Study on the Characteristics of Self-Stabilizing Height Distribution for Deep Foundation Pit Vertical Sidewall in Binary Strata of Upper Soil and Lower Rock

)e self-stability height of the foundation pit sidewall is an important criterion for evaluating the safety degree and designing the supporting structure. )e strength reduction elastic-plastic finite element numerical calculation method has been adopted in this paper. Based on comparative analysis of the stability characteristics for deep foundation pit in binary strata of upper soil and lower rock under multiple working conditions, the potential fracture surface of deep foundation pit and the evolution law of corresponding safety factor have been revealed under differentHs andH. A new idea that the vertical soil sidewall height (Hs) and the vertical rock sidewall height (Hr) are used as two independent evaluation indexes, respectively, for deep foundation pit stability in binary strata of upper soil and lower rock has been put forward. )e distribution characteristics and variation law of Hs0 and Hr0 under different Hs and different H have been revealed, respectively. )e spatial distribution map of the self-stabilizing height for deep foundation pit vertical sidewall in upper soil and lower rock binary stratum has been constructed, and the mathematical fitting equation between Hr0 and Hs has been obtained. Finally, combined with the implementation effect of the deep foundation pit project of Ningxia Road Station for Qingdao Metro Line 3, the rationality of the conclusions is verified. )e research results provide theoretical basis for quickly determining the self-stability characteristics of foundation pit vertical sidewall.


Introduction
With the accelerating process of urbanization in China, a type of deep foundation pit whose bottom is above the interface between soil stratum and rock stratum comes into being. e unique feature of this deep foundation pit type is that the strata within its excavation depth are composed of soil and rock from top to bottom, and the difference of the main mechanical parameters such as cohesion and elastic modulus between the two strata is almost thousands of times, such as Wusi Square Station foundation pit of Qingdao Metro Line 3 [1], Anshan Road Station foundation pit of Qingdao Metro Line 4 [2,3], and Chashan station foundation pit of Shenzhen Metro Line 7 [4]. In this paper, this type of deep foundation pit is uniformly called deep foundation pit in the binary strata of upper soil and lower rock.
e self-stability height of foundation pit sidewall is an important criterion for evaluating the safety degree and designing the supporting structure. As early as the 1860s, Culann [5] deduced the formula for calculating the vertical sidewall critical instability height according to the balance condition of force. After that, Terzaghi et al. [6][7][8][9][10] modified the Culann method and formed a series of theoretical formulas for the vertical sidewall critical instability height. Pufahl [11] deduced the self-stable critical height of the foundation pit vertical excavation slope by calculating and analyzing the condition that the sliding wedge is in the limit equilibrium state. Zhang et al. [12] adopted the beam column mechanical model under the action of self-weight and obtained the critical instability height of vertical layered rock slope. Liu et al. [13,14] constructed the instability calculation model of vertical layered rock slope based on statistical damage model and obtained the critical height, based on Euler compression bar theory and capacity method. Based on the upper bound theorem of limit analysis method, Chen [15] and Wang et al. [16] deduced the calculation formula of double-layer slope critical height at any layered position under different failure mechanisms and obtained the linear variation law of double-layer slope critical height with layered depth under different conditions. Li et al. [17,18] studied the overall stability and failure mode of deep foundation pit slope in binary stratum of soil and fully weathered rock, and soil and strongly weathered rock, respectively.
Strength reduction method (SRM) was first proposed by Zienkiewicz et al. in 1975 and used for slope stability analysis [19]. And then, many scholars have done a lot of work on the applicability and feasibility of SRM in slope stability analysis, such as Ugai [20], Matsui and San [21], Griffiths and Lane [22], and Dawson [23] et al. For the whole safety storage of the slope based on the double safety factors, nonproportional correlative reduction finite element method with the contribution of the shear strength parameter to the sliding resistance force as weight is proposed by Xue et al. [24]. A parallel-local strength reduction method is proposed by Zhang et al. [25], which is based on the idea of the local strength reduction method. For the heterogeneous slope, a novel hierarchical multiscale strength reduction method is proposed by Meng et al. [26]. For the stability evaluation of rock slope, the strength reduction method considering the ubiquitous joint model is proposed by Liu et al. [27]. Based on the strength reduction method, the changing positions of the slope sliding surface during the filling process are studied by Yuan et al. [28][29][30].
e self-stability of deep foundation pit sidewall has been taken under serious consideration, and the SRM method has been used to evaluate it as well. However, the vertical sidewall of deep foundation pit in the binary strata of upper soil and lower rock as the independent factor is less considered. ere are few reports on the research based on the self-stable height of vertical sidewall for deep foundation pit. In this paper, the strength reduction elastic-plastic finite element numerical analysis method is adopted to calculate and analyze the potential fracture position and FOS of the vertical sidewall for deep foundation pit in the binary strata of upper soil and lower rock. And then, the distribution characteristics and variation law of Hs 0 and Hr 0 under different Hs and different H have been revealed, respectively. e spatial distribution map of the self-stabilizing height for deep foundation pit vertical sidewall in upper soil and lower rock binary stratum has been constructed, and the mathematical fitting equation between Hr 0 and Hs has been obtained. Finally, combined with the implementation effect of the deep foundation pit project of Ningxia Road Station of Qingdao Metro Line 3, the rationality of the conclusions is verified.

