) Sensor calibration measurements were conducted under a 1g
gravity field and an ambient temperature of 28�C (summer in Beijing), and the results were
used as a reference. (ii) A thermal coupling test was conducted under 50g with no
excavation and the wall was heated to 50�C to analyze the thermal effect on the soil
pressure, with the thermal loading denoted as t. (iii) Mechanical tests were conducted
under 50g with the wall excavated and a constant ambient temperature of around 28�C to
determine the influence of mechanical unloading on the mechanism of the wall, with the
mechanical loading denoted as m. (iv) Finally, TM tests were conducted under 50g with the
wall excavated on one side and heated to 50�C to achieve a TM coupled field (denoted as
tm). Overall, the tests aimed to simulate the geothermal energy circulating in the absorber
tubes enclosed in the diaphragm wall embedded in the sand.
2. Interpretation of the Test Results.
2.1. Thermal Loading Simulations under 50g. The centrifuge tests were performed at
50g , and the scaling relationships are listed in Table 1. As shown in Fig. 4, the temperature
close to the wall drops quickly. In contrast, due to the heat transfer, the temperature of the
soil (50 cm distance) slightly increases.
The unacceptably high strain on the wall might have been induced by the large
expansion of the copper, which had a thermal expansion coefficient (189 10 6. �
�
�
�C 1),
twice that of concrete (9 10 6
�
�
�
�C 1).The strain shows a downtrend as the temperature
decreases (Fig. 5).
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 75
Centrifuge Simulation of the Thermal Response ...
T a b l e 2
Test Program
Test Gravity field Temperature (�C) Loading sequence
i g 28 none
ii 50g 50 t
iii 50g 28 m
i� 50g 50 tm
Fig. 4 Fig. 5
Fig. 4. Temperature distribution along the wall with the time.
Fig. 5. Strain distribution along the wall with the time.
Figure 6 shows the increased stress induced by the heating of the wall and the average
thermal stresses at the depths of 100 and 200 mm. Overall, the thermal stress increased with
the depth and the stress recovered as the temperature decreased closer to the wall (Fig. 6).
Note: tensile stress is defined as positive, compressive stress as negative.
2.2. Mechanical Unloading Simulation under 50g. Under the constant ambient
temperature of about 28�C (Fig. 7), the strain changed smoothly due to the mechanical
unloading (Fig. 8). Compressive strain was observed at points 3 and 6, which were
constrained by the soil.
The increased stress induced by the excavation and the average stress at the depths of
100 and 200 mm are shown in Fig. 9. Compressive stress could be observed at the bottom
of the wall and there was a greater distribution of stress on the excavated side than on the
reverse face. Note: tensile stress is defined as positive, compressive stress as negative.
2.3. TM Coupling Simulation under 50g. After the wall was heated to 50�C and a
steady temperature was attained, the heating instrument was disassembled. During the test,
the temperature dropped quickly close to the wall, but increased slightly in the soil (50 cm
from the wall), as is shown in Fig. 10.
Figure 11 shows that the strain decreased with the depth, while strain on the excavated
side of the wall was higher than that in the corresponding point of its reverse side.
76 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
S. You, C. H. Zhang, X. H. Cheng, and M. Zhu
Fig. 6. Thermal stress distribution along the wall with the time.
Fig. 7 Fig. 8
Fig. 7. Temperature distribution along the wall with the time.
Fig. 8. Strain distribution along the wall with the time.
Unacceptably high levels of strain were induced by the difference between the thermal
expansion of copper (189 10 6. �
�
�
�C 1) and that of the concrete (9 10 6
�
�
�
�C 1). During the
test (30 min), the strain recovered as the temperature decreased (Fig. 11).
Figure 12 shows the increases in thermal stress and the average thermal stresses at the
depths of 100 and 200 mm under the TM coupling conditions. The thermal loading had a
distinct effect on the distribution of the increases in stress. However, the stress recovered as
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 77
Centrifuge Simulation of the Thermal Response ...
Fig. 9. Thermal stress distribution along the wall with the time.
Fig. 10 Fig. 11
Fig. 10. Temperature distribution along the wall with the time.
Fig. 11. Strain distribution along the wall with the time.
Fig. 12. Thermal stress distribution along the wall with the time.
the temperature decreases (Fig. 12). Note: tensile stress is defined as positive, compressive
stress as negative.
2.4. Comparison. Comparison of the average stress distributions on the wall at the
depths of 100 and 200 mm shows that the stress induced by the thermal transfer in the wall
was greater than the excavation-induced stress (Fig. 13). The thermal expansion coefficient
of copper (189 10 6. �
�
�
�C 1) was twice as large as that of concrete (9 10 6
�
�
�
�C 1), which
might have caused the unacceptably high stress in the wall.
Conclusions. In this study, centrifuge tests were performed on four models to
investigate the thermal-excavation coupling mechanism of a cantilevered wall embedded in
sand. The preliminary experimental tests show that the thermal stress in the wall was
greater than the excavation-induced stress. The thermal stress was not uniformly distributed
in the wall, with the maximum values observed near the bottom of the wall. The thermal
stress was affected by the increased temperature in the wall and the constraining effects of
the surrounding soil.
Acknowledgments. The authors are grateful for the funding provided by the National
Nature Science Foundation of China (51774021), and the ‘Geo-energy systems simulator:
from building scale to city scale’ of the Low Carbon Energy University Alliance of
Tsinghua–Cambridge University–MIT LCEUA (20123010002). The first author gratefully
acknowledges the financial support from China Scholarship Council (201706465003).
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78 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1
S. You, C. H. Zhang, X. H. Cheng, and M. Zhu
Fig. 13. Comparison of the thermal stress distributions in the wall at depths of 100 and 200 mm with
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10. R. N. Taylor, Geotechnical Centrifuge Technology, CRC Press, London (2004).
Received 15. 03. 2018
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2019, ¹ 1 79
Centrifuge Simulation of the Thermal Response ...
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|