Application of Flow Velocity and Direction Measurement System in Slope Stability Analysis

water

Article Application of Flow Velocity and Direction Measurement System in Slope Stability Analysis

Qi Ge 1, Jingjing Zhang 2, Zhongxuan Chen 3,* and Jin Li 4

1 College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China; [email protected] 2 Petrochina Hangzhou Research Institute of Geology, Hangzhou 310023, China; [email protected] 3 Ocean College, Zhejiang University, Zhoushan 316021, China 4 College of Biomedical Engineering & Instrument Science, Zhejiang University, Hangzhou 310007, China; [email protected] * Correspondence: [email protected]; Tel.: +86-137-3552-3519

Abstract: Hydrodynamic pressure is often a crucial factor in the evaluation of slope stability analysis, especially for many rainfall-triggered landslides. Nevertheless, hydrodynamic pressure is rarely considered in the traditional limit equilibrium slice method of slope stability analysis since effective and reliable hydrodynamic pressure data are often lacking in practice. Moreover, efficient methods to involve these data in slope stability analysis are an urgent need. To overcome these concerns, the flow velocity and direction system (FVDS) is employed to measure the groundwater flow velocity, which can be used to generate hydrodynamic pressure samples at different monitoring points. Based on these samples, the hydrodynamic pressure of each soil strip is estimated using artificial neural networks (ANNs). Afterward, an improved Bishop method that considers hydrodynamic pressure is proposed. The effectiveness and significance of the proposed method are illustrated with a case Citation: Ge, Q.; Zhang, J.; Chen, Z.; study, the Fanshantou landslide in Zhejiang Province, China. The safety factor before and after taking Li, J. Application of Flow Velocity and drainage countermeasures is also calculated and compared. The results indicate that hydrodynamic Direction Measurement System in pressure plays an important role in the stability analysis of the Fanshantou landslide. Compared Slope Stability Analysis. Water 2021, 13, 700. https://doi.org/10.3390/ with the classical Bishop method, the improved method is shown to agree better with the actual w13050700 deformation characteristics of the landslide.

Academic Editor: Keywords: landslide; slope stability analysis; hydrodynamic pressure; groundwater monitoring; Francesco Gallerano artiﬁcial neural networks

Received: 1 February 2021 Accepted: 1 March 2021 Published: 5 March 2021 1. Introduction Groundwater is an important factor and is usually considered a static quantity [1–3], Publisher’s Note: MDPI stays neutral while the dynamic component [4] is rarely considered in slope stability analysis. Specif- with regard to jurisdictional claims in ically, current research on investigating groundwater-related impact factors is mostly published maps and institutional affil- limited in scope to the hydrostatic aspects, such as pore water pressure, water content, and iations. groundwater level [5,6]. Though significant, these factors cannot represent all the impact of groundwater on landslides. Meanwhile, even though the movement of groundwater in certain areas is dynamic, the hydrodynamic factors of groundwater, such as groundwater flow velocity and flow direction, are rarely exploited in related studies [7]. With Copyright: © 2021 by the authors. the improvement of monitoring equipment and the application of digitized facilities, the Licensee MDPI, Basel, Switzerland. hydrodynamic aspect of groundwater provides a promising research topic for exploring This article is an open access article the influential factors that can lead to landslides. distributed under the terms and The velocity and direction of groundwater flow are the two main influential factors [8] conditions of the Creative Commons in terms of the hydrodynamic characteristics of groundwater. As a powerful and advanced Attribution (CC BY) license (https:// technique in the geotechnical survey of landslides, the flow velocity and direction system creativecommons.org/licenses/by/ (FVDS) has been applied to measure the velocity and direction of groundwater in slope 4.0/).

Water 2021, 13, 700. https://doi.org/10.3390/w13050700 https://www.mdpi.com/journal/water Water 2021, 13, 700 2 of 15

areas [9,10]. In 1987, Itanium and others first used the FVDS to explore the state of groundwater movement and determined the accuracy of the results through experiments [8]. In 1997 and 1999, Kreal and others used the FVDS to measure the flow direction of groundwater again in the United States and compared the results with the results from the traditional measurement methods [11]. Olea et al. [12] evaluated the velocity and direction of groundwater by applying the FVDS in the basin of Mexico. In 2015, Pan et al. [13] used the FVDS to analyze the stability of the Heifangtai landslide in Gansu, China, but only performed a qualitative analysis. In the previous studies, the FVDS was applied to the transport of pollutants in groundwater on the one hand and to explore the direction of groundwater flow on the other hand. However, the flow rate information was often overlooked. At the same time, in slope stability analysis, little attention is paid to the influence of groundwater flow on the safety factor. Therefore, the FVDS still has broad application prospects in landslide stability analysis. Applying the FVDS to landslide stability analysis is innovative research. However, it is impossible to use the FVDS to measure the groundwater flow velocity of each soil strip for slope stability calculations when the powerful FVDS is combined with the traditional limit equilibrium slice method. Based on the assumption that the velocities of groundwater flow are always continuous, the artificial neural network (ANN) [14] is employed to estimate the velocity of continuously changing flow by using the FVDS-based flow velocity data. Therefore, in this study, the Fanshantou landslide in Zhejiang Province, China, is taken as a case to illustrate the application of the FVDS in the geotechnical survey. We have proposed an improved calculation method of the safety factors according to the measurement results of the flow velocity, compared with those of the traditional calculation, by incorporating the hydrodynamic characteristic of the groundwater. The results in the case study show that the safety factor of the landslide decreased significantly and agreed better with the actual situation of the case on considering the effect of hydrodynamic pressure, which indicates that hydrodynamic pressure plays an important role in the stability analysis of the Fanshantou landslide. Although this article only discusses the impact of hydrodynamic pressure on the safety factor in one case, it shows that ignoring hydrodynamic pressure may lead to misjudgment of landslide stability. It shows that detailed investigations and research on groundwater are very important for the evaluation of slope stability.