Strength Reduction Method (SRM).
e strength reduction method is a method combining strength reduction technology, limit equilibrium principle, and elastic-plastic finite element calculation principle. Firstly, the stress and deformation state under the condition of original material parameters is calculated. en, the material strength parameters c and tanφ are reduced simultaneously according to formula, and a (1) set of new strength parameters c ′ and tan φ ′ are obtained and calculated as new material strength parameters. Finally, the critical fracture surface is obtained by continuously adjusting the reduction factor k until the material is in the limit equilibrium state. At this time, the reduction factor k of the material is the stability FOS.
where k is the reduction factor. e calculation principle of SRM [31] is shown in Figure 1.

Implementation Process and Example Analysis.
e numerical calculation of deep foundation pit stability analysis adopts Midas GTS analysis software and is modeled according to 3D solid element. e upper boundary of the calculation model is taken to the surface. e lower boundary is taken to 3 times of the excavation depth below the base, and the horizontal boundary is more than 3 times of the excavation depth from the sidewall of the foundation pit. e thickness is taken as 1.0 m. Gravity constraints and model boundary constraints are applied. A uniform ground load of 20 kPa is applied to the upper surface of the calculation model without considering the effects of groundwater and earthquake. e grid size of the foundation pit excavation part is set as 0.5 m, and the other grid sizes are set as 2.0 m. e improved Mohr-Coulomb constitutive model is adopted for rock and soil mass, and the effects of rock and soil self-weight, ground load, and boundary constraints are considered in the initial stress. e calculation model is shown in Figure 2. e implementation process is completed by six key steps. Now, take the deep foundation pit in the binary strata of upper soil and lower rock with the upper soil stratum thickness of 10 m and the excavation depth of 15 m as an example.
Step 1: import the drawn calculation model into Midas GTS software, as shown in Figure 3(a).
Step 2: expand the whole part of the model by 1.0 m along the z-axis, and then control the size of the foundation pit location entity and other parts, as shown in Figure 3(b).
Step 3: divide the grid into 4 parts: soil stratum excavation part, rock stratum excavation part, soil stratum unexcavated part, and rock stratum unexcavated part.
e grid size of the excavation part is Step 4: apply self-weight, boundary constraints, and 20 kPa ground uniformly distributed load, as shown in Figure 3(d).
Step 5: carry out analysis and calculation. e solution type is set as SRM calculation of slope stability. e solution type is set as the SRM calculation model of slope stability. Passivate the grid distributed in the excavated soil stratum and rock stratum. Activate the grid of the unexcavated soil stratum and rock stratum. At the same time, activate the self-weight of rock and soil mass, boundary constraint, and uniformly distributed load.
Step 6: run the calculation, and get the results. Get the foundation pit stability FOS and the corresponding distribution diagram of potential fracture surface, as shown in Figure 3(e).

Analysis Model and Calculation
Parameters. e deep foundation pit in binary strata of upper soil and lower rock is that the strata within their excavation depth are composed of soil and rock from top to bottom, and the difference of the main mechanical parameters such as cohesion and elastic modulus between the two strata is almost thousands of times. For the convenience of description, the part of foundation pit vertical sidewall in the soil stratum is called foundation pit vertical soil sidewall, and its height is called the vertical soil sidewall height (Hs). Correspondingly, the part of the foundation pit vertical sidewall in the rock stratum is called the foundation pit vertical rock sidewall, and its height is called the vertical rock sidewall height (Hr), as shown in Figure 4.
According to the statistical analysis of indoor test data of rock and soil mass at the site of deep foundation pit project of Ningxia Road Station of Qingdao metro, combined with the latest research results, we perform the stability analysis of vertical sidewall of deep foundation pit in upper soil and lower rock binary stratum, and the values of physical and mechanical parameters of rock and soil mass are shown in Table 1.

