The Influence of Regional Freeze–Thaw Cycles on Loess

Article The Inﬂuence of Regional Freeze–Thaw Cycles on Loess Landslides: Analysis of Strength Deterioration of Loess with Changes in Pore Structure

Zuyong Li * , Gengshe Yang and Hui Liu

School of Architecture and Civil Engineering, Xi’an University of Science and Technology, Xi’an 710054, China; [email protected] (G.Y.); [email protected] (H.L.) * Correspondence: [email protected]

Received: 25 September 2020; Accepted: 28 October 2020; Published: 30 October 2020

Abstract: The loess landslide in Gaoling District of Xi’an, Shaanxi in China is closely related to the seasonal freeze–thaw cycle, which is manifested by the destruction of pore structure and strength deterioration of the loess body under freeze–thaw conditions. In order to study the relationship between macro-strength damage and pore structure deterioration of saturated loess under freeze–thaw conditions and its influence on the stability of landslides, this paper explores the effect of freeze–thaw cycles on the strength of saturated undisturbed loess through triaxial compression test, and explores the micro-microstructure changes of saturated undisturbed loess through scanning electron microscopy (SEM) and nuclear magnetic resonance (NMR). This is to analyze the evolution of the pore structure and strength loss evolution of saturated loess during the freeze–thaw process, and to describe the freeze–thaw damage of saturated undisturbed loess through the change of porosity and strength deterioration. Then, the internal correlation expression between the porosity change and the strength degradation is established to realize the verification analysis of the test data based on the correlation model. The research results show that: (1) As the number of freeze–thaw cycles increases, the peak strength loss rate gradually increases, and the strength deterioration of saturated loess becomes more and more obvious. (2) The freeze–thaw cycle will lead to the development of pores and cracks in the sample, accompanied by the generation of new cracks, which will cause the deterioration of the pore structure of the sample as a whole. (3) The response of strength damage and porosity deterioration of saturated undisturbed loess is roughly similar under the freeze–thaw cycle. The change in porosity can be measured to better reflect the strength deterioration of saturated loess. Therefore, the change of pore structure of undisturbed loess under freeze–thaw cycle conditions is tested by field sampling and indoor tests to reflect the phenomenon of strength deterioration, thereby analyzing the stability of loess slopes.

Keywords: freeze–thaw damage; scanning electron microscopy; nuclear magnetic resonance; porosity; strength degradation; landslide

1. Introduction Loess is characterized by looseness, porosity, and easy water seepage. It is easily eroded by ﬂowing water to form gullies, which can easily cause subsidence and collapse [1–4]. Loess is widely distributed in Northwestern China, as shown in Figure1. Due to the special geographical location and climatic conditions, the annual temperature diﬀerence is large about 35 ◦C forming a seasonal frozen soil area with regional characteristics. The region lies in a process of freezing and melting cycles all the year round, and is sensitive to thermal disturbances in the external environment [5]. The freeze–thaw cycle is part of the main factors that cause the deterioration of the physical and

Water 2020, 12, 3047; doi:10.3390/w12113047 www.mdpi.com/journal/water Water 2020, 12, 3047 2 of 18 Water 2020, 12, x FOR PEER REVIEW 2 of 18 mechanical propertiesproperties ofof loess, loess, which which aggravates aggravates the the landslide landslide hazard hazard problem problem in thein the loess loess area. area. In the In projectthe project under under construction construction and proposed, and proposed, the yellow the yellow soil foundation soil foundation and slope and are slope prone are to instabilityprone to instabilityand damage and under damage the e ﬀunderect of seasonalthe effect freeze–thaw of seasonal cycles, freeze–thaw which will cycles, endanger which the will construction endanger andthe constructionassociated safety and [associated6,7]. For example, safety [6,7]. during For theexam occurrenceple, during of athe slope occurrence failure, theof a freeze–thawslope failure, cycle the playsfreeze–thaw a catalytic cycle role. plays When a catalytic frozen, role. the When ice crystal frozen, frost the expansion ice crystal force frost destroys expansion the force soil structure.destroys Thethe soil deformation structure. is The unrecoverable deformation during is unrecoverable melting, resulting during in melting, a decrease resulting in strength in a anddecrease spalling in strengthunder the and softening spalling action under of waterthe softening and the action catalysis of ofwater ice. Theand freeze–thawthe catalysis cycle of ice. will The cause freeze–thaw relatively cycleintense will freeze–thaw cause relatively erosion intens on thee freeze–thaw loess, changing erosion the soil on structurethe loess, and changing causing the uneven soil structure settlement and of causingthe foundation. uneven Therefore,settlement inof seasonallythe foundation. frozen Therefor soil areas,e, in the seasonally freeze–thaw frozen cycle soil is areas, closely the related freeze– to thawthe instability cycle is closely of loess. related So, it to is the necessary instability to furtherof loess. explore So, it is the necessary eﬀects ofto freeze–thawfurther explore cycles the effects on the physicalof freeze–thaw and mechanical cycles on the properties physical of and loess. mechanical properties of loess.

Figure 1. SpatialSpatial distribution distribution of of landslides landslides in in the the Loess Plateau of the Yellow River Basin [[8].8].

The freeze–thaw cycle is extremelyextremely destructive, which can change the internal structure of the loess and weaken its mechanical properties, leading to a decrease in the bearing capacity of the loess and causing engineering disasters. Xu et al. [[9]9] studied the meso-structuralmeso-structural characteristics of loess after freeze–thaw cycles, such as equivalent diameter, diameter, particle orientation, circularity, circularity, and pore area ratio, by comparing remolded loess with undisturbed loess.loess. Wang etet al. [[10]10] studied the rate of change of loess volume before and after freeze–thaw by changingchanging the blending ratio, in order to determine the reasonable reasonable ratio ratio so so that that the the loess loess can can maintain maintain its its microstructure microstructure during during the the freeze–thaw freeze–thaw cycle. cycle. Li etLi al. et al.[11] [11 aimed] aimed at the at thestrength strength degradation degradation and and structural structural degradation degradation of compacted of compacted loess loess under under the dualthe dual effects effects of wet of wet and and dry dry and and freeze–thaw. freeze–thaw. Li Liet etal. al. [12] [12 used] used nuclear nuclear magnetic magnetic resonance resonance (NMR) (NMR) technology toto studystudy the the degradation degradation characteristics characteristics of sandstone of sandstone microstructure microstructure in freeze–thaw in freeze–thaw cycles, cycles,and used and fractal used theoryfractal totheory calculate to calculate the fractal the dimension fractal dimension of rock poreof rock development pore development after diff erentafter differentfreeze–thaw freeze–thaw cycles. Tian cycles. et al. Tian [13 ]et studied al. [13] the studied freeze–thaw the freeze–tha propertiesw properties of three soilof three with soil diff erentwith differentcompositions compositions based on nuclearbased on magnetic nuclear resonancemagnetic (NMR)resonance proton (NMR) spin proton relaxation spin time relaxation (T2) distribution time (T2) distributionand free induction and free decay induction (FID) measurements.decay (FID) measurements. Testing the strength of freeze–thaw cycle loess is of great importance for evaluating the stability of slopes and and foundations foundations in in loess loess areas. areas. In In order order to to explore explore the the changes changes of ofmechanical mechanical properties properties of loessof loess under under the the action action of freeze–thaw of freeze–thaw cycles, cycles, it is itfound is found that that the change the change of water of water content content and andthe rate the ofrate freezing of freezing have have a great a great influence influence on onthe the strength strength change change [9,11,14]. [9,11,14 ].Yan Yan et et al. al. [15] [15] studied the unconfinedunconfined compressive strength strength and and pore pore distributi distributionon characteristics characteristics of of lime lime fly fly ash ash loess loess through through a seriesa series of of experiments experiments under under freeze–thaw freeze–thaw cycles. cycles. Xu Xu et et al. al. [16] [16] carried carried out out freeze–thaw tests, direct

