Influence of water content to the thermal conduction characteristics of soils in Beijing

Guo-Hang TANG1*, Jing-Wei CHEN2, Wei CHEN3

1*Master student, Department of Civil Engineering, Beihang University, Beijing, China

2Master student, Department of Civil Engineering, Beihang University, Beijing, China

3Master student, Department of Civil Engineering, Beihang University, Beijing, China

Corresponding author:Guo-Hang TANG, Master student, Department of Civil Engineering, Beihang University, Xueyuan Road No. 37, Haidian District, Beijing, 100191, China, E-mail:2410851776@qq.com

Citation: TANG GH, CHEN JW, CHEN W (2021) Influence of water content to the thermal conduction characteristics of soils in Beijing. J Civil Engg ID 2(2):18-28.

Received Date: June 02, 2021; Accepted Date: June 14, 2021; Published Date: June 21, 2021

Abstract

In this paper, the thermal conduction characteristics of sandy soil, silty clay and clay in Beijing area with different volumetric water content are researched via laboratory tests. Based on the test data and the equation of unsteady heat conduction in semi-infinite solid, the thermal diffusivity of three kinds of the soils was back calculated. The relationship between the volumetric water content and the thermal diffusivity is analyzed. It is found that the thermal diffusivity of silty clay or clay is linearly related to the volumetric water content, and the thermal diffusivity of sandy soil is nonlinearly related to the volumetric water content. The characteristic of thermal diffusivities of Beijing soils is different to that of other soils, and should be noticed in geotechnical field.

Key words: Soil; Temperature Field; Volumetric Water Content; Test; Thermal Diffusivity

1. Introduction

The water content has great influence on the distribution of temperature field for soils. Since Gardner et al. (1955; 1959) found that it was difficult to quantitatively analyze the influence, lots of researchers began to pay attention to the relationship between soil temperature field and soil water content (Cray,1966; Haridasan & Jensen, 1972; Nakano et al.,1984). Hopmans & Dane (1986) added different amounts of water to the soil, and found that the depth of soils affected by the same ambient temperature changed with the initial water content. Wang & Li (2018) pointed out that the influence depth was about 40cm with the top cryogenic boundary at 0℃ in the silty soil, and the temperature field of the soil had a certain relation with the initial water content of the soil. Using the measured data collected by the observatory, the relationship between soil water content and soil thermal diffusivity had also been studied (Roxy et al., 2010; Roxy et al.,2014). Their research showed that soil thermal diffusivity increased first and then decreased with the increase of water content.

Many models for simulating soil thermal characteristics had been developed. Parikh et al. (1979) used an unstable method to detect the thermal diffusivity of silty soil. Côté & Konrad (2005) modified the thermal conductivity model to calculate the dry thermal conductivity of soil; Balland & Arp (2005) considered the influence of the soil organic matter based on the Johansen model; Lu et al. (2007) modified the model of Côté& Konrad (2005) to suit the finegrained soils at low-saturation. Barryet al. (2015) evaluated most of soil thermal models. Lukiashchenko& Arkhangelskaya (2018) considered the influence of soil texture in simulating thermal characteristics of soils.

The soil in Beijing is seasonally frozen, which is harmful to urban engineering construction. However, there is still a lack of research on the thermal conduction characteristics of soils in Beijing area. Therefore, in this paper, we take three common soil types in Beijing area as research samples: sandy soil, silty clay and clay. We measure the temperature field of soil samples in a test barrel under 0℃ temperature boundary. Based on the related theory and test results of soil temperature field, we back calculate the thermal diffusivity of soil with different volumetric water content, and analyze the relationship between the thermal diffusivity and the volumetric water content of soils.

2. Tests

2.1 Soil samples in test

Three kinds of soil samples are selected in Beijing area for the tests. As shown in Fig.1, the sandy soil sample is from Mentougou District in Beijing (115°50′N, 40°3′E); the silty clay sample is from Daxing District in Beijing (116°25′N, 39°30′E); the clay sample is from Haidian District in Beijing (116°21′N, 40°0′E).Fig.2 shows the photographs of the soil samples of sandy soil, silty clay and clay, respectively. The basic characteristics of the soil samples are given in Table 1.