2. Overview of the Case Landslide 2.1. Regional Geological Condition The case landslide is located in Songyang County, Lishui City, Zhejiang Province, China (Fanshantou landslide in Figure1). The area has a subtropical monsoon climate, and the precipitation is mainly concentrated in the seasons of rainy and typhoon rainy, from March to September each year. From March to June is the rainy season, and the average cumulative rainfall is 822.05 mm, which accounts for 52.32% of the total annual rainfall. During this period, cold and warm air currents meet, the rainfall is abundant, the rainfall time is long, and geological disasters are prone to be induced. It is the typhoon rainy season from July to September, and the average cumulative rainfall is 367.05 mm, which makes 24.23% of the annual rainfall. It is characterized by extensive short-duration, high-intensity rainfall concentrated in small areas, leading to a high possibility of geological disasters. The total volume of the potential landslide area was about 285 × 104 m3, and the volume of the soil with creep deformation at the front edge was about 15 × 104 m3.A landslide is a translational landslide in which the surface soil slides along the bedrock surface. The overall landslide area presents the characteristics of being high in the south while being low in the west. The azimuth of the sliding direction is about 220◦. The leading-edge elevation is about 440 m. The trailing edge elevation is about 560 m, and the maximum elevation difference is 120 m. The plan view of the landslide area is shown in Figure2. Water 2021, 13, x FOR PEER REVIEW 3 of 15

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low in the west. The azimuth of the sliding direction is about 220°. The leading-edge ele- Water 2021, 13, 700 vationlow in is the about west. 440 The m. azimuth The trailing of the edge sliding elevation direction is about is about 560 220°.m, and The the leading-edge maximum3 of 15 ele- ele- vationvation difference is about 440 is 120 m. Them. The trailing plan edgeview elevationof the landslide is about area 560 is m, shown and thein Figure maximum 2. elevation difference is 120 m. The plan view of the landslide area is shown in Figure 2.

FigureFigure 1. Position ofof thethe Fanshantou Fanshantou landslide. landslide. Figure 1. Position of the Fanshantou landslide.

Figure 2. Plan view of the Fanshantou landslide. FigureFigure 2. 2.Plan Plan view view of of the the Fanshantou Fanshantou landslide. landslide. The section view in the main direction (section A-A’) of the landslide is shown in FigureTheThe 3. The section section stratum view view (including in in the the main main the direction soildirection layer (section and(section the A-A’) rock A-A’) oflayer) theof landslidethestructure landslide isof shownthe is landslideshown in in bodyFigureFigure can3 .3. The beThe stratumdivided stratum (including into (including obvious the the soilupper, soil layer layer mi andddle, and the and the rock rocklower layer) layer) layers. structure structure The of theupper of landslide the layer landslide con- body can be divided into obvious upper, middle, and lower layers. The upper layer consists sistsbody of can gravel be divided with clay into with obvious a thickness upper, of mi 1.4–9.4ddle, m,and of lower poor layers.permeability The upper (k = 7.16 layer × 10con-−8 of gravel with clay with a thickness of 1.4–9.4 m, of poor permeability (k = 7.16 × 10−8 m/s). m/s).sists Theof gravel color withof this clay layer with is agrayish thickness yellow, of 1.4–9.4 and the m, contentof poor permeabilityof breccia is about (k = 7.16 5%. × The 10− 8 The color of this layer is grayish yellow, and the content of breccia is about 5%. The grain grainm/s). sizeThe ofcolor the ofgravel this layeris 0.2–2 is grayishcm, and yellow, the rest and is cohesive the content soil. of The breccia number is about of hammers 5%. The size of the gravel is 0.2–2 cm, and the rest is cohesive soil. The number of hammers in grain size of the gravel is 0.2–2 cm, and the rest is cohesive soil. The number of hammers inthe the cone cone dynamic dynamic penetration penetration test test is 5–9 is 5–9 per per 10 cm,10 cm, with with a relatively a relatively mixed mixed and and uniform uniform in the cone dynamic penetration test is 5–9 per 10 cm, with a relatively mixed and uniform composition.composition. TheThe middlemiddle layer layer is is silty silty clay clay with with breccia. breccia. The The breccia breccia may may be relatedbe related to the to the nearbynearbycomposition. faults, butbutThe detaileddetailed middle geological layergeological is silty surveys surveys clay with do do not breccia.not ﬁnd find any Theany fault brecciafault activity activity may that be that affects related affects the to the the stabilitystabilitynearby faults, ofof thethe slope.butslope. detailed TheThe trailing trailing geological edge edge surveys is is very very thick, do thick, not while find while theany the leading fault leading activity edge edge is that not. is affects not. The The the permeabilitystability of the is is good goodslope. (k (k =The = 4.85 4.85 trailing× ×10 10−6−6 m/s),edgem/s), is andand ve thethery particlethick, particle while size size is the is between between leading 2 cm 2edge cm and andis 15 not. cm. 15 cm.The Thepermeability color isis graygray is good toto graygray (k = yellow, yellow,4.85 × the10 the−6 particle m/s), particle and size size the distribution particledistribution size is poor,isis betweenpoor, and and the 2 cm changethe andchange is15 cm. is large.The color The contentis gray ofto gravelgray yellow, is 50–75%. the Someparticle boreholes size distribution contain boulders, is poor, the and diameter the change of is

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large. The content of gravel is 50–75%. Some boreholes contain boulders, the diameter of which is 20–40 cm. The parent rock of the gravel is tuff. It is easy for it to collapse and fall off. The lower layer is the underlying bedrock, of which the surface is strongly weathered Water 2021, 13, orx FOR fully PEER weathered, REVIEW and the main components are tuff and muddy siltstone. The color4 of 15is

gray to gray black, and the structure is silty, layered, tuffaceous, or block and relatively Water 2021, 13complete., 700 The landslide area has been affected by faults in history, and more fractures4 of 15 were developed,large. but The there content has of been gravel no is active 50–75%. fault Some since boreholes the Quaternary. contain boulders, the diameter of which is 20–40 cm. The parent rock of the gravel is tuff. It is easy for it to collapse and fall off.which The islower 20–40 layer cm. is The the parent underlying rock ofbedrock, the gravel of which is tuff. the It issurface easy for is itstrongly to collapse weathered and fall off. The lower layer is the underlying bedrock, of which the surface is strongly weathered or fully weathered, and the main components are tuff and muddy siltstone. The color is or fully weathered, and the main components are tuff and muddy siltstone. The color is gray to gray black, and the structure is silty, layered, tuffaceous, or block and relatively gray to gray black, and the structure is silty, layered, tuffaceous, or block and relatively complete. The landslide area has been affected by faults in history, and more fractures complete. The landslide area has been affected by faults in history, and more fractures were were developed, but there has been no active fault since the Quaternary. developed, but there has been no active fault since the Quaternary.

Figure 3. Section view of A-A’.