Water 2020, 12, 3047 3 of 18 Water 2020, 12, x FOR PEER REVIEW 3 of 18 shearshear test test and and scanning scanning electron electron microscope microscope on on loess loess to to study study the the strength strength characteristics characteristics of of loess loess after after freeze–thawfreeze–thaw cycles. cycles. AtAt present, present, there there are are few few studies studies on on the the correlati correlationon between between loess loess strength strength and and pore pore structure. structure. ThisThis paper paper considers considers predicting predicting the the change change in in streng strengthth with with a a relatively relatively easy easy to to measure measure porosity. porosity. TheThe saturatedsaturated undisturbedundisturbed loess loess from from Xi’an Xi’an was was subjected subjected to triaxial to triaxial compression compression tests under tests di underﬀerent differentfreeze–thaw freeze–thaw cycles to cycles explore to explore the law the of law strength of strength degradation degradation of samples. of samples. The The pore pore structure structure of ofthe the sample sample after after freeze–thaw freeze–thaw cycles cycles was was observed observed byby scanningscanning electronelectron microscopy and nuclear nuclear magneticmagnetic resonance. resonance. Based Based on on the the test test results results of of strength strength deterioration deterioration and and porosity porosity change change of of saturatedsaturated undisturbed undisturbed loess loess after after freeze–thaw freeze–thaw cycles cycles,, the the correlation correlation between between the the two two is is discussed, discussed, whichwhich provides provides a a new new idea idea for for the the non-destructive non-destructive analysis analysis of of the the strength strength damage damage status status of of saturated saturated loessloess by by freeze–thaw. freeze–thaw.

2.2. Test Test Scheme Scheme

2.1.2.1. Materials Materials and and Methods Methods

TheThe soil soil sample sample used in the experiment waswas QQ33 undisturbed loessloess ininGaoling Gaoling District, District, Xi’an, Xi’an, with with a adepth depth of of 5–8 5–8 m. m. The The particle particle gradation gradation curve curve is is shown shown in in Figure Figure2. 2. Prepare Prepare a a standard standard cylinder cylinder with with a asize size of of 39.1 39.1 mm mm ×80 80 mmmm (diameter(diameter × height), dry and saturate the prepared sample, and and seal seal it it for for × × laterlater test test use. use.

FigureFigure 2. 2. SoilSoil sample sample particle particle grading grading curve. curve.

2.2.2.2. Freeze–Thaw Freeze–Thaw Cycle Cycle Tests Tests FrozenFrozen undisturbed undisturbed loess loess samples samples were were subjected subjected to toa freeze–thaw a freeze–thaw cycle cycle test. test. According According to the to actualthe actual climate climate and andenvironmental environmental conditions conditions in the in field, the field, the freezing the freezing temperature temperature of the of test the was test was selected to be 10 C and the melting temperature was chosen to be 20 C. Place the sample selected to be −10 °C− and◦ the melting temperature was chosen to be 20 °C. Place◦ the sample in the highin the and high low and temperature low temperature tester (type tester RTP-175BU, (type RTP-175BU, located in XUST), located setting in XUST), the freezing setting temperature the freezing temperature to 10 C for 12 h, and melt the temperature at 20 C for 12 h, respectively, for 5, 10, 20, 30, to −10 °C for 12− h, and◦ melt the temperature at 20 °C for 12 h,◦ respectively, for 5, 10, 20, 30, and 50 cycleand50 tests. cycle tests. 2.3. SEM 2.3. SEM The sample preparation process required for scanning electron microscopy is easy. Scanning The sample preparation process required for scanning electron microscopy is easy. Scanning electron microscopy has the advantages of three-dimensional imaging, wide magnification of images electron microscopy has the advantages of three-dimensional imaging, wide magnification of images and high resolution. Scanning electron microscopy can directly observe the fine structure of the and high resolution. Scanning electron microscopy can directly observe the fine structure of the uneven surface of numerous samples. Scanning electron microscopy is generally widely used in

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Water 2020, 12, x FOR PEER REVIEW 4 of 18 uneven surface of numerous samples. Scanning electron microscopy is generally widely used in biology, physics,physics, andand chemistrychemistry [[17–19].17–19]. Due to the advantages of scanning electron microscopy in observing the microstructure microstructure of of samples, samples, domestic domestic and and foreign foreign experts experts have have cited cited this this technology technology in invarious various fields ﬁelds of geotechnical of geotechnical engineering engineering [20–24]. [20–24 Af].ter After the thefreeze–thaw freeze–thaw cycle, cycle, the theflat ﬂatsurface surface of the of thesample sample is selected is selected as the as scanning the scanning observation observation surface. surface. A small A smallpiece of piece about of about10 × 10 10 × 5 mm10 (length5 mm × × (length× width ×width height)height) was prepared was prepared as a asscanning a scanning electron electron microscope microscope sample. sample. Scanning Scanning electron × × microscopy (type JSM-6460LV, locatedlocated inin XUST)XUST) waswas usedused toto observe the microstructural changes of the loess samples under thethe freeze–thawfreeze–thaw cycle.cycle.