Figure 1: Location of the soil samples in Beijing

2.2 Test instrument

The schematic drawing of instrument is shown in Fig. 3. The soil sample is laid in a test barrel. The size of the test barrel is 100cm in height, 18cm in inner diameter and 20cm in outer diameter. The material of test barrel is polymethyl methacrylate. The test barrel is wrapped with a thermal insulation layer to avoid the influence of external temperature. The temperature control devices are at the top and bottom of the barrel, respectively. The top temperature control device keeps 0℃, and the bottom temperature control device keeps 22℃ which is the same as the room temperature.

The probes of the temperature sensor are placed at 1cm, 2cm, 5cm, 9cm, 15cm, 25cm and 40cm in depth respectively. The probes are placed in the middle of the soil column to reduce the boundary influence. The work range of temperature sensor is -50℃~50℃; the accuracy is 0.1℃; the sampling interval is two seconds.

2.3 Procedure of test

The room temperature is kept at 22℃ during the experiment. The soils are prepared under a constant dry density with different volumetric water content. Then, the soils and temperature sensors are laid into the test barrel. For the three kinds of soils, each one has five sets of tests with different volumetric water content. The volumetric water content and the dry density of the laid soil samples are shown in Table 2.

Apply the temperature control devices at the top and the bottom of the soil sample respectively, and the data of temperature sensors is recorded in the meantime. With the working of the temperature control devices and the recording of the temperature sensors, the test lasts 24 hours.

3. Test results

3.1 Sandy soil

For the sandy soil with different volumetric water content, the temperature curves changing with time of each sensor in soil samples are obtained as shown in Fig. 4.

It can be seen from Fig. 4 that, the temperature of the soil in depth of 25cm drops rapidly in five hours, while the temperature of the soil deeper than 25cm almost do not change. From Fig. 4(c) ~ (e), we can see the temperature of soil deeper than 25cm start to slowly drop after five hours. From Fig. 4 (a) and (b), it can be seen that the temperature of the soil at the depth of 40 cm nearly do not change in 24 hours.

3.2 Silty clay

The temperature curves changing with time for silty clay are obtained as shown in Fig. 5.

Similar to the sandy soil, it can be seen from Fig. 5 that the temperature of the silty clay in depth of 25cm drops rapidly in four hours, while the temperature of the sample deeper than 25cm almost do not change. From Fig. 5 (c) ~ (e), we can see the temperature of the silty clay deeper than 25cm start to slowly drop after four hours. From Fig. 5 (a) and (b), it can be seen that the temperature of the sample at the depth of 40 cm nearly do not change in 24 hours.

Figure 2: Soil samples: (a) sandy soil; (b) silty clay; (c) clay

Table 1: Basic characteristics of three kinds of soils

Soil

Particle-size distribution, %

Plasticity index

Specific gravity

Mass water content,%

Bulk density, g/cm³

2mm~0.5mm

0.5mm~0.075mm

≤0.075mm

Sandy soil

43.79

53.72

2.49

\

2.67

\

1.69

Silty clay

\

15.41

2.69

9.21

1.66

Clay

\

18.15

2.70

12.41

1.58

Figure 3: Schematic drawing of the test instrument

Table 2: The volumetric water content and dry density of three kinds of soils



Volumetric Water content, m3m-3

Number

Sandy soil

Silty clay

Clay

(a)

0.008

0.025

0.030

(b)

0.012

0.052

0.060

(c)

0.020

0.084

0.091

(d)

0.054

0.123

0.150

(e)

0.091

0.170

0.203

Dry density, g/cm³

1.70

1.52

1.41

Figure 4:The temperature curve changing with time for sandy soil: volumetric water content of (a)0.008m3 m-3; (b)0.012m3 m-3; (c)0.020m3 m-3; (d)0.054m3 m-3; (e)0.091m3 m-3

Figure 5:The temperature curve changing with time for silty clay: volumetric water content of (a)0.025m3 m-3; (b) 0.052m3 m-3; (c)0.084m3 m-3; (d)0.123m3 m-3; (e)0.170m3 m-3

3.3 Clay

The temperature curves changing with time for clay are obtained as shown in Fig.6.