Figure 3. Section view of A-A’. The landslideFigure area 3. Section belongs view of to A-A’. a fault block in the mid-mountain landform area that is dominated by pyroclasticThe landslide rocks area and belongs metamo to a faultrphic block rocks in thein southwestern mid-mountain landform Zhejiang. area The that direction of the isslope dominatedThe islandslide 220°, by pyroclasticand area thebelongs elevat rocks to a andion fault metamorphicof block the slopein the rocks mid-mountaintoe inis southwestern350 m. landform The Zhejiang.maximum area that The elevation of theis direction catchmentdominated of theby area pyroclastic slope where is 220 rocksthe◦, and land and the metamoslide elevation isrphic located of therocks slope is in 578.12 southwestern toe is 350m, m.and TheZhejiang. the maximum height The difference is 228.12directionelevation m. Theof of the thesl slopeope catchment is is steep220°, area and in wherethe the upperelevat the landslideion area, of the moderately is slope located toe is is 578.12 steep350 m. m, in The andthe maximum themiddle height elevationdifference of isthe 228.12 catchment m. The area slope where is steep the in land theslide upper is area,located moderately is 578.12 steepm, and in the the height middle part, and steepdifference inpart, the and lower is steep 228.12 part in m. the (Figure The lower slope part 4); is (Figuresteepand inthe4 );the andgradient upper the gradientarea, of moderatelythe of upper the upper steep slope slope in isthe is25–35°, middle 25–35 ◦ , the middle partpart, theis 5–15° middleand steep (lands part in isthelide 5–15 lower ◦section),(landslide part (Figure and section), the 4); anlower andd the the partgradient lower is part 25–35°. of the is 25–35 upper Residential◦. Residentialslope is 25–35°, areas areas and cultivated thelandand middle cultivated are locatedpart is land 5–15° in are a(lands locatedrelativelylide in section), a relativelyflat sectionand ﬂatthe lowersectionin the part inmiddle theis 25–35°. middle of Residentialthe ofthe slope. slope. areas The The Tongcun HighwayandTongcun cultivated winds Highway up land along are winds located the up mountain alongin a relatively the mountain from flat thesection from steep thein the steeplower middle lower part, of part, the cutting slope. cutting Thethe the mountain moreTongcun mountainand forming Highway more anda slopewinds forming withup along a slopea general the with mountain a height general from of height 3–5 the of m.steep 3–5 There m.lower There is part, a isgully acutting gully at at thethe the mountainfront edge more of the and landslide. forming However,a slope with since a general no damage height feature of 3–5 is m. found There in is the a gully gully at range the front edge of thefrontand landslide. edge it is located of the However, landslide. far from the However,since landslide, no sincedamage the no inﬂuence damage feature of feature the is gullyfound is found is notin thein considered the gully gully range range here. and it is locatedand far it fromis located the far landslide, from the landslide, the influence the influence of the ofgully the gully is not is notconsidered considered here. here.

Figure 4. The Fanshantou landslide.

2.2. Failure Characteristics of the Case Landslide Figure 4. The Fanshantou landslide.Figure 4. The Fanshantou landslide. The Fanshantou landslide is a translational landslide, and the sliding surface is the top2.2. surface Failure of Characteristics the bedrock. of The the discovery Case Landslide of deformation and failure features was made 2.2. Failure Characteristics of the Case Landslide The Fanshantou landslide is a translational landslide, and the sliding surface is the The Fanshantoutop surface landslide of the bedrock.is a translational The discovery landslide, of deformation and the and failuresliding features surface was is madethe top surface of thefrom bedrock. the reports The of discovery the residents of anddeformation on-site inspections and failure by investigators. features was The made failure

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from the reports of the residents and on-site inspections by investigators. The failure char- characteristicsacteristics of the of thelandslide landslide were were first first discovered discovered in in July July 2010, 2010, and and many many cracks appearedappeared onon thethe frontfront edgeedge ofof thethe landslidelandslide areaarea (Figure(Figure5 a,b).5a,b). AA large large crack crack L1 L1 appeared appeared on on the the trailingtrailing edgeedge onon thethe northnorth sideside ofof thethe landslide.landslide. TheThe widestwidest pointpoint ofof L1L1 reachedreached 1515 cm,cm, andand thethe crackcrack graduallygradually expanded.expanded. ByBy August 2010,2010, thethe maximum width of L1 reached 25 cm. AlthoughAlthough somesome emergencyemergency measuresmeasures werewere taken,taken, suchsuch asas fillingfilling thethe crackscracks withwith cement,cement, thethe cracks were were found found to to expand expand again again in in June June 2012 2012 (Figure (Figure 5c).5c). From From then, then, the the widths widths and anddepths depths of the of cracks the cracks increased increased after after several several rains. rains. In September In September 2013, 2013, an engineering an engineering geo- geologicallogical survey survey of the of theentire entire landslide landslide body body showed showed that that there there were were many many new new cracks cracks in the in thearea area (Figure (Figure 5d).5 d).In June In June 2015, 2015, the thelandslide landslide area area was was re-examined re-examined and and it was it was found found that thatsome some houses houses on the on landslide the landslide body bodywere signific were significantlyantly inclined, inclined, so it was so decided it was decided to relocate to relocatethe village the (Figure village 5e). (Figure 5e).

FigureFigure 5.5. TheThe deformation and failure characterist characteristicsics of of the the Fanshant Fanshantouou landslide. landslide. (a (a):): Collapse Collapse in in thethe frontfront ofof thethe landslide;landslide; ((bb):): CracksCracks inin thethe frontfront of of the the landslide; landslide; ( c(c):): Cracks Cracks in in the the north north side side of of the the landslide; (d): New cracks in the north side of the landslide; (e): Cracks of buildings in the mid- landslide; (d): New cracks in the north side of the landslide; (e): Cracks of buildings in the middle of dle of the landslide. the landslide. 3.3. Materials and MethodsMethods 3.1.3.1. Measuring PrinciplePrinciple ofof thethe FVDSFVDS TheThe flowflow velocity and and direction direction system system (FVDS) (FVDS) is isa device a device that that combines combines a high-res- a high- resolutionolution magnetic magnetic flux flux valve valve compass compass and and a ahigh-magnification high-magnification colloidal colloidal particle trackingtracking camera.camera. TheThe compositioncomposition andand probeprobe structurestructure ofof thethe FVDSFVDS areare shownshown inin FigureFigure6 .6. Both Both the the compasscompass andand thethe cameracamera areare locatedlocated inin thethe probe.probe. TheThe measurementmeasurement principleprinciple ofof thethe FVDSFVDS isis toto obtainobtain aa seriesseries ofof imagesimages ofof colloidalcolloidal particlesparticles inin groundwatergroundwater byby settingsetting aa shortershorter cameracamera shooting interval. interval. The The processing processing softwa softwarere combines combines the the two two adjacent adjacent images images into into one image and connects the positions of the same particle in the two images. The