2.4. Nuclear Magnetic Resonance Tests At present, NMR technology is gradually applied to geological exploration engineering due to its magnetic fieldfield characteristicscharacteristics [[25–27].25–27]. NMR tec technologyhnology can observe the internal pore structure of the porous material, the molecular motion state in the pores and the reaction process through fluidfluid changes in the pores,pores, andand thethe relationshiprelationship betweenbetween thesethese phenomena.phenomena. Therefore, nuclearnuclear magneticmagnetic resonance technology is cited in the fieldfield of geotechnicalgeotechnical engineering to observe the meso-structural changes ofof the the rock rock and and soil. soil. After After the the freeze–thaw freeze–thaw cycle, cycle, the pore the sizepore distribution size distribution of the loess of the samples loess undersamples the under freeze–thaw the freeze–thaw cycle was observed cycle was using observ a large-apertureed using a nuclear large-aperture magnetic resonancenuclear magnetic imaging analyzerresonance (type imaging MacroMR12-150H-I, analyzer (type MacroMR12-150H-I, located in XUST, Xi’an, located China). in XUST, Xi’an, China).

2.5. Triaxial Compression TestsTests In order to studystudy thethe influenceinfluence ofof freeze–thawfreeze–thaw cyclescycles on the mechanical properties of loess, the TSZ-6A strain-controlled triaxial apparatus was used to carry out triaxial compression tests under didifferentfferent confiningconfining pressurespressures onon thethe samplessamples that reached the cycle number. The stress–strain curves and correspondingcorresponding mechanical mechanical parameters parameters of samplesof samples under under different different freeze–thaw freeze–thaw cycles are cycles obtained. are Theobtained. changing The responsechanging ofresponse the mechanical of the mechanical properties properties of Gaoling of loessGaoling under loess the under coupling the coupling effect of dieffectfferent of different confining confining pressures pressures and freeze–thaw and freeze–t cycleshaw cycles was analyzed. was analyzed. The instrumentThe instrument used used in the in experimentthe experiment is shown is shown in Figure in Figure3. 3.

Figure 3. Test equipment.

3. Test Results

3.1. SEM Results Scanning electron microscopy (SEM) was used to observe the microstructure changes of saturated undisturbed loess samples after freeze–thaw cycles. Select 500 , 1000 , 1500 , and 2000 saturated undisturbed loess samples after freeze–thaw cycles. Select 500×,× 1000×,× 1500×,× and 2000×× magnifications in order from high to low magnification in five representative areas to take pictures. The microstructure image of the sample after the freeze–thaw cycle is obtained, as shown in Figure 4. The 500× magnification photo can provide more analysis objects in the same field of view. Under

Water 2020, 12, 3047 5 of 18 magnifications in order from high to low magnification in five representative areas to take pictures. The microstructure image of the sample after the freeze–thaw cycle is obtained, as shown in Figure4. Water 2020, 12, x FOR PEER REVIEW 5 of 18 The 500 magnification photo can provide more analysis objects in the same field of view. Under the × thecondition condition that that the the soil soil particles particles are are heterogeneous heterogeneous and and anisotropic, anisotropic, the the geometricgeometric analysisanalysis results meet the statisticalstatistical requirements,requirements, avoiding avoiding the the occurrence occurrence of of large large data data errors, errors, which which is convenientis convenient for forquantitative quantitative analysis. analysis. It can It becan seen be fromseen thefrom results the results that there that are there pores are of pores different of different sizes and sizes shapes and in shapesthe loess in samples. the loess Particle samples. connection Particle methodsconnection mainly methods include mainly cementation, include point-to-surfacecementation, point-to- contact, surfaceand surface-to-surface contact, and surface-to-surface contact. contact.

(a) (b)

FigureFigure 4.4.SEM SEM Image.Image. ((aa)) 500500×,,( (b) 10001000×,,( (cc)) 1500×, 1500 ,((dd)) 2000×. 2000 . × × × × 3.2. NMR NMR Test Test Results A nuclear magnetic resonance imaging analyzer (NMR) was used to observe the mesostructure change of the saturated undisturbed loess sample after the freeze–thaw cycle, thereby obtaining a T22 spectrum distribution curve of the sample, as shown in Figure5 5(T (T2 isis the the relaxation relaxation time time of the pore fluid).ﬂuid). The The T 22 spectralspectral distribution distribution showed showed a a significant signiﬁcant ri rightght shift after the freeze–thaw cycle. As the number of freeze–thaw cycles increases, the the two peaks move upwards as a whole, and the trough between the two peaks becomes less obvious as the curve moves up. It shows that the expansion of the internal pores of the loess is in a process of dynamic change under the the conditions conditions of of freeze–thaw freeze–thaw cycles. Therefore, Therefore, the micropores micropores in the soil are grad graduallyually transitioning to larger pores as the number of freeze–thaw cycles increases.

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FigureFigure 5. T5.2 Tspectral2 spectral curve distribution distribution under under different different freeze–thaw freeze–thaw cycles (N cycles is the (N number is the of number freeze– of freeze–thawthaw cycles). cycles). Figure 5. T2 spectral curve distribution under different freeze–thaw cycles (N is the number of freeze– 3.3. Triaxial3.3. Triaxialthaw Compression cycles). Compression Test Test Results Results A TSZ-6AA TSZ-6A strain-controlled strain-controlled triaxial triaxial apparatus apparatus was was used used to to perform perform aa triaxialtriaxial compressioncompression test test on 3.3. Triaxial Compression Test Results the saturatedon the saturated undisturbed undisturbed loess processedloess processed through thro freeze–thawugh freeze–thaw cycles cycles to obtain to obtain stress–strain stress–strain curves undercurves diAfferent TSZ-6Aunder freeze–thaw different strain-controlled freeze–thaw cycles, triaxial as cycles, shown apparatus as in shown Figure wa ins6 Figure.used to 6. perform a triaxial compression test on the saturated undisturbed loess processed through freeze–thaw cycles to obtain stress–strain (1) The freezing and thawing times of loess are divided into 6 gradients. The peak intensity curves under different freeze–thaw cycles, as shown in Figure 6. (1) Thedecreases freezing andwith thawing increasing times freeze–thaw of loess aretimes, divided under into different 6 gradients. confining The pressure peak intensity conditions. decreases (1)(2)with TheThe increasing freezinggreater the freeze–thawand number thawing of times, timesfreeze–thaw underof loess cycles, di ffareerent dividedthe confining less intothe peak6 pressure gradients. intensity conditions. The degradation peak intensity of the (2) Thedecreasesgradient greater compared thewith number increasing to the of freeze–thawprevious freeze–thaw one. times, cycles, under the different less the confining peak intensity pressure degradation conditions. of the (2)(3)gradient TheAs thegreater compared confining the number topressure the previousof increases,freeze–thaw one. the cycles, phenomenon the less of the peak peak intensity intensity degradation degradation becomes of the (3) Asgradient theless confiningobvious. compared pressure to the increases,previous one. the phenomenon of peak intensity degradation becomes (3)less As obvious. the confining pressure increases, the phenomenon of peak intensity degradation becomes less obvious.

(a) (b)

(c)

Figure 6. Stress–strain curves under different confining pressures under freeze–thaw cycles. (a) σ3 = (c) 200 kPa, (b) σ3 = 300 kPa, (b) σ3 = 300 kPa, (c) σ3 = 400 kPa.