It can be seen from Fig. 6 that the temperature of the clay in depth of 25cm drops rapidly in three hours, while the temperature of the sample deeper than 25cm almost do not change. From Fig. 6 (c) ~ (e), we can see the temperature of the clay deeper than 25cm start to slowly drop after four hours. From Fig. 6 (a) and (b), it can be seen that the temperature of the sample at the depth of 40 cm nearly do not change in 24 hours.

4. Analysis

4.1 Temperature field

To research the influence of volumetric water content to the temperature field for soils in Beijing, the final (t=24 h) temperature field is monitored from tests of three kinds of soils in depth of 40 cm are drawn in Fig. 7.

As can be seen from Fig. 7, it can be found that no matter sandy soil, silty clay or clay, the temperature of the same embedment depth of soil is lower than that of soil with higher value of water content.

Figure 6: The temperature curve changing with time for clay: volumetric water content of (a)0.030m3 m-3; (b)0.060m3 m-3; (c)0.091m3 m-3; (d)0.150m3 m-3; (e)0.203m3 m-3

It indicates that in range of volumetric water content for sandy soil (0.008m3 m-3~0.091m3 m-3), silty clay (0.025m3 m-3~0.170m3 m-3) and clay (0.030m3 m-3~0.203m3 m-3) as given in tests, the heat transfer capability of soil will be higher when the volumetric water content of soils rises.

Figure 7: The final temperature filed of soils with different volumetric water content in the 24h tests: (a) sandy soil; (b) silty clay; (c) clay

4.2 Thermal diffusivity

In order to further research therelationship between Volumetric water content and its heat transfer capability, based on the temperature curves in Figs. 3~5 and theunsteady heat conduction theory in semi-infinite soild,the thermal diffusivity of soil samples are back calculated.

The temperature t in test samples can be calculated via the eqution from the classic theory of heat transfer, which is presented as:

t(x,t)=( t 0 t w )erf x 2 aτ + t w        (1) MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiaacI cacaWG4bGaaiilaiaadshacaGGPaGaeyypa0JaaiikaiaadshadaWg aaWcbaGaaGimaaqabaGccqGHsislcaWG0bWaaSbaaSqaaiaadEhaae qaaOGaaiykaiaadwgacaWGYbGaamOzamaabmaabaWaaSaaaeaacaWG 4baabaGaaGOmamaakaaabaGaamyyaiabes8a0bWcbeaaaaaakiaawI cacaGLPaaacqGHRaWkcaWG0bWaaSbaaSqaaiaadEhaaeqaaOGaaeii aiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabIcacaqGXa Gaaeykaaaa@54C6@

Where τ is the time, in s;x is the depth of soil,in m;α is the thermal diffusivity, in m2 /s;t is the initial temperature , in ℃; tw is the boundary temperature , in ℃; erf( ) is the Gaussian Error function, which can be expressed as:

erf(η)= 2 π   0 η exp( x 2 ) dx    (2) MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyzaiaabk hacaqGMbGaaeikaiabeE7aOjaabMcacaqG9aWaaSaaaeaacaaIYaaa baGaeqiWdahaaiaabccadaWdXbqaaiGacwgacaGG4bGaaiiCaiaacI cacqGHsislcaWG4bWaaWbaaSqabeaacaaIYaaaaOGaaiykaaWcbaGa aGimaaqaaiabeE7aObqdcqGHRiI8aOGaaeizaiaabIhacaqGGaGaae iiaiaabccacaqGGaGaaeikaiaabkdacaqGPaaaaa@520C@