Calculation Results and Analysis.
e thickness of upper soil stratum for deep foundation pit in binary strata of upper soil and lower rock is taken as 4 types, which are 5 m, 10 m, 15 m, and 20 m in turn. e foundation pit excavation depth of each stratum type is taken as 5 working conditions, which    Figure 5, and the calculation results of FOS are shown in Table 2 and Figure 6. e following conclusions can be drawn from Figures 5 and 6: (1) the potential fracture surfaces of deep foundation pit in binary strata of upper soil and lower rock are located within the upper soil stratum excavation depth. e potential fracture surface penetrates from the top of foundation pit to the interface between soil stratum and rock stratum, which is approximately in the circular arc. e failure mechanism of foundation pit is basically consistent with that of the homogeneous soil stratum slope. (2) When the foundation pit is excavated in the upper soil stratum, FOS decreases with the increase of excavation depth; when the excavation depth completely enters the lower rock stratum, FOS is approximately unchanged. (3) e stability is mainly controlled by the excavation height of upper soil stratum and is less affected by the excavation height of lower rock stratum. As the traditional index to measure the stability of deep foundation pit, excavation depth is not suitable for deep foundation pit in binary strata of upper soil and lower rock. It has important theoretical value and practical significance to study vertical soil sidewall height and vertical rock sidewall height as the independent evaluation indexes of deep foundation pit in binary strata of upper soil and lower rock.

Evaluation Criteria.
FOS is an important index to measure the stability of deep foundation pit, which has been widely used in geotechnical engineering [32]. Due to the complexity of foundation pit itself, the uncertainty of rock and soil characteristics, the limitation of human cognitive level, and other factors, FOS with certain reserve is generally used for stability evaluation of deep foundation pit. According to the national standard of the People's Republic of China "Technical code for building slope engineering" (GB 50330-2013), the slope is divided into two types: temporary slope and permanent slope. According to the stability coefficient, it is divided into 4 states: stable, basically stable, basically unstable, and unstable (as shown in Table 3). e slope stability safety factor (F ST ) is taken as shown in Table 4.
In this paper, the deep foundation pit vertical sidewall is considered as the conservative situation of Class I permanent slope, and FOS � 1.35 is taken as the foundation pit slope self-stability criterion. at is, when FOS of foundation pit vertical soil sidewall (or rock sidewall) is greater than or equal to 1.35, it is the foundation pit vertical soil sidewall (or rock sidewall) to meet the self-stability requirements. On the contrary, when FOS is less than 1.35, it does not meet the self-stability requirements. In this paper, the critical height when the foundation pit vertical soil wall meets self-stable state is called self-stable critical height of vertical soil wall (Hs 0 ); similarly, the critical height when the foundation pit vertical rock wall meets the self-stable state is called the selfstable critical height of vertical rock wall (Hr 0 ).

Study on the Self-Stabilizing Height of Vertical Soil
Sidewall.
e thickness of upper soil stratum is taken as 11 types, which are 5 m, 6 m, 7 m, 8 m, 9 m, 10 m, 11 m, 12 m, 13 m, 14 m, and 15 m in turn. e excavation depth of the foundation pit is the same as the thickness of the upper soil stratum, and the calculation parameters and calculation process are the same as those in Section 3.1. e calculation results of FOS under different Hs are shown in Table 5 and Figure 7. e following conclusions can be drawn from Table 5 and Figure 7: (1) FOS of foundation pit vertical soil sidewall decreases with the increase of soil wall excavation height. According to the criterion of F ST �1.35, Hs 0 is 6.92 m. (2) According to the relationship between Hs and Hs 0 , the stable state of the vertical soil wall can be quickly determined: when Hs ≤ Hs 0 , soil wall excavation meets the self-stability requirements. On the contrary, when Hs > Hs 0 , soil wall excavation cannot meet the requirements of self-stability.

Computational Assumptions.
It can be seen from Section 3 that it is impossible to directly obtain the potential fracture surface and its corresponding FOS of the foundation pit vertical rock sidewall. erefore, the improved calculation model is adopted. Firstly, the action of upper soil          Table 7 and Figure 9. e following conclusions can be drawn from Figure 9: Hr 0 is large as a whole, in the range of 100∼125 m, and Hr 0 decreases approximately linearly with the increase of Hs. e mathematical fitting equation between Hr 0 and Hs is shown as follows:

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Hr 0 � 123.012 − 1.1528Hs(R − Sqare 0.99499). (2) According to the relationship between Hr and Hr 0 , the stable state of the vertical rock wall can be quickly determined: (1) When Hr ≤ Hr 0 , the rock sidewall excavation of deep foundation pit can meet the requirements of selfstability (2) when Hr > Hr 0 , the rock sidewall excavation of deep foundation pit cannot meet the requirements of selfstability