Water 2021, 13, x FOR PEER REVIEW 6 of 15

one image and connects the positions of the same particle in the two images. The compass in the probe can get the movement direction of the connection. The movement speed of the colloidal particles can be obtained from the length of the connection line and the interval of the shooting time. The movement direction and speed of these colloidal particles represent the flow direction and velocity of the groundwater. It should be noted that because a probe that is just placed in the borehole will interfere with the flow state of the groundwater, it is necessary to leave the probe in the borehole for a while to get a more realistic measurement result. In the system, the direction and speed of the movement of the groundwater are rep- resented by the direction and speed of the movement of the tiny particles in the groundwater. During field measurement, the FVDS uses the boreholes in the survey and ensures that the instrument probe is below the groundwater surface. Because the tiny particles that naturally exist in the water flow with the water, if the direction and speed of these particles are obtained, then the direction and speed of the groundwater could be obtained. The smaller the particles, the better the true flow rate of the groundwater could be rep- resented. With the help of a camera on top of the probe that can give a magnification of ×130, the instrument can capture and take pictures of tiny particles in the groundwater. The camera of the instrument also has the function of taking pictures continuously and saving the shooting time of each picture. At the same time, the compass in the probe automatically marks the position of each photo. The cable is for transferring the captured photos to the computer for subsequent processing. The computer could compare one or several consecutive photos and find the Water 2021, 13, 700 6 of 15 same particles in the two photos. According to the time interval between the two photos, first the distance the particle has moved and the change of the movement position are compassobtained in and the then probe the can particle’s get the movement speed and direction movement of thedirection connection. are obtained. The movement Finally, the speedflow direction of the colloidal and velocity particles of can the be groundwater obtained from are the obtained. length of the connection line and the intervalIn previous of the studies, shooting the time. FVDS The was movement applied direction to the transpor and speedt of ofpollutants these colloidal in ground- particleswater on represent the one thehand ﬂow and direction to explore and the velocity direction of the of groundwater. the groundwater It should flow be on noted the other thathand. because However, a probe the that flow is justrate placedinformation in the boreholeis often overlooked. will interfere At with the the same ﬂow time, state in of slope thestability groundwater, analysis, it islittle necessary attention to leaveis paid the to probe the influence in the borehole of groundwater for a while flow to get on a morethe safety realisticfactor. Therefore, measurement applying result. the FVDS to landslide stability analysis is innovative research.

FigureFigure 6. 6.Composition Composition and and probe probe structure structure of the of ﬂow the velocityflow velocity and direction and direction system (FVDS).system ((FVDS).a) Photo (a) ofPhoto the FVDS of the in FVDS use on-site. in use (bon-site.) Composition (b) Composition of the FVDS. of the (c) ProbeFVDS. structure (c) Probe of structure the FVDS. of the FVDS.

In the system, the direction and speed of the movement of the groundwater are repre- sented by the direction and speed of the movement of the tiny particles in the groundwater. During field measurement, the FVDS uses the boreholes in the survey and ensures that the instrument probe is below the groundwater surface. Because the tiny particles that naturally exist in the water flow with the water, if the direction and speed of these particles are obtained, then the direction and speed of the groundwater could be obtained. The smaller the particles, the better the true flow rate of the groundwater could be rep-resented. With the help of a camera on top of the probe that can give a magnification of ×130, the instrument can capture and take pictures of tiny particles in the groundwater. The camera of the instrument also has the function of taking pictures continuously and saving the shooting time of each picture. At the same time, the compass in the probe automatically marks the position of each photo. The cable is for transferring the captured photos to the computer for subsequent processing. The computer could compare one or several consecutive photos and find the same particles in the two photos. According to the time interval between the two photos, first the distance the particle has moved and the change of the movement position are obtained and then the particle’s speed and movement direction are obtained. Finally, the flow direction and velocity of the groundwater are obtained. In previous studies, the FVDS was applied to the transport of pollutants in groundwater on the one hand and to explore the direction of the groundwater flow on the other hand. However, the flow rate information is often overlooked. At the same time, in slope Water 2021, 13, x FOR PEER REVIEW 7 of 15

Water 2021, 13, 700 7 of 15 3.2. Improved Bishop Method Considering Hydrodynamic Pressure stability analysis, little attention is paid to the inﬂuence of groundwater ﬂow on the safety factor. Therefore,Among applying the the FVDSmany to landslide methods stability analysis for calculating is innovative research. the slope safety factor, the Bishop method

3.2.has Improved been Bishop widely Method Considering used Hydrodynamic for its Pressure good accuracy [15,16]. However, the Bishop method only considersAmong the many the methods hydrostatic for calculating thepressure slope safety factor, effect the Bishop of the method groundwater. Although some researchers has been widely used for its good accuracy [15,16]. However, the Bishop method only considerstried the to hydrostatic introduce pressure effecthydrodynamic of the groundwater. Although pressure some researchers or seepage force into the Bishop method, the tried to introduce hydrodynamic pressure or seepage force into the Bishop method, the calculationcalculation process of theprocess improved methodof the was improved still not convincing method enough [17,18 was]. For still not convincing enough [17,18]. For landslide areas, the situation of the groundwater is very complicated and the groundwater ﬂowlandslide along the sliding areas, direction the will havesituation an effect on of the slopethe safetyground factor. Therefore,water is very complicated and the groundwa- based on the Bishop method, the hydrodynamic pressure was introduced to calculate the safetyter factor flow of the along slope. the sliding direction will have an effect on the slope safety factor. Therefore, basedIn the improved on the method, Bishop the stress method, analysis of the ithe-th soil hydrodynamic strip is shown in Figure7. pressure was introduced to calculate the In the calculation, it is assumed that the component forces of the vertical inter-strip force aresafety equal in value factor and opposite of the in direction. slope.Ji is the hydrodynamic pressure on the strip, and the direction of the pressure is down along the bottom of the strip. Then the vertical force balanceIn equation the improved of the soil strip is asmethod, follows: the stress analysis of the i-th soil strip is shown in Figure 7.

In the calculation,Wi + Ji sin α iit= isTi sin assumedαi + (Ni + uili) costhatαi the component(1) forces of the vertical inter-strip force

whereareW equali is the weight in ofvalue the i-th soiland trip opposite (see Figure7), and in its direction. unit is kN/m; J iJisi theis the hydrodynamic pressure on the strip, seepage force of the i-th soil trip, and its unit is kN/m; αi is the slope of the bottom of the i-thand soil trip; theTi and directionNi are the tangential of the force pressure and the normal forceis down of the i-th along soil trip on the bottom of the strip. Then the vertical the bottom surface, respectively, and the unit is kN/m; and uili is the pore water pressure offorce the i-th soil balance trip, and the equation units are kPa for ofui and th me for soilli. strip is as follows:

FigureFigure 7. Diagram 7. ofDiagram the force analysis of of the the i-th force soil trip. analysis of the i-th soil trip.