FigureFigure 6. Stress–strain 6. Stress–strain curves curves under under different different confining confining pressures pressures under under freeze–thaw freeze–thaw cycles. cycles. (a) σ 3(a=) 200σ3 = kPa, 200 kPa, (b) σ3 = 300 kPa, (b) σ3 = 300 kPa, (c) σ3 = 400 kPa. (b) σ3 = 300 kPa, (b) σ3 = 300 kPa, (c) σ3 = 400 kPa.

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4.Water Discussion2020, 12, 3047 7 of 18

4.1. Strength Damage 4. Discussion According to the Mohr Coulomb strength criterion, combined with the results of the triaxial shear4.1. Strength test of Damageloess, the shear strength and corresponding mechanical parameters under different conditionsAccording are obtained, to the Mohr as Coulombshown in strengthFigure 7. criterion, Figure 7 combined shows the with relationship the results between of the triaxial the shear shear strengthtest of loess, loss therate shear of saturated strength undisturbed and corresponding loess and mechanical the number parameters of freeze–thaw under di cycles.ﬀerent conditionsThe shear strengthare obtained, degradation as shown loss in Figurerate 7 .is: Figure 7 shows the relationship between the shear strength loss rate of saturated undisturbed loess and the number of freeze–thaw cycles. The shear strength degradation Q0  Qn   (1) loss rate λ is: Q Q0 Q0(n) λ = − (1) Q0 where Q0 is the shear strength of the unfrozen-thawed saturated undisturbed loess; Qn is the shearwhere strengthQ0 is the when shear the strength number of of the freeze–thaw unfrozen-thawed cycles saturatedis n times. undisturbed loess; Q(n) is the shear strength when the number of freeze–thaw cycles is n times.

(a) (b)

FigureFigure 7. 7. StrengthStrength degradation. degradation. (a) Shear (a) strength Shear strength loss rate loss under rate freeze–thaw under freeze–thaw cycles. (b) Mechanical cycles. (b) parameters.Mechanical parameters.

ItIt can can be be seen seen from from Figure Figure 7 thatthat as as the the number number of of freeze–thaw freeze–thaw cycles increases, the shear strength lossloss rate rate increases increases gradually, gradually, and and the the saturated saturated un undisturbeddisturbed loess loess strength strength degradation degradation phenomenon phenomenon becomesbecomes more more and and more more obvious, obvious, and and the the evolution evolution law law of of peak peak strength strength loss loss rate rate under under different different confiningconfining pressures pressures is is about about the the same. same. ItIt can can be be seen seen from from Figure Figure 77bb that as the number of freeze–thaw cycles increases, the cohesion of loessloess shows aa tendencytendency to to decrease decrease first, first, then then increase increase slightly, slightly, and graduallyand gradually stabilize stabilize and the and internal the internalfriction anglefriction showed angle showed a trend of a increasingtrend of increasing first, then first, decreasing then decreasing and gradually and gradually stabilizing. stabilizing. When the Whenfreezing the and freezing thawing and cycle thawing is 0~10 cycl times,e is the0~10 cohesion times, ofthe the cohesion soil sample of the is obviously soil sample reduced, is obviously and the reduced,internal frictionand the angle internal is obviously friction increased.angle is obvi Afterously 10 freeze–thawincreased. After cycles, 10 thefreeze–thaw cohesion and cycles, internal the cohesionfriction angle and internal of the soil friction sample angle increased of the soil slowly, sample and increased tended to slowly, be stable. and tended to be stable. ThisThis is is because because the the freeze–thaw freeze–thaw cycle cycle destroys destroys the the inherently inherently strong strong cementation cementation between between the the loessloess particles. particles. The The water water in in the the soil soil generates generates frost frost heave heave force force and and migration migration force force due due to to freezing freezing andand migration, migration, which which constantly constantly weakens weakens the the bonding bonding force force between between the the soil soil particles, particles, resulting resulting in ina decreasea decrease in incohesion. cohesion. In the In the process process of rearrangement of rearrangement of soil of soilparticles, particles, the thecontact contact points points between between the particlesthe particles are increased, are increased, resulting resulting in an inincrease an increase in the ininternal the internal friction friction angle. As angle. the number As the numberof freeze– of thawfreeze–thaw cycles increases, cycles increases, the soil pa therticles soil particlesgradually gradually form a new form stable a new structure. stable structure.The contact The point contact and contactpoint and mode contact between mode the between particlesthe is changed. particles The is changed. effect of freeze–thaw The effect of cycles freeze–thaw on the bonding cycles on force the andbonding internal force friction and internal angle gradually friction angle decreases. gradually Due decreases. to the formation Due to theof new formation structural of new features, structural the bondfeatures, between the bond the soil between particles the is soil stabilized. particles It isreflects stabilized. the resistance It reflects to the freeze–thaw resistance damage, to freeze–thaw so the damage, so the cohesive force and internal friction angle change are small. Therefore, it is believed that

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cohesive force and internal friction angle change are small. Therefore, it is believed that when the whennumber the number of freeze–thaw of freeze–thaw cycles is cycles small, is the small, effect the of eﬀ freeze–thawect of freeze–thaw cycles cycleson cohesive on cohesive force and force the and theinternal internal friction friction angle angle is ismore more obvious. obvious. As As the the number number of offreeze–thaw freeze–thaw cycles cycles increases, increases, its itseffect eﬀect graduallygradually decreases. decreases.

4.2.4.2. SEM SEM Test Test Result Result Analysis Analysis TheThe binarization binarization of of the the image image is conduciveis conducive to theto th furthere further processing processing of the of image,the image, making making the imagethe simple,image reducing simple, thereducing amount the of amount data, and of highlightingdata, and highlighting the outline ofthe the outline target. of The the microstructure target. The ofmicrostructure the loess sample of wasthe loess obtained sample by was scanning obtained electron by scanning microscopy, electron and microscopy, the SEM image and the (Figure SEM4 a, 500image) was (Figure selected 4a, for500×) quantitative was selected analysis. for quantitative In order analysis. to obtain In the order characteristic to obtain the parameters characteristic of the × microstructureparameters of of the the microstructure loess, the SEM of imagethe loess, is binarized,the SEM image as shown is binarized, in Figure as8 shown. in Figure 8.

(a) (b)

(e) (f)

FigureFigure 8. 8.SEM SEM image.image. (a) 0, ( b)) 5, 5, ( (cc)) 10, 10, (d (d) )20, 20, (e (e) )30, 30, (f ()f 50.) 50.