The least square method is applied to calculate the value of the thermal diffusivity, and the calculation method of minimum error is given as:

minΔT(α)= i=1 d [T( α i ) T i ] 2 /d      (3) MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyBaiaacM gacaGGUbGaeuiLdqKaamivaiaacIcacqaHXoqycaGGPaGaeyypa0Za aabCaeaacaGGBbGaamivaiaacIcacqaHXoqydaWgaaWcbaGaamyAaa qabaGccaGGPaaaleaacaWGPbGaeyypa0JaaGymaaqaaiaadsgaa0Ga eyyeIuoakiabgkHiTiaadsfadaWgaaWcbaGaamyAaaqabaGccaGGDb WaaWbaaSqabeaacaaIYaaaaOGaai4laiaadsgacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabccacaqGOaGaae4maiaabMcaaaa@56F3@

Where α is the thermal diffusivity, in m2/s; T(αi) is the temperature prediction value of the set thermal diffusivity on the sequence i, in ℃; Ti is the monitored temperature value in tests on sequence i, in ℃; d is the sequence number; ΔT(α) is the error value between the predicted value and the monitored value.

According to the data consulted (Oscar et al., 2018; Krishnaiah & Singh, 2004; Mikailsoy & Shein, 2019; Arkhangelskaya & Lukyashchenko, 2018), the thermal diffusivity of soil is between 1.22 × 10-7m2 /sand 8.04 × 10-7m2 /s. So the initial value α0 is set as 1.00×10-7m2 /s, and the step value is set as 1.00 ×10-10m2 /s. The calculated thermal diffusivities of three kinds of soils with different volumetric water content are shown in Table 3.

Table 3: The calculated thermal diffusivities of three kinds of soils with different volumetric water content

Soil

Volumetric water content,m3m-3

Thermal diffusivity,m2/s×10-7

Error value



Sandy soil

0.008

1.494

0.450

0.012

1.603

0.422

0.020

2.467

0.925

0.054

2.728

0.370

0.091

3.143

0.606



Silty clay

0.025

1.603

0.722

0.052

1.991

0.741

0.084

2.423

0.490

0.123

2.658

0.491

0.170

3.068

0.602



Clay

0.030

1.358

0.702

0.060

1.521

0.900

0.091

2.162

0.403

0.150

2.706

0.773

0.203

3.363

0.569

Based on the calculated thermal diffusivity in Table 3, the temperature field of soil samples in tests can be predicted. For example, the simulated temperature curves of sandy soil sample (volumetric water content, 0.008m3 m-3), the silty clay sample (volumetric water content, 0.084m3 m-3) and the clay sample (volumetric water content, 0.091m3 m-3)are compared to the test monitored results as shown in Fig. 8, respectively.

Figure 8: The simulated temperature curves versus the monitored data in tests: (a) Sandy soil, volumetric water content of 0.008m3 m-3; (b) Silty clay, volumetric water content of 0.084m3 m-3; (c) Clay, volumetric water content of 0.091m3 m-3

It can be seen from the Fig. 8 that the simulated temperature curves can better fit the monitored temperature curves in tests. However, from Fig. 8 we can see that the simulated temperature curves are all lower than the monitored curves in the time range of 20 h ~ 24 h. It can be explained that it is difficult to thoroughly prevent test samples from the influence of ambient temperature in the test period time (24 hours).

Figure 9: Comparison of the relationship between threethermal diffusivities of sample soil and volumetric water content

Based on the value in Table 3, the thermal diffusivities of sandy soil, silty clay and clay with different volumatric water content can be ploted in Fig. 9.

It can be seen from Fig. 9 that the thermal diffusivities of sandy soil samplespresent an nonlinear relationship with the volumetric water content (in the range of 0.008m3 m-3~0.091m3 m-3). The thermal diffusivities of silty clay samples present an approximately linear relationship with the volumetric water content (in the range of 0.025m3 m-3~ 0.170m3 m-3). The thermal diffusivities of clay samples also present an approximately linear relationship with the volumetric water content (in the range of 0.030m3 m-3~0.203m3 m-3).