𝑊 + 𝐽𝑠𝑖𝑛𝛼 =𝑇𝑠𝑖𝑛𝛼 + (𝑁 +𝑢𝑙)𝑐𝑜𝑠𝛼 (1)

where 𝑊 is the weight of the i-th soil trip (see Figure 7), and its unit is kN/m; 𝐽 is the seepage force of the i-th soil trip, and its unit is kN/m; 𝛼 is the slope of the bottom of the i-th soil trip; 𝑇 and 𝑁 are the tangential force and the normal force of the i-th soil trip on the bottom surface, respectively, and the unit is kN/m; and 𝑢𝑙 is the pore water pressure of the i-th soil trip, and the units are kPa for ui and m for li. Because in the calculation, there is a fixed relationship between 𝑇 and 𝑁: 1 𝑇 = (𝑐𝑙 +𝑁𝑡𝑎𝑛𝜑) (2) 𝐹

where 𝑐 (kPa) is the cohesion of the i-th soil trip and 𝜑 is the internal friction of the i- th soil trip. Simultaneously, from Equations (1) and (2), the following derivation can be obtained:

1 𝑐𝑙𝑠𝑖𝑛𝛼 𝑁 = (𝑊 + 𝐽𝑠𝑖𝑛𝛼 − −𝑢𝑙𝑐𝑜𝑠𝛼) (3) 𝑚 𝐹

where

𝑡𝑎𝑛𝜑𝑠𝑖𝑛𝛼 𝑚 =𝑐𝑜𝑠𝛼 + (4) 𝐹

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Because in the calculation, there is a ﬁxed relationship between Ti and Ni:

1 Ti = (cili + Ni tan ϕi) (2) FS

where ci (kPa) is the cohesion of the i-th soil trip and ϕi is the internal friction of the i-th soil trip. Simultaneously, from Equations (1) and (2), the following derivation can be obtained:

Water 2021, 13, x FOR PEER REVIEW c l 8 of 15 1 i i sin αi Ni = Wi + Ji sin αi − − uili cos αi (3) mi Fs

where When the forces of the soil strip are summedtan ϕ toi sin theα icenter of the sliding arc, the in- mi = cos αi + (4) ternal force between the soil strips does not appearF ins the equilibrium equation. In addition, in order to simplify the calculation, the center of the bottom of the soil strip is re- When the forces of the soil strip are summed to the center of the sliding arc, the internal garded as the point of the action of 𝐽 . force between the soil strips does not appear in the equilibrium equation. In addition, in order to simplify the calculation, the center of the bottom of the soil strip is regarded as the 𝑇𝑟=𝑊𝑟𝑠𝑖𝑛𝛼 +𝐽 𝑟 point of the action of Ji. (5) ∑ Tir = ∑ Wir sin αi + ∑ Jir (5) where 𝐹 is the safety factor and r is the distance to the point of action and its unit is m. where FS is the safety factor and r is the distance to the point of action and its unit is m. Substituting Equations (1)–(4) into Equation (5) and substituting 𝑏 =𝑙𝑐𝑜𝑠𝛼 at the Substituting Equations (1)–(4) into Equation (5) and substituting b = l cos α at the same time, we obtain the following equation for the calculation of the safetyi i factori after same time, we obtain the following equation for the calculation of the safety factor after the hydrodynamic water pressure is considered: the hydrodynamic water pressure is considered:

1 𝑐𝑏 +(𝑊 + 𝐽𝑠𝑖𝑛𝛼 −𝑢𝑏)𝑡𝑎𝑛𝜑 𝐹 = 1 cibi + (Wi + Ji sin αi − uibi) tan ϕ (6) FS = ∑(𝑊𝑠𝑖𝑛𝛼 + 𝐽) ∑ 𝑚 (6) ∑ (Wi sin αi + Ji) mi Since the real geological profile is very complicated, especially the interface of each Since the real geological profile is very complicated, especially the interface of each layer being difficult to deal with in the calculation, the geological profiles of the landslides layer being difficult to deal with in the calculation, the geological profiles of the landslides need to be simplified. Based on the real stratum structure, the curve boundary of the stra- need to be simplified. Based on the real stratum structure, the curve boundary of the tum is transformed into a straight line and the thickness and position of the stratum after stratum is transformed into a straight line and the thickness and position of the stratum simplification are basically consistent with the real situation. The simplified geological after simplification are basically consistent with the real situation. The simplified geological profile of the Fanshantou landslide is shown as Figure 6. In the process of simplification profile of the Fanshantou landslide is shown as Figure6. In the process of simplification of of the section, the characteristics of the original local layer are retained. For the Fanshan- the section, the characteristics of the original local layer are retained. For the Fanshantou toulandslide, landslide, the the most most important important geological geological features features are theare followingthe following (see (see Figure Figure8 for illus-8 for illustration):tration): (1) There(1) There is a is silty a silty clay clay layer layer on the on surface.the surface. (2) The (2) gravelThe gravel soil layersoil layer is very is very thick thickat the at trailing the trailing edge edge and and thin thin at the at leadingthe leading edge. edge. (3) The(3) The bedrock bedrock has has a large a large inclination inclina- tionat the at trailingthe trailing edge, edge, but but it is it fairly is fairly flat flat atthe at the leading leading edge. edge. The The physical physical and and mechanical mechan- icalparameters parameters of each of each soil soil layer layer are are shown shown in Table in Table1. 1.

FigureFigure 8. 8. SimplifiedSimpliﬁed section section for for calculation calculation of of the the safety safety factor. factor.

Table 1. Physical and mechanical parameters of soil layers.

Soil 𝛄/kN·m−3 c/kPa 𝛗 Gravel with clay 18.19 12.5 12.5° Silty clay with breccia 18.66 3 24.5° Strongly weathered bedrock 19.30 22 16.0°

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Table 1. Physical and mechanical parameters of soil layers.

Soil γ/kN ·m−3 c/kPa ϕ Gravel with clay 18.19 12.5 12.5◦ Silty clay with breccia 18.66 3 24.5◦ Strongly weathered bedrock 19.30 22 16.0◦

3.3. Estimation of Hydrodynamic Pressure Based on ANNs According to Section 3.2, the equation to calculate the safety factor of a slope has been obtained by considering the hydrodynamic pressure. However, in Equation (6), the hydrodynamic pressure Ji of each soil strip needs to be considered. According to Darcy’s law, the relationship between groundwater ﬂow velocity and hydrodynamic pressure is: v J = γ (7) i k w