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Water 2020, 12, 3047 9 of 18 The fractal dimension can vividly reflect the morphological characteristics, arrangement characteristics and size distribution characteristics of loess particles. In order to explore the influence of freeze–thawThe fractal times dimension on the distribution can vividly of reflectloess pa therticles, morphological the SEM image characteristics, was binarized arrangement to obtain the characteristicsstatistical parameters and size of distribution the statistical characteristics particles of saturated of loess particles. loess under In order different to explore freeze–thaw the influence times. ofProbability freeze–thaw entropy times and on thearea distribution probability of distribution loess particles, index the are SEM selected image wasto elaborate binarized the to obtainfractal thedimension statistical of loess. parameters of the statistical particles of saturated loess under different freeze–thaw times.(1) Probability Probability entropy entropy and area probability distribution index are selected to elaborate the fractal dimensionProbability of loess. entropy is a structural parameter describing the arrangement of particles, which can (1)be Probabilityused to analyze entropy the arrangement of soil particles after the freeze–thaw cycle. The calculation equationProbability of probability entropy entropy is a structural is parameter describing the arrangement of particles, which can be used to analyze the arrangement of soil particles after the freeze–thaw cycle. The calculation equation of probability entropy is n mi ln(mi / M ) H  n  (2) m X mi ln(mi/M) Hm = i1 M ln n (2) − M · ln n i=1 where Hm is the probability entropy, and the value range is [0,1]. The larger the value, the lower the whereorder ofH mtheis particle the probability arrangement entropy, and and the themore value chao rangetic the is arrangement. [0,1]. The larger Divide the value,0~180° the into lower n zones, the order of the particle arrangement and the more chaotic the arrangement. Divide 0~180◦ into n zones, and the angle range of each zone. mi is the number of particles whose particle long axis is in the i-th and the angle range of each zone. m is the number of particles whose particle long axis is in the i-th interval. M is the total number of particles.i interval. M is the total number of particles. It can be seen from Figure 9a that the probability entropy of soil particles gradually increases It can be seen from Figure9a that the probability entropy of soil particles gradually increases under under the action of freeze–thaw cycles. As the number of freeze–thaw cycles increases, this is a neat the action of freeze–thaw cycles. As the number of freeze–thaw cycles increases, this is a neat method, method, which indicates that the orientation of the soil particles changes under the action of freeze– which indicates that the orientation of the soil particles changes under the action of freeze–thaw cycles. thaw cycles. As the number of freeze–thaw cycles increases, the order of particle arrangement As the number of freeze–thaw cycles increases, the order of particle arrangement gradually changes gradually changes from a regular state to a chaotic state, and the direction of particle arrangement from a regular state to a chaotic state, and the direction of particle arrangement becomes worse and becomes worse and worse. This is because, during the freeze–thaw cycle, changes in external worse. This is because, during the freeze–thaw cycle, changes in external temperature conditions cause temperature conditions cause the pore water to undergo a phase change, forming a certain volume the pore water to undergo a phase change, forming a certain volume of ice crystal structure. Adjacent of ice crystal structure. Adjacent soil particles are relatively displaced by the wedge-shaped force of soil particles are relatively displaced by the wedge-shaped force of ice crystals. Due to the weakening ice crystals. Due to the weakening of the bonding force, the bonding between the soil particles of the bonding force, the bonding between the soil particles becomes weak, which provides conditions becomes weak, which provides conditions for the displacement of the soil particles. Therefore, under for the displacement of the soil particles. Therefore, under the action of freeze–thaw cycles, deflection the action of freeze–thaw cycles, deflection and displacement occur between the soil particles, and and displacement occur between the soil particles, and the relative displacement between the particles the relative displacement between the particles changes the arrangement of the soil particles. changes the arrangement of the soil particles.

(a) (b)

Figure 9. Fractal dimension. ( (aa)) Probability Probability entropy, entropy, (b)) AreaArea probabilityprobability distributiondistribution index.index.

(2)(2) AreaArea probabilityprobability distributiondistribution indexindex The significancesignificance of the area probabilityprobability distribution index is that it can eeffectivelyffectively quantifyquantify thethe distribution of the particle area, which is defineddefined by the probability distribution function and reflectsreflects thethe densitydensity ofof thethe particleparticle areaarea inin aa specificspecific area.area. TheThe probabilityprobability distributiondistribution functionfunction isis

b b ff(dd) =axax− (3)(3)

Water 2020, 12, 3047 10 of 18 where f (d) is the density of particles of corresponding diameter; b is the probability distribution index; the value of a is related to b. The probability distribution index describes the changing trend of the number of particles when the area of the particles changes from small to large, showing a power function relationship. When the probability distribution index is small, it indicates that there are fewer particles in small area and more particles in large area. It can be found from Figure9b that under the action of freeze–thaw cycles, the area probability distribution index of particles decreases first and then increases, and gradually stabilizes, which indicates that with the increase of the number of freeze–thaw cycles, the number of large-area particles first increase and then decrease, and the quantity change tends to be stable. This is due to the weakening of the binding force under the action of freeze–thaw cycles, which causes the separation of the base-type aggregates. The process of debris detachment makes the space volume of the basal-type aggregates increase continuously, and the surface area gradually increases. Until the debris is separated, the surface area of the base-type aggregate decreases. Moreover, the structural characteristics of the aggregates have changed to form attachment-type and breccia-type aggregates. Therefore, it can be obtained by SEM technology that when the number of freeze–thaw cycles is small, the internal pores of the saturated undisturbed loess change from larger micropores to smaller micropores. After reaching a certain number of cycles, pores and fissures develop and gradually transform into medium and large pores. Large holes appear and the soil structure is basically destroyed. Under the action of freeze–thaw cycle, the saturated undisturbed loess develops pores and cracks in the sample, and is accompanied by new cracks. The soil skeleton structure is destroyed, resulting in reduced bearing capacity. Therefore, the loess samples show the phenomenon of increased pores and decreased shear strength.