Confirmatory
Analysis. e confirmatory analysis model of deep foundation pit in binary strata of upper soil and lower rock still converts the action of upper soil stratum into equivalent uniform load and applies the load directly to the lower rock stratum. At the same time, it is assumed that the sliding body is a rigid body when the foundation pit rock wall is damaged, and the sliding surface is a plane. us, the analysis model of vertical rock wall stability is constructed, as shown in Figure 10.
It is assumed that the foundation pit sliding body is ABC, the length of the sliding surface AC is s, and the included angle between the sliding surface and the horizontal plane is α. e sliding weight is c. e cohesion is c and the internal friction angle is φ. e sum of the ground load and the equivalent uniformly distributed load of the upper soil stratum is q.
For ease of description, the sliding body self-weight and the overlying load are combined into force G′. e normal component of the force on the sliding surface is F n . e tangential component is F T .
When the sliding body slides, the tangential component is F T equal to shear strength of sliding body, as shown in the following equation: According to the mechanical equilibrium relationship, equations (4) and (5) can be obtained.

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where G ′ and s are, respectively, as shown in (6) and (7).
Substituting equations (3), (6), and (7) into (4) and (5), the critical depth H cr can be obtained when the deep foundation pit vertical rock wall is in limit equilibrium state, as shown in In order to obtain the most dangerous sliding surface critical height h cr0 of the deep foundation pit vertical rock wall, let dh cr /dα � 0, and (9) can be obtained  10 Advances in Civil Engineering By introducing (9) into equation (8), the following equation can be obtained: When the upper soil stratum thickness is 0 m, 5 m, 10 m, 15 m, and 20 m, H cr0 can be obtained by SRM, and theoretical calculations are adopted, respectively, as shown in Table 8 and Figure 11.
It can be seen from Table 8 and Figure 11 that, compared with the theoretical calculation, the calculation results of the h cr0 obtained by SRM have the same change trend. e calculation results of SRM are slightly larger overall, but there are few differences, all in the range of 5.2%∼7.4%, which verifies the reliability of the calculation results for SRM.

Self-Stable Spatial Distribution Characteristics and Discussion
If we take F ST �1.35 as the critical point, the deep foundation pit vertical sidewall in binary strata of upper soil and lower rock is divided into two types of spatial distribution areas: self-stable spatial distribution area and non-self-stable spatial distribution area, which are called E area and D area, respectively, in this paper. According to the stratum distribution type, it can be further divided into the self-stable height spatial distribution area of vertical soil sidewall and the non-self-stable height spatial distribution area of vertical soil sidewall (called E 1 area and D 1 area, respectively), and

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the self-stable height spatial distribution area of vertical rock sidewall and the non-self-stable height spatial distribution area of vertical rock sidewall (called E 2 area and D 2 area, respectively), as shown in Figure 12.
In the actual project, due to the limited excavation depth, the deep foundation pit generally will not enter the D 2 area. When the thickness of the over soil stratum is less than or equal to Hs 0 , the D 1 area disappears. at is, the foundation pit directly enters E 2 area from E 1 area, and the foundation pit is in a stable state as a whole. When D 1 area exists, it shall be key protected during the excavation of foundation pit. e significance of dividing the spatial distribution characteristics of self-stable height is that the unique spatial distribution characteristics of deep foundation pit self-stable area in the binary strata of upper soil and lower rock are clarified, which provides a theoretical basis for determining its reasonable support measures.