4.3 Comparison

The characteristic of Beijing sandy soils is compared with those of the Lammelic Arenosols (Arkhangelskaya & Lukyashchenko, 2018) and Brunic Arenosols (Lukiashchenko & Arkhangelskaya, 2018) in Fig. 10, from which we can see that the thermal diffusivities of the three kinds of sandy soil all present nonlinear relationships with thevolumetricwater content. On the other hand, the thermal diffusivity of Beijing sandy soil is much lower than the other sandy soils. It can be explained that there may be much clay or silt in the Beijing sandy soil samples.

The characteristic of Beijing silty clay is compared with those of Moscow silty clays (Arkhangelskaya & Lukyashchenko, 2018; Mady & Shein, 2018) in Fig. 11. We can see that the thermal diffusivities of the three kinds of silty clay present linear relationships with the volumetric water content. Furthermore, the thermal diffusivity of

Figure 10: The thermal diffusivityof sandy soilin Beijing vesus other sandy soils (data ofLammelic Arenosols is from Arkhangelskaya & Lukyashchenkoin 2018; data of Brunic Arenosolsis from Lukiashchenko & Arkhangelskayain 2018)

Figure 11: The thermal diffusivity of silty clayin Beijing vesus Moscow silty clays (data of Moscow silty clay 1is from Arkhangelskaya & Lukyashchenkoin 2018; data of Moscow silty clay 2 is from Mady & Sheinin 2018)

Figure 12: The thermal diffusivityof clayin Beijing vesus other calys (data ofKamennaya Steppe clayis from Arkhangelskaya & Lukyashchenkoin 2018;data of Anthrosols is from Lukiashchenko & Arkhangelskayain 2018)

Beijing silty clay is slightly higher than the Moscow silty clays.

The characteristic of Beijing clay is compared with those of Kamennaya Steppe clay (Arkhangelskaya & Lukyashchenko, 2018) and Anthrosols (Lukiashchenko & Arkhangelskaya, 2018) in Fig. 12. We can see that the thermal diffusivities of Beijing clay present a linear relationship with the volumetric water content, and the thermal diffusivitie of Beijing clay is higher than those of Kamennaya Steppe clay and Anthrosols.

5. Conclusion

The influence of water content to the soil temperature field are researched for the sandy soil, silty clay and clay samples in Beijing area. Via laboratory tests, the temperature curves of soil samples with different volumetric water content are monitored, and the according thermal diffusivities of soil samples are back calculated and analyzed. There are three conclusionsas following:

  1. In the range of volumetric water content(sandy soil, 0.008~0.091m3 m-3; silty clay, 0.025~0.170m3 m-3; Clay, 0.030~0.203m3 m-3) for soils in Beijing area, the thermal diffusivity of sandy soil (dry density, 1.70 g/cm3 ) has a nonlinear relationship with the volumetric water content, that of silty clay (dry density, 1.52 g/cm3 ) has an appoximate linear relationship with the volumetric water content, and that of clay (dry density, 1.41 g/ cm3 ) also has an appoximate linear relationship with the volumetric water content.
  2. Based on the monitored temperature field in tests and the least square method in this paper, the thermal diffusivity of soils can be effectively back calculated and the temperature field can be reasonably simulated.
  3. The thermal diffusivity of Beijing sandy soil is lower than those of Lammelic Arenosol sand Brunic Arenosols; the thermal diffusivity of Beijing silty clay is similar as the Moscow silty clays; the thermal diffusivitie of Beijing clay is higher than those of Kamennaya Steppe clay and Anthrosols. The characteristic of the thermal diffusivity of Beijing soils should be noticed in geotechnical field.

Acknowledgements

This paper is supported by the National Natural Science Foundation of China, NSFC (Grant No. 51978028).