4.3. NMR Test Result Analysis In the NMR test, the pore water content and its distribution curve of the sample can be obtained by inverting the T2 spectrum distribution curve in Figure5. The T2 value and pore structure in the soil satisfy the following equation: 1 S ρ2 (4) T2 ≈ V where ρ2 is the transverse relaxation rate; S and V is the surface area and volume of the pores where the moisture is located. Assuming that the pore shape is cylindrical, Equation (4) is simpliﬁed as:

1 2 ρ2 (5) T2 ≈ R where R is the pore radius. It can be seen from Equation (5) that the T2 spectral value is proportional to the pore radius. The T2 spectrum curve obtained by the NMR experiment was subjected to the inversion of the Equation (5) to obtain a pore distribution curve of saturated undisturbed loess, as shown in Figure 10. It can be seen from Figure8 that the pore distribution of the loess mainly has two peaks, and the larger the peak value, the larger the proportion of the pore volume corresponding to the pore diameter. When NMR is used to test the water in the soil, according to the relaxation time (T2) of the water in diﬀerent occurrence states, after inversion by Equation (5), it can be divided into 4 types of pores according to the pore size [28]. Water 2020, 12, x FOR PEER REVIEW 11 of 18 Water 2020, 12, 3047 11 of 18 Water 2020, 12, x FOR PEER REVIEW 11 of 18

Figure 10. Pore distribution curve of saturated undisturbed loess. Figure 10. Pore distribution curve of saturated undisturbed loess. It can be observed in Figure 11 that the internal structure of saturated undisturbed loess changes underIt can the be action observed of freeze–thaw in Figure 11 cycles. thatthat the the The internal internal intergranular structure structure cementation of saturated saturated ability undisturbed is weakened. loess changes Large underparticles thethe actionare action decomposed of of freeze–thaw freeze–thaw into cycles. small cycles. The particles The intergranular inte undergranularr cementation the cementationaction abilityof force ability is weakened. and is migrate weakened. Large toparticles nearby Large areparticlesmicrocracks, decomposed are resultingdecomposed into small in a particles decreaseinto small under in microporesparticles the action unde ofand forcer anthe andincrease action migrate ofin tosmallforce nearby pores.and microcracks, migrate As the numberto resulting nearby of inmicrocracks,freeze–thaw a decrease incyclesresulting micropores increases, in a and decrease anmicro-cracks increase in micropores in smalland micro-voids pores. and an As increase the develop number in small ofnew freeze–thaw pores.cracks. As Micro cyclesthe numberand increases, small of micro-cracksfreeze–thawpores are reduced, andcycles micro-voids increases,and medium develop micro-cracks and new large cracks. and pores micro-voids Micro are andincreased. small develop pores The new are soil reduced, cracks. structure Micro and is medium essentiallyand small and largeporesdestroyed. poresare reduced, areTherefore, increased. and with medium The the soil increase structureand largeof the is essentiallypores number are of destroyed.increased. freeze–thaw Therefore,The cycles, soil structure withthe microporosity the increaseis essentially of and the numberdestroyed.small pores of freeze–thawTherefore, in the soil with cycles,show the an the increase overall microporosity decreasinof the number andg trend, small of freeze–thaw poresand the in themedium soilcycles, show and the anlarge microporosity overall pores decreasing show and an trend,smalloverall pores and increasing the in mediumthe trend.soil andshow large an overall pores show decreasin an overallg trend, increasing and the trend. medium and large pores show an overall increasing trend.

Figure 11. Pore distribution map of loess under freeze–thaw cycles. Figure 11. Pore distribution map of loess under freeze–thaw cycles. As shown in Figure 1212,, micropore volumevolume accountsaccounts forfor 28.35%28.35% toto 37.93%.37.93%. The small pore volume accounts for 40.06% to 52.11%. Medium pore volume accounts for 7.93% to 17.48%. The large pore accountsAs shown for 40.06% in Figure to 52.11%. 12, micropore Medium volume pore volumeaccounts accounts for 28.35% for to 7.93% 37.93%. to 17.48%.The small The pore large volume pore volume accounts for 2.04% to 10.7%. The soil has the largest number of small pores, followed by accountsvolume accounts for 40.06% for to 2.04% 52.11%. to 10.7%.Medium The pore soil volume has the accounts largest number for 7.93% of tosmall 17.48%. pores, The followed large pore by micropores, mesopores, and macropores. It can be found from Figure 12 that as the number of volumemicropores, accounts mesopores, for 2.04% and tomacropores. 10.7%. The It soilcan beha sfoun the dlargest from Figure number 12 thatof small as the pores, number followed of freeze– by freeze–thaw cycles increases, the variation of pore volume of different types is different, indicating that micropores,thaw cycles mesopores,increases, the and variation macropores. of pore It canvolume be foun of differentd from Figure types 12 is thatdifferent, as the indicatingnumber of thatfreeze– the the soil has different freeze–thaw damage rates at different stages. thawsoil has cycles different increases, freeze–thaw the variation dama ofge porerates volume at different of different stages. types is different, indicating that the soil has different freeze–thaw damage rates at different stages.

Water 2020, 12, 3047 12 of 18

Water 2020, 12, x FOR PEER REVIEW 12 of 18 (1) The freeze–thaw cycle is 0 to 10 times, and the pore volume of each type varies greatly, (1) Thewhich freeze–thaw indicates cycle that the is 0 soil to 10 mesostructure times, and the has po are higher volume degree of each of freeze–thawtype varies greatly, damage which and a indicatesfaster damage that the rate. soil mesostructure has a higher degree of freeze–thaw damage and a faster (2) damageWhen the rate. number of freeze–thaw cycles is 10~30, the change of pore volume of each type is (2) Whensmall, the which number shows of thatfreeze–thaw the degree cycles of freeze–thawis 10~30, the damage change of thepore mesostructure volume of each of thetype soil is small,body which is reduced shows and that the thedamage degree of rate freeze–thaw is reduced. damage This of is the because mesostructure the soil forms of the newsoil body pore isstructure reduced characteristics,and the damage which rate changesis reduced. the degreeThis is ofbecause inﬂuence the ofsoil the forms freeze–thaw new pore cycle structure on the characteristics,microstructure which of the soil.changes After the the numberdegree of freeze–thawinfluence of cycles the reachedfreeze–thaw 50 times, cycle there on wasthe microstructurealmost no change of the in soil. the poreAfter volumethe number of each of freeze–thaw type. This wascycles because reached the 50 soil times, was there basically was almostdestroyed no change and the in pore the structure pore volume was stabilized of each type. to a certain This was extent. because the soil was basically destroyed and the pore structure was stabilized to a certain extent.

FigureFigure 12. 12. PorePore volume volume distribution. distribution.

4.4.4.4. Correlation Correlation Between Between Strength Strength and and Pore Pore Structure Structure 4.4.1. Changes in Porosity 4.4.1. Changes in Porosity The porosity of saturated undisturbed loess under diﬀerent cycle times is obtained by saturation The porosity of saturated undisturbed loess under different cycle times is obtained by saturation net weight method. Figure 13 shows the relationship between the change in porosity of saturated net weight method. Figure 13 shows the relationship between the change in porosity of saturated undisturbed loess and the number of freeze–thaw cycles. The amount of change in porosity is: undisturbed loess and the number of freeze–thaw cycles. The amount of change in porosity is:

∆P = P(n) P0 (6) ΔP  Pn− P0 (6) wherewhere PP(nn) is is the the porosity porosity of of saturated saturated undisturbed undisturbed loess loess when when the the number number of freeze–thawof freeze–thaw cycles cycles is n ; P0 is the porosity of saturated undisturbed loess during unfrozen and thaw. is n; P0 is the porosity of saturated undisturbed loess during unfrozen and thaw.

