Method for evaluating stability of sheet pile embedded foundation considering unsaturated effect

Abstract

The application discloses a kind of plate pile embedded stability evaluation method of foundation pit considering unsaturated effect.Model test and numerical simulation results show that the failure sliding surface of foundation pit is the combination of curve and straight line, and the combination is not yet applied to the research of unsaturated foundation pit stability at present.Based on the upper limit principle of limit analysis, a kind of horizontal piece half analytical analysis method is proposed, the external power done by unsaturated soil gravity is calculated using this method, and based on the maximum energy consumption principle, the explicit semi-analytical solution of the moment of the lowest way of internal support point by active and passive earth pressure is obtained, and then the stability safety factor of plate pile embedded foundation pit is obtained.The semi-analytical analysis method constructed by the application has the advantages of analytical method and numerical method, effectively combines the unsaturated soil strength theory with limit analysis method, can reasonably explain the strengthening mechanism of suction effect, and has certain practical guiding significance for guiding the design and excavation of foundation pit under complex conditions.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for evaluating the stability of a geotechnical retaining structure, in particular to a method for constructing a semi-analytical analysis model for evaluating the stability of a sheet pile embedded foundation pit in unsaturated soil, and belongs to the field of engineering slope stability evaluation and reinforcement, as well as disaster prevention and mitigation. BACKGROUND

[0002] A foundation pit is an important component of a building and a structure. With the acceleration of urbanization, urban land resources are increasingly scarce, and the demand for building space is rapidly increasing. Foundation pit engineering is also facing new challenges and developing in the direction of being deeper, larger and more comprehensive. Foundation pit engineering is the foundation of a building, and plays a decisive role in ensuring the stability and safety of the building, as well as the safety of people's lives and property. Therefore, in the design and construction of a foundation pit, a number of analyses and calculations need to be performed on the foundation pit engineering, among which, the stability calculation of the foundation pit is particularly important.

[0003] The stability calculation of a foundation pit retaining structure needs to calculate the embedded depth of the retaining structure, the anti-heave stability of the foundation pit bottom and the overall stability of the foundation pit slope, etc. Different forms of foundation pit retaining structures and different calculation contents result in differences in the calculation methods. In addition, the stability calculation of foundation pit engineering under different geological conditions is also different.

[0004] In the current Technical Specification for Building Foundation Pit Support (JGJ120-2012), the stability safety factor of an internal support type foundation pit retaining structure is calculated using the classical Rankine earth pressure theory. The classical Rankine earth pressure assumes that the angle between the sliding surface and the vertical plane is π / 4±φ' / 2 (φ' is the internal friction angle of the soil). This straight-line type sliding surface is significantly different from the nonlinear sliding surface obtained from model tests and numerical simulations, which inevitably leads to unreasonable analysis results. Moreover, the specification does not consider the influence of the foundation pit width on the stability of the foundation pit. In addition, after dewatering, the soil around the foundation pit is in a state of obvious unsaturation. The conventional stability analysis of the foundation pit often assumes that it is in a saturated state, ignoring the strengthening effect of the soil suction on the stability, which inevitably underestimates the stability of the foundation pit.

[0005] So far, there have been relatively few studies on the stability of unsaturated foundation pits reinforced by sheet piles using the limit analysis method. This is mainly because the limit analysis method needs to assume a static or velocity field, making it difficult to solve the time and space variability of the suction and to construct the energy balance equation