References

  1. Arkhangelskaya T, Lukyashchenko K. Estimating soil thermal diffusivity at different water contents from easily available data on soil texture, bulk density, and organic carbon content. Biosyst. Eng. 2018;168:83-95.

  2. Balland V, Arp PA. Modeling soil thermal conductivities over a wide range of conditions. J. Environ. Eng. Sci. 2005;4(6):549-558.

  3. Barry MD, Bouazza A, Wang B, Singh RM. Evaluation of soil thermal conductivity models. Can. Geotech. J. 2015;52(11):1892-1900.

  4. Cheng LZ, Wang ND, Chen JW. Research of the moisture migration in soil affected by water content. New. Adv. Geotech. Eng. 2018;127-131.(in Chinese)

  5. Cray JW. Soil moisture transport due to thermal gradients: practical aspects. Soil Sci. Soc. Amer. Proc. 1966;30:428-433.

  6. Côté J, Konrad JM. A generalized thermal conductivity model for soils and construction materials. Can. Geotech. J. 2005;42(2):443-458.

  7. Côté J, Konrad JM. Thermal conductivity of base-course materials. Can. Geotech. J. 2005;42(1):61-78.

  8. Gardner WR. Solution of the flaw equation for the drying of soils and the porous media. Soil Sci. Soc. Axn. Pros. 1959;23:183-187.

  9. Gardner Robert. Relation of Temperature to moisture tension of soil. Soil Sci. 1955;79(4):257-266.

  10. Haridasan M, Jensen RD. Effect of temperature on pressure head-water content relationship and conductivity of two soils. Soil Sci. Soc. Amer. J. 1972;36:703-708.

  11. Hopmans JW, Dane JH. Temperature dependence of soil hydraulic properties. Soil Sci. Soc. Amer. J. 1986;50:4-9.

  12. Krishnaiah S, Singh DA. A Device for Determination of Thermal Properties of Soil. J. Test. Eval. 2004;32(2):114-119.

  13. Lu S, Ren T, Gong Y, Horton R. An improved model for predicting soil thermal conductivity from water content at room temperature. Soil Sci. Soc. Amer. J. 2007;71(1):8-14.

  14. Lukiashchenko KI, Arkhangelskaya TA. Modelling Thermal Diffusivity of Differently Textured Soils. Eurasian. Soil. Sci. 2018;51(2):183-189.

  15. Mady AY, Shein E. Estimating Soil Thermal Diffusivity Using Pedotransfer Functions with Nonlinear Regression.Open Agriculture Journal. 2018;12(1):164-173.

  16. Mikailsoy FD, Shein EV. Comparison of four classical algorithms to determine the apparent thermal diffusivity of heavy clay soil in field and laboratory column experiments. IOP. Conf. Series. Earth & Environ. Sci. 2019;368(Conf 1):012033.

  17. Nakano Y, Tice AR, Oliphant JL. Transport of water in frozen soil III: experiment on the effects of ice content. Adv. Water. Resour. 1984;7(1):28-34.

  18. Oscar FSA, Jorge AAA, Beatris AET, Artemio JBF. Determining the In Situ Apparent Thermal Diffusivity of a Sandy Soil. Rev. Bras. Cienc.Solo. 2018;42:e0180025. doi.org/10.1590/18069657rbcs20180025

  19. Parikh RJ, Havens JA, Scott HD. Thermal diffusivity and conductivity of moist porous media. Soil Sci. Soc. Amer. J. 1979;43(5):1050-1052.

  20. Roxy MS, Sumithranand VB, Renuka G. Variability of soil moisture and its relationship with surface albedo and soil thermal diffusivity at Astronomical Observatory. Thiruvananthapuram, South Kerala. J. Earth. Syst. Sci. 2010;119(4):507-517.

  21. Roxy MS, Sumithranand VB, Renuka G. Estimation of soil moisture and its effect on soil thermal characteristics at Astronomical Observatory. Thiruvananthapuram, South Kerala. J. Earth. Syst. Sci. 2014;123(8):1793-1807.