Water 2020, 12, 3047 13 of 18 Water 2020, 12, x FOR PEER REVIEW 13 of 18

FigureFigure 13. 13. RelationshipRelationship between between freeze–thaw freeze–thaw cycles cycles and and porosity porosity change.

TheThe most most obvious obvious manifestation manifestation of of the the damage damage caused caused by by the the freeze–thaw freeze–thaw cycle cycle is is the the increase ofof the porosity of the porous sample [29]. [29]. Therefor Therefore,e, the the change change in in porosity porosity can can directly directly reflect reﬂect the the evolutionevolution of of freeze–thaw damage. damage. So, So, the the change change in in porosity porosity can can be be used used to to calculate the damage variable. According According to to the the strain strain equivalence equivalence principle principle proposed proposed by by Lematire Lematire [30], [30], considering the damagedamage state of a sectionsection ofof thethe material,material, thethe damage damage variable variableD Dcan can be determinedbe determined according according to theto thepore pore area, area, eﬀective effective bearing bearing area area and and total total area area of the of section.the section.

AA0  DD= (7)(7) AA where AA0 isis thethe areaarea ofof thethe porespores inin a section of of the the material; material; A isis thethe totaltotal areaarea onon aa section of the the material.material. WhenWhen studying studying the the damage damage mechanical mechanical properties properties of of a asection section of of porous porous media, media, AA/0/AA isis the the damagedamage variable on the section and the surface porosity of the section. Jia Jia et et al. al. [31] [31] proposed proposed a a certain certain correspondingcorresponding conversion relationship betw betweeneen surface porosity and volume porosity.

AA0  DD= = ff(PP) (8)(8) AA where P is the sample porosity; f (P) is the conversion relationship between the surface porosity and where P is the sample porosity; f P is the conversion relationship between the surface porosity the volume porosity. and the volume porosity. Considering that the material is subjected to freeze–thaw cycles, the freeze–thaw damage variable Considering that the material is subjected to freeze–thaw cycles, the freeze–thaw damage Dn can be deﬁned as: variable Dn can be defined as: Dn = f (Pn) f (P ) (9) − 0 Dn  f Pn  f P0 (9) where Dn is the damage when the number of freeze–thaw cycles is n; Pn is the porosity when the number of freeze–thaw cycles is n; P0 is the initial porosity. where Dn is the damage when the number of freeze–thaw cycles is n; Pn is the porosity when the In order to study the relationship between surface porosity and volume porosity in detail, the number of freeze–thaw cycles is n; P0 is the initialS porosity. parameters k and the concept of feature voxels Ve are introduced to obtain the relationship between surfaceIn order porosity to study and volume the relationship porosity [ 31between]. surface porosity and volume porosity in detail, the S parameters k and the concept of feature voxels Ve are introduced to obtain the relationship S between surface porosity and volume porosityf (P) = kP [31].( k = mVe ) (10) S f P  kP (k  mVe ) (10)

Water 2020, 12, 3047 14 of 18

S where m is a constant, Ve is the volume of the characteristic voxel. The deﬁnition of the characteristic S voxel is as follows: Take a series of voxels Ve (S = 1, 2, ...) around any point p in the medium. Corresponding to each voxel, an average porosity can be obtained. As the volume of the voxel changes from small to large, the corresponding porosity ﬂuctuations gradually decrease. When the porosity stabilizes to a certain value, the corresponding voxel is called the characteristic voxel Ve. The porosity at this time is the porosity of the medium. Substituting Equation (10) into Equation (9) gives:

Dn = k(Pn P ). (11) − 0 Since the porosity changes ﬁnitely when the material is subjected to freeze–thaw damage, that is, the volume change is not obvious, the parameter k is considered to be constant. As shown in Figure 13, the change in porosity of saturated undisturbed loess increases with the number of freeze–thaw cycles. It is assumed that the loess porosity is P(n) after n freeze–thaw cycles, and it is a microscopic function. When the freeze–thaw cycle is (n + ∆n) times, the porosity is P(n + ∆n). From Equation (1), the amount of change in porosity from n to (n + ∆n) freeze–thaw cycles is: P(n + ∆n) P(n) = ∆P. (12) − Then, the relationship between the amount of porosity change and freeze–thaw damage can be obtained from Equations (11) and (12).

k[P(n + ∆n) P(n)] = D (13) − According to the strain equivalence principle proposed by Lematire [30], the initial damage state of the material is deﬁned as the baseline damage state. Considering that the material will deteriorate after the freeze–thaw cycle, the freeze–thaw damage variable Dn can be determined by the stress change before and after freeze–thaw cycle.

σ0 σn Dn = − (14) σ0

As shown in Figure7a, the shear strength loss rate of saturated undisturbed loess increases with the number of freeze–thaw cycles. The shear strength of saturated undisturbed loess after n freeze–thaw cycle is Q(n), and it is a diﬀerentiable function. The shear strength of the loess with (n + ∆n) freeze–thaw cycles is Q(n + ∆n). From Equation (10), shear strength loss rate from n freeze–thaw cycles to (n + ∆n) freeze–thaw cycles is:

Q(n) Q(n + ∆n) − = λ. (15) Q(n)

Then, the relationship between the shear strength loss rate and the freeze–thaw damage can be obtained from the Equations (14) and (15).

Q(n) Q(n + ∆n) − = D (16) Q(n)

The degree of strength deterioration is characterized by the change of porosity of the loess sample under the freeze–thaw cycle. Equations (13) and (16) indicate the freeze–thaw damage of the sample by the change of porosity and shear strength, respectively. Then it can be concluded:

Q(n) Q(n + ∆n) − = k[P(n + ∆n) P(n)]. (17) Q(n) − Water 2020, 12, x FOR PEER REVIEW 15 of 18

Water 2020, 12, 3047 15 of 18 dQn  kdPn . (18) Q n Available from Equation (17)  dQ(n) Integrate the two sides of Equation (18) = kdP(n). (18) Q(n) −

Qn kPn P0 Integrate the two sides of Equation (18)  e . (19) Q0 Q(n) k[P(n) P0] Letting P  Pn  P0 , k is considered= eas− the −strength. degradation factor of saturated (19) Q0 undisturbed loess freeze–thaw cycles. Considering the influence of external conditions on the peak strengthLetting test ∆results,P = P( then) correctionP0, k is considered coefficient as the strengthis introduced degradation to correct factor the of equation, saturated see undisturbed Equation − (20).loess freeze–thaw cycles. Considering the inﬂuence of external conditions on the peak strength test results, the correction coeﬃcient α is introduced to correct the equation, see Equation (20). Qn kP   e ( ) (20) Q Qn0 k ∆P = α e− · (20) Q0 · It can be seen from Equation (20) that the relationship between the shear strength of saturated undisturbedIt can be loess seen and from the Equation change in (20) porosity that the obey relationships an exponential between function the shear under strength the freeze–thaw of saturated cycle.undisturbed loess and the change in porosity obeys an exponential function under the freeze–thaw cycle.