In the formula, Ji is the hydrodynamic pressure of the groundwater in the i-th soil strip, v is the flow velocity of the groundwater, k is the permeability coefficient of the soil at the measurement location, and γw is the gravity of the water. However, for landslides, it is impossible to measure the groundwater flow velocity for each soil strip. When measuring groundwater flow velocity, the FVDS has certain requirements in terms of the diameter and wall conditions of the borehole and the number of boreholes in the area is limited. In addition, the groundwater velocity is affected by many factors, such as the groundwater level, the inclination of the bedrock, and the distribution of geological structures. Therefore, it is difficult to establish an equation to calculate the regional groundwater flow velocity from the monitoring data of boreholes. However, in a landslide, the groundwater velocity curve on a profile line should be continuous and smooth. Therefore, the velocity of the groundwater cannot be calculated accurately but it can be estimated by using the borehole data. It is a typical curve fitting problem to estimate the velocity of continuously changing flow by using the known flow velocity data. The objective of curve fitting is to construct a curve or derive mathematical functions that can exhibit close proximity to the real observations. Traditional curve fitting methods, such as linear and cubic polynomials, can provide a simple solution for the nonlinear curve fitting problem. However, substantial performance improvement can be obtained using the artificial neural network (ANN). Though the calculation of the ANN is generally more computationally intensive than that of the linear algorithm, the predictive ability of the model is usually optimal. Therefore, the ANN is employed in this study. Some advanced methods, such as artificial-delay- based methods [19,20] can also be alternate ways to estimate an unknown function via input/output data. When fitting a curve by using the generalized regression neural network (GRNN), with only limited points, the curve can be well fitted [21]. The GRNN is a radial basis function neural network that has a simple training procedure and unique adjustment parameters. The GRNN consists of four layers: the input layer, the pattern layer, the T summation layer, the and output layer [22]. The input vector is X = (x1, x2, ... , xm) and T the corresponding output is Y = (y1, y2, ... , yk) . The dimension of the input vector is m, the dimension of the output vector is k, and the number of samples is n. The GRNN could adjust the network structure according to the training samples automatically. In addition, the number of nodes need not be determined by the users. The transfer function of the i-th neuron in the model layer is: " # (X − X )T(X − X ) P = exp − i i (8) i 2σ2 Water 2021, 13, 700 10 of 15

where X is the input variable of the network, Xi is the corresponding training sample of the i-th neuron, and σ is the smoothing parameter. The summation layer contains two types of neurons. One type performs the arithmetic Water 2021, 13, x FOR PEER REVIEW 10 of 15 summation of all the output of the model layer, and the connection weight between each neuron and this neuron in the model layer is 1. The other type performs a weighted summation of all the output of the pattern layer. The number of neurons in the output sample.layer is equal As a toresult, the dimension the GRNN of is the more output convenie vectornt in than the model the other sample neural [23]. networks. Therefore, As the GRNNthe structure is an and updated weight version of the GRNN of the are basic fully ANN determined model, after we the refer selection to it as of ANN the model instead in sample. As a result, the GRNN is more convenient than the other neural networks. As the the following sections for consistency. GRNN is an updated version of the basic ANN model, we refer to it as ANN instead in the following sections for consistency. 4. Result 4. ResultWhen the FVDS was used to measure the groundwater flow velocity in the area, there wereWhen high therequirements FVDS was used for tothe measure conditions the groundwater of the borehole flow velocity diameter in theand area, the there hole wall. wereWhen high there requirements are at least two for the sets conditions of orthogonal of the through-holes borehole diameter in the and perforated the hole wall.pipe of the Whenborehole there wall, are atthe least accuracy two sets of ofthe orthogonal measurem through-holesent results can in thebe perforatedguaranteed pipe [13]. of At the samethe borehole time, the wall, diameter the accuracy of the of borehole the measurement should be results more canthan be twice guaranteed that of [ 13the]. probe At di- the same time, the diameter of the borehole should be more than twice that of the probe ameter. In the landslide area, only a few boreholes meet the measurement conditions. The diameter. In the landslide area, only a few boreholes meet the measurement conditions. measurement results of the groundwater flow velocity of five boreholes (ZK2, ZK3, ZK6, The measurement results of the groundwater flow velocity of five boreholes (ZK2, ZK3, ZK7,ZK6, ZK7,and andZK8) ZK8) are areshown shown as as Figure Figure 99.. AsAs for for the the direction direction data data of the of flow, the itflow, basically it basically points toto the the main main sliding sliding direction direction of the of landslide the landslide or the adjacent or the gully.adjacent Since gully. this research Since this re- wassearch focused was focused on regional on regional groundwater groundwater flow velocity flow data, velocity the flowdata, direction the flowdata direction is not data is notdiscussed discussed in more in more detail. detail.

Figure 9.9.Groundwater Groundwater ﬂow flow velocity velocity of ﬁveof five boreholes. boreholes.

FigureFigure9 9shows shows that that the the groundwater groundwater flow flow velocity velocity in the in area the varies area varies greatly; greatly; the the highest flowflow velocity velocity reaches reaches 26 26 m/d m/d (ZK8), (ZK8), while while the lowestthe lowest in the in measurement the measurement is only is only 3 m/d (ZK3). Large changes in flow velocity indicate that the groundwater movement 3 m/d (ZK3). Large changes in flow velocity indicate that the groundwater movement in in the landslide is active. However, from the monitoring data of the groundwater level, the landslide is active. However, from the monitoring data of the groundwater level, it is it is difficult to identify the change in the groundwater velocity intuitively. In addition, difficultthe distribution to identify of the the groundwater change in flow the velocitygroundwater in Fanshantou velocity landslide intuitively. shows In thataddition, the the distributionflow is fast at of the the trailing groundwater edge and flow the velocity leading edgein Fanshantou but it is slow landslide at the middleshows that of the the flow islandslide. fast at the Such trailing velocity edge characteristics and the leading are closely edge related but it tois slow the hydrogeological at the middle conditionsof the landslide. Suchof the velocity region. characteristics are closely related to the hydrogeological conditions of the region. By taking the average of the measurement results of each borehole in Figure 9, the groundwater velocity of the borehole could be obtained. Because all the measured boreholes are on the A-A’ profile, the groundwater velocity information on this profile can be restored. Based on the groundwater velocity of five boreholes, the fitted curve can be obtained by using the ANN method. In the ANN model, the dimension of the input data is 2 (velocity and distance); R-squared is taken as the evaluation metric; the 5-fold cross- validation method was used (i.e., 4 samples for training and 1 for testing in each turn) to validate the model. The result of curve fitting is shown as Figure 10. In Figure 10, the horizontal axis is the distance from the trailing edge to the leading edge of the landslide

Water 2021, 13, 700 11 of 15

By taking the average of the measurement results of each borehole in Figure9, the groundwater velocity of the borehole could be obtained. Because all the measured boreholes are on the A-A’ profile, the groundwater velocity information on this profile can be restored. Based on the groundwater velocity of five boreholes, the fitted curve can be obtained by using the ANN method. In the ANN model, the dimension of the input Water 2021, 13, x FOR PEER REVIEWdata is 2 (velocity and distance); R-squared is taken as the evaluation metric; the 5-fold 11 of 15 cross-validation method was used (i.e., 4 samples for training and 1 for testing in each turn) to validate the model. The result of curve fitting is shown as Figure 10. In Figure 10, the horizontal axis is the distance from the trailing edge to the leading edge of the landslide and theand vertical the vertical axis is axis the flow is the velocity flow velocity of the groundwater of the groundwater in the landslide. in the Thelandslide. groundwater The ground- velocitywater velocity of landslides of landslides is closely is related closely to hydrogeologicalrelated to hydrogeological conditions. Hydrogeologicalconditions. Hydrogeo- conditionslogical conditions not onlydetermine not only thedetermine inclination the of inclination the groundwater of the ingroundwater the rock and soilin the layer, rock and thesoil recharge layer, the and recharge discharge and conditions discharge of the conditions groundwater, of the and groundwater, the hydraulic gradient, and the buthydraulic alsogradient, determine but thealso type determine of groundwater. the type Submersibleof groundwater. water andSubmersible confined waterwater usuallyand confined havewater different usually flow have speeds. different flow speeds.