Typical Project
Ningxia Road Station of Qingdao Metro Line 3 is located in the south of the intersection of Nanjing Road and Ningxia road, Shibei District, Qingdao, and in the prosperous urban area along the Nanjing road from south to north. e surrounding environment of the station is complex, with an urban overpass in the north, a demolished residential community in the East, and 6-storey business building in the West. Station mileage from start to end is K9 + 362.229∼K9 + 516.979. e total length of the station main foundation pit is 154.75 m, and the excavation depth is 18.5∼20.6 m. e excavation width of the foundation pit standard section is 20.60 m, and that of the hanging section outside the equipment room with K9 + 473.279∼K9 + 516.979 is 22.60 m, as shown in Figure 13.
Overall, the project site is high in the north and low in the south, with the maximum elevation difference of 5.26 m. e geomorphic type is Piedmont erosion accumulation sloping fields. e strata distribution types from the surface top to bottom are Quaternary soil stratum (Q 4 ), late Yanshanian intrusive granite (c 5 3 ), and lamprophyre stratum (x 5 3 ) in turn. Lamprophyre is vein interspersed in granite, and cataclastic rocks are seen in contact zones of different lithology. e bedrock can be divided into strongly weathered stratum, moderately weathered stratum, and slightly (non)weathered stratum according to the weathering degree. According to the statistical analysis of the test data of undisturbed soil physical property test, rock and soil compression test, and rapid shear test, the physical and mechanical parameters of each layer of the project site are shown in Table 9.
It can be seen from Table 9 that the difference of main strength and deformation parameters such as cohesion and elastic modulus between Quaternary soil stratum and moderately weathered and slightly weathered rock stratum is thousands of times. e original rock structure of the strongly weathered zone has been damaged, and the rock core is in the state of half rock and half soil or breccia. Before disturbance, it is relatively dense and has high bearing capacity. After disturbance, the strength decreases rapidly, softens, and disintegrates, and the self-stability is poor, but its engineering properties are still slightly better than that of  the Quaternary soil stratum as a whole. In order to simplify the analysis, the Quaternary soil stratum and strongly weathered rock stratum are collectively referred to as soft soil stratum. e moderately weathered rock stratum and slightly (non)weathered rock stratum are collectively referred to as hard rock stratum. us, the binary strata of upper soil and lower rock are constructed [33]. A total of 17 geological exploration holes are arranged in the project site, including 6 control holes and 11 general holes. e controlled drilling hole enters about 10 m below the foundation pit bottom. If there is medium∼slightly weathered rock stratum below the foundation pit bottom, it shall be drilled 3∼5 m. e general drilling hole enters about 6 m below the foundation pit bottom. If there is medium-∼slightly weathered rock stratum below the foundation pit bottom, it shall be drilled 3∼5 m. e borehole located at the fault fracture zone shall open the upper and lower walls so as to reveal the basic situation of the fault. e statistical analysis results of geological survey hole survey data are shown in Table 10.
It can be seen from Foundation pit retaining structure adopts φ800 mm@ 1200 mm reinforced concrete bored pile, and the soil between piles is protected by C20 net shotcrete with the thickness of 20 cm. e first internal support adopts φ690 mm@16 mm supported steel pipe, and its lower part is supported by prestressed anchor cable. e pile bottom of the retaining pile is driven into the moderately weathered rock stratum with the depth of 2.0 m. e rock shoulder with the width of 1.0 m is reserved at the pile bottom, and the prestressed anchor cable is set at the pile foot to ensure that the stability of the pile meets the requirements. In order to protect the reserved rock shoulder, φ168 mm@1200 mm steel pipe piles are set on the foundation pit rock wall. e steel pipe pile is embedded 1.0 m below the foundation pit bottom, and M30 cement mortar is poured into the pipe. e typical supporting structure section of deep foundation pit in binary strata of upper soil and lower rock of Ningxia road station of Qingdao Metro is shown in Figure 14.
According to the statistical analysis of the field measured data of 11 surface settlement monitoring points (No. DC12∼dc18, DC24∼dc27, and dc36), 6 pile top vertical displacement monitoring points (No. QC06∼QC11), 6 pile top horizontal displacement monitoring points (No. QW06∼QW11), and 2 pile horizontal displacement monitoring points (No. CX02, CX04) are arranged by the thirdparty monitoring unit around the station foundation pit. e maximum surface settlement around the foundation pit is 19.25 mm, the minimum value is 4.16 mm, and the average value is 12.83 mm. e maximum vertical displacement of pile top is 8.72 mm, the minimum is 1.10 mm, and the average is 3.47 mm. e maximum horizontal displacement of pile top is 5.72 mm, the minimum is 0.24 mm, and the average is 2.27 mm. e maximum value of pile body is 18.63 mm, the minimum value is 11.25 mm, and the average value is 14.78 mm, as shown in Table 11. e layout of monitoring points is shown in Figure 15. Typical time history curves of monitoring data are shown in Figure 16.   It can be seen from Table 11 that the ground settlement around the foundation pit and the deformation of retaining pile support structure caused by the foundation pit excavation of Ningxia Road Station of Qingdao metro are within the allowable range. It shows that the stability of the foundation pit is good, and the rationality of the conclusion of the foundation pit vertical sidewall self-stable height is verified.

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Data Availability e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.

Authors' Contributions
Ziguang Zhang is in charge of the paper and completed the construction of thesis framework system and thesis writing. Jiesheng Zhang and Tao Xu completed the collection, sorting, and analysis of relevant project case data in the paper. Yihang Li and Guangyong Cao assisted in completing the related work of numerical calculation in the paper. YiKang Xu completed the related work of the language check and editable picture design in the paper.