4.4.2.4.4.2. Verification Verification of Test Results BasedBased on on theoretical theoretical derivation, derivation, Equation Equation (20) (20) is is used used to to fit fit the the peak peak strength of of saturated undisturbedundisturbed loess loess and and the the change change of of porosity porosity under under the the action action of of freeze–thaw cycles, cycles, as as shown shown in in FigureFigure 14.14. The peak strength ofof saturatedsaturated undisturbedundisturbed loess loess has has a a good good correlation correlation with with the the change change of ofporosity. porosity. Therefore, Therefore, using using the porositythe porosity change change of saturated of saturated undisturbed undisturbed loess before loess andbefore after and freezing after freezingand thawing and thawing can effectively can effectively simulate simulate the strength the strength deterioration deterioration law. law.

FigureFigure 14. 14. TheThe relationship relationship between between shear shear strength strength and and porosity porosity change. change.

AsAs the the confining confining pressure pressure increases, increases, the the ability ability of of the the sample sample to to resist resist deformation deformation is is enhanced, enhanced, andand the the deterioration phenomenon is is weakened. As As shown shown in in Figure Figure 15,15, the the strength strength degradation degradation factorfactor gradually gradually decreases decreases as as the the confining confining pressure pressure increases. increases. The The variation variation range range of of the the correction correction coefficientcoefficientαisis small, small, and and the the values values are are not not much much different. different. It It can can be be concluded concluded that that this this test test was was realizedrealized under under the the same same external influence, influence, and the data obtained are true and reliable.

Water 2020, 12, 3047 16 of 18 Water 2020, 12, x FOR PEER REVIEW 16 of 18

FigureFigure 15.15. ParameterParameter changes.changes.

5.5. Conclusions ThisThis articlearticle aimsaims toto studystudy thethe problemproblem ofof loessloess landslideslandslides causedcaused byby freeze–thawfreeze–thaw cycles.cycles. Taking saturatedsaturated undisturbedundisturbed loessloess asas thethe researchresearch object,object, thethe relationshiprelationship betweenbetween itsits strengthstrength andand porepore structurestructure isis analyzed.analyzed. The changes of pore structurestructure in loessloess werewere observedobserved byby scanningscanning electronelectron microscopymicroscopy andand nuclearnuclear magneticmagnetic resonanceresonance techniques,techniques, andand analyzinganalyzing thethe variationvariation ofof porosityporosity andand shearshear strength.strength. TheThe followingfollowing mainmain conclusionsconclusions werewere obtained:obtained: (1)(1) The freeze–thaw damage evolution of saturated undisturbed loessloess under freeze–thaw cyclescycles waswas observed by scanning electron microscopy. It is found that thethe micromicro andand smallsmall porespores inin thethe soilsoil increase first first and then decrease, and the medium and large pores reduce first first and then increase. This is closely relatedrelated toto changeschanges inin thethe internalinternal microstructuremicrostructure ofof thethe soil.soil. TheThe T2T2 spectrumspectrum distribution curvecurve of of saturated saturated undisturbed undisturbed loess loess under under freeze–thaw freeze–thaw cycles cycles was obtainedwas obtained by using by usingnuclear nuclear magnetic magnetic resonance resonance technology. technology. The pore The distributionpore distribution curve curve of loess of loess under under freeze–thaw freeze– thawcycles cycles is obtained is obtained by equation by equation inversion, inversion, which which shows shows that thethat microthe micro and and small small pores pores in the in theloess loess are graduallyare gradually transitioning transitioning to the to largerthe larger medium medium and and large large pores pores with with the increasethe increase of the of thenumber number of freeze–thaw of freeze–thaw cycles. cycles. It is It reported is reported that that the the freeze–thaw freeze–thaw cycle cycle is a is dynamic a dynamic process process for forthe internalthe internal pore pore expansion expansion of loess. of loess. The results The results obtained obtained by NMR by and NMR SEM and experiments SEM experiments confirm confirmeach other, each and other, the poreand the distribution pore distribution has similar has changes. similar changes. (2)(2) For saturated undisturbed loess, the freeze–thaw cyclecycle breaksbreaks thethe originaloriginal balancebalance ofof thethe samplesample itself. During During the the freezing freezing process, process, the the soil partic particlesles are squeezed by the growth of ice crystals,crystals, the volume expands, and pores and fissuresfissures develop,develop, forming a new soil skeleton structure. During the melting process, the melting of solid ice insideinside thethe rockrock samplesample cannotcannot causecause thethe complete restoration of the deformation of thethe soilsoil skeletonskeleton particles.particles. Therefore,Therefore, duringduring thethe freeze–thaw cycle, due to the eeffectffect of the frost-heavingfrost-heaving force,force, thethe loessloess samplesample showsshows aa decreasedecrease in strength and an increase inin porosity.porosity. (3)(3) The strength of of saturated saturated undisturbed undisturbed loess loess under under freeze–thaw freeze–thaw cycles cycles is isrelated related to tothe the change change of porosity.of porosity. The The measurement measurement of ofporosity porosity is isrelative relativelyly simple. simple. Therefore, Therefore, consider consider establishing establishing a functionala functional relationship relationship with with the the shear shear strength strength based based on on the the change change in inporosity. porosity. According According to theto the concept concept of offreeze–thaw freeze–thaw damage, damage, an an exponent exponentialial function function distribution distribution between between the the two isis derived. Fitting Fitting the the variation variation of of the porosity and the shear strength under different different cycle times, the correlation between the two is good. Therefore, this research providesprovides aa newnew methodmethod forfor thethe non-destructive analysis of the strength of saturated loess by freezing and thawing, and a new idea for analyzing the loess landslide caused by the freezing and thawing cycle.

Water 2020, 12, 3047 17 of 18

non-destructive analysis of the strength of saturated loess by freezing and thawing, and a new idea for analyzing the loess landslide caused by the freezing and thawing cycle.

Author Contributions: Writing—Original Draft Preparation, Z.L.; Funding Acquisition, G.Y. and H.L. All authors have read and agreed to the published version of the manuscript. Funding: This work has been supported by the National Natural Science Foundation of China (grant No. 51774231, 41702339), National Key Research and Development Program of China (grant No. 2018YFC0808705). Acknowledgments: We thank the entire team for their efforts to improve the quality of the article. At the same time, we would like to thank editor for his timely handling of the manuscripts. Conflicts of Interest: The authors declare no conflict of interest.

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