FigureFigure 10. 10.Groundwater Groundwater ﬂow flow velocity veloci andty and ﬁtting fitting curve. curve.

TheThe flow flow velocity velocity distribution distribution law inlaw Figure in Figure 10 is consistent 10 is consistent with the with stratum the structure stratum struc- characteristicsture characteristics of the Fanshantou of the Fanshantou landslide. landsl For theide. Fanshantou For the Fanshantou landslide, the landslide, permeability the perme- of the silty clay and bedrock on the surface of the slope is poor, so groundwater mainly ability of the silty clay and bedrock on the surface of the slope is poor, so groundwater exists in the gravel soil layer. The inclination and thickness of the gravel soil layer have becomemainly theexists main in influencingthe gravel soil factors layer. of theThe groundwater inclination and velocity. thickness At the of trailing the gravel edge ofsoil layer thehave landslide, become because the main the influencing thickness of factors the gravel of th soile groundwater layer with good velocity. permeability At the is trailing large, edge theof the groundwater landslide, flow because rate mainly the thickness depends onof thethe inclinationgravel soil of layer the bedrock. with good In the permeability middle is oflarge, the landslide, the groundwater the bedrock flow is rate flat (the mainly inclination depends of theon rockthe inclination formation isof less thethan bedrock. 20◦) In the andmiddle the hydraulic of the landslide, gradient decreases,the bedrock so theis flat groundwater (the inclination flow velocity of the decreases. rock formation At the is less leadingthan 20°) edge and of the the landslide, hydraulic the thicknessgradient ofdecrea the gravelses, soilso the layer groundwater decreases rapidly flow and velocity the de- areacreases. of the At groundwater the leading overflowedge of the cross-section landslide, decreasesthe thickness rapidly, of the resulting gravel in soil an layer increase decreases inrapidly the groundwater and the area flow of velocity. the groundwater The monitoring overfl dataow of cross-section groundwater decreases velocity also rapidly, shows result- that the slope of the bedrock will lead to an increase in the speed of the groundwater, but ing in an increase in the groundwater flow velocity. The monitoring data of groundwater compared with the reduction of the flow section, the latter will accelerate the velocity of the velocity also shows that the slope of the bedrock will lead to an increase in the speed of groundwater more significantly. This is because apart from the increase in the slope, the groundwaterthe groundwater, velocity but will compared also be affected with the by otherreduction factors, of such the asflow the section, permeability the latter of the will ac- rockcelerate and soil.the velocity In confined of the water, groundwater the reduction more of thesignificantly. flow cross-section This is isbecause more intuitive apart from the andincrease the effect in the on slope, the velocity the groundwater is more significant. velocity Therefore,will also be the affected estimated by distributionother factors, such as the permeability of the rock and soil. In confined water, the reduction of the flow cross- section is more intuitive and the effect on the velocity is more significant. Therefore, the estimated distribution of the groundwater flow velocity conforms to the flow velocity law of the Fanshantou landslide and can be used as the basis for calculating the hydrodynamic pressure of each soil strip. Based on the improved Bishop method and the groundwater velocity information in Section 3.2, the safety factor of the Fanshantou landslide is calculated. Table 2 shows the safety factor of the Fanshantou landslide under three kinds of groundwater conditions. Without considering the effect of the groundwater, the safety factor of the Fanshantou landslide is 1.443. This safety factor indicates that the slope is quite stable and basically no landslide hazards would occur. When only considering the hydrostatic pressure of the landslide groundwater, the safety factor of the landslide is 1.129. There is a decrease of

Water 2021, 13, 700 12 of 15

of the groundwater flow velocity conforms to the flow velocity law of the Fanshantou landslide and can be used as the basis for calculating the hydrodynamic pressure of each soil strip. Based on the improved Bishop method and the groundwater velocity information in Section 3.2, the safety factor of the Fanshantou landslide is calculated. Table2 shows the safety factor of the Fanshantou landslide under three kinds of groundwater conditions. Without considering the effect of the groundwater, the safety factor of the Fanshantou landslide is 1.443. This safety factor indicates that the slope is quite stable and basically no landslide hazards would occur. When only considering the hydrostatic pressure of the landslide groundwater, the safety factor of the landslide is 1.129. There is a decrease of 0.314 compared to when the effect of the groundwater was not considered and the decline is very obvious. However, neither safety factors seem to agree with the obvious damage characteristics of the case landslide. With such safety factors, so many landslide cracks should not occur. When considering the hydrodynamic pressure of the landslide, the safety factor is 1.009, which is a decrease of 0.12 compared to when only the hydrostatic effect is considered. Combined with the landslide damage characteristics of the case, it is believed that this safety factor could reflect the true state of the landslide.

Table 2. Safety factor considering different groundwater conditions.

No Consideration of Traditional Bishop Improved Bishop Drainage Conditions Groundwater Method Method Before drainage 1.443 1.129 1.009 After drainage 1.443 1.389 1.321

The calculation result of the safety factor when considering the hydrodynamic pressure proves that for some landslides with strong groundwater activity, such as the case landslide, the stability of the slope cannot be accurately described without considering the groundwater effect or only considering the water pressure of the groundwater pore. For the case landslide, the safety factor calculated without considering the hydrodynamic pressure indicates that the landslide is pretty stable. However, when considering the hydrodynamic pressure, the calculation results show that the landslide is not stable and the results agree with the actual failure characteristics of the landslide. Therefore, the meticulous investigation of the hydrogeological conditions of landslides is very important. It is also necessary to evaluate the geological condition carefully because the geological and morphological settings of an area guide the physics of the soil. They will provide important data to evaluate the stability of the slope. The calculation results show that groundwater is an important factor affecting the stability of the Fanshantou landslide. Therefore, the most effective way to control this type of landslide is to reduce the groundwater level of the landslide. After the groundwater level drops, the groundwater in an area changes in two ways. On the one hand, a drop in the groundwater level (measured by a pressure gauge) causes a decline in the hydraulic gradient of the landslide, which lowers the groundwater flow velocity at the trailing edge of the landslide. On the other hand, the drop in the groundwater level makes the confined water pressure of the leading edge drop or even disappear where the groundwater flow velocity is reduced. On these bases, the siphon drainage method was used to control the landslide. After siphon drainage of 100 days, the flow velocity of the slope was measured again (shown as Figure 11). Compared with the situation before treatment, the groundwater flow velocity at the leading edge and trailing edge of the slope decreased significantly. The safety factor of the landslide with the groundwater level and flow velocity after the treatment is recalculated. When only considering the pore water pressure, the safety factor of the landslide is 1.389, and when considering the hydrodynamic pressure, the safety factor of the landslide is 1.321. This shows that after the groundwater level drops, the safety factor of the landslide is obviously improved. Water 2021, 13, x FOR PEER REVIEW 13 of 15 Water 2021, 13, 700 13 of 15

FigureFigure 11. 11.Groundwater Groundwater ﬂow flow velocity velocity and and ﬁtting fitting curves curves before before and and after after drainage. drainage.

5.5. DiscussionDiscussion The FVDS can measure the velocity of the groundwater in an area and obtain the The FVDS can measure the velocity of the groundwater in an area and obtain the hydrodynamic pressure of the groundwater on the soil. The application of the FVDS to hydrodynamic pressure of the groundwater on the soil. The application of the FVDS to slope stability analysis is innovative research. The monitoring of hydrodynamic pressure is indeedslope stability very important analysis for is theinnovative stability research. of some landslides, The monitoring at least of for hydrodynamic the case studied pressure in thisis indeed article. very However, important whether for hydrodynamic the stability of pressure some landslides, will affect theat least stability for ofthe all case slopes studied remainsin this article. to be explored. However, On whether the one hand,hydrodynamic it is related pressure to the hydrogeological will affect the conditions stability of all ofslopes the landslide, remains andto be on explored. the other On hand, the itone is relatedhand, it to is the related monitoring to the conditionshydrogeological of the con- landslide.ditions of Therefore, the landslide, this limitsand on the the wide other application hand, it ofis therelated FVDS. to However,the monitoring indoor conditions trials seemof the to landslide. solve this problem.Therefore, Ivanov this limits et al. [the24] wide used indoorapplication experiments of the FVDS. to carefully However, explore indoor thetrials influence seem to of solve groundwater this problem. on the stabilityIvanov analysiset al. [24] of used shallow indoor landslides experiments and confirmed to carefully thatexplore indoor the experiments influence of can groundwater reflect all the on problems the stability of the originalanalysis scale of shallow according landslides to Buck- and ingham’sconfirmed law. that Therefore, indoor indoorexperiments experiments can reflect using all the the FVDS problems can ensure of the more original systematic scale ac- applicationscording to Buckingham’s of the system. Thelaw. ANN Therefore, method in alsodoor played experiments an important using rolethe FVDS in this can analy- ensure sis.more The systematic application applications of this method of the is basedsystem. on The the continuityANN method of groundwater also played flowan important rate. Discussionrole in this on analysis. the accuracy The application and extensiveness of this method of its fitting is based is still on needed. the continuity However, of ground- the models and results used in this article are adequate when explaining trends and conducting water flow rate. Discussion on the accuracy and extensiveness of its fitting is still needed. preliminary analysis. However, the models and results used in this article are adequate when explaining trends 6.and Conclusions conducting preliminary analysis. In this study, an improved Bishop method was proposed by incorporating hydrody- namic6. Conclusions pressure and the artificial neural networks and the effectiveness of the framework was validatedIn this study, based an on improved a case slope Bishop using method the FVDS. was The proposed conclusions by incorporating can be summarized hydrody- asnamic follows: pressure and the artificial neural networks and the effectiveness of the framework wasFirst, validated the FVDS based provides on a case a fast,slope convenient, using the FVDS. and simple The conclusions solution for can measuring be summarized the directionas follows: and velocity of groundwater. The hydrodynamic information about groundwater in a landslideFirst, the area FVDS can thereforeprovides be a extracted,fast, convenient, which is and of great simple significance solution in for analyzing measuring the the stabilitydirection of and the landslide.velocity of Meanwhile, groundwater. the ANN The hydrodynamic exhibits optimal information performance about on fitting groundwa- the curveter in ofa thelandslide groundwater area can flow therefore velocity be in extracted, a landslide. which The results is of great obtained significance from the ANNin analyz- correspond with the actual hydrogeological conditions and measurement results and can ing the stability of the landslide. Meanwhile, the ANN exhibits optimal performance on be applied to subsequent analysis and calculation. The application of ANN can overcome fitting the curve of the groundwater flow velocity in a landslide. The results obtained from the problem of limited data points caused by the strict requirements of the FVDS in the measurementthe ANN correspond procedure with in the the real-world actual hydrog application.eological conditions and measurement results and can be applied to subsequent analysis and calculation. The application of ANN can overcome the problem of limited data points caused by the strict requirements of the FVDS in the measurement procedure in the real-world application.

Water 2021, 13, 700 14 of 15

Secondly, the original Bishop method has been improved by considering the hydrodynamic pressure. An updated approach is derived and proposed that can improve the calculation of the safety factor by adding a simple yet effective term of hydrodynamic pressure. Finally, in the case landslide, the improved safety factor calculation formula was used to calculate the stability. As shown in the results section for the case landslide, the safety factors using the baseline methods without considering groundwater and incorporating only the pore water pressure were 1.443 and 1.129, respectively. The safety factors by these two baseline methods did not match the failure characteristics of the case landslide. On the other hand, the safety factor considering the hydrodynamic pressure was 1.009, which conforms to the landslide failure characteristics. The feasibility and effectiveness of the proposed improved calculation method of safety factor in evaluating the stability of landslide is therefore shown. Moreover, we found that slope drainage is the most effective intervention strategy for the case of landslides. The result shows that the safety factor increased to 1.321 after the water level dropped.

Author Contributions: Conceptualization, Q.G. and Z.C.; methodology, Q.G.; software, Z.C.; validation, J.Z. and J.L.; formal analysis, J.Z.; investigation, Q.G.; resources, Z.C.; data curation, Z.C.; writing—original draft preparation, Z.C.; writing—review and editing, Q.G. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Due to the nature of this research, participants of this study did not agree for their data to be shared publicly, so supporting data is not available. Acknowledgments: The authors acknowledge the support of the National Key R&D Program of China (Project no. 2018YFC1504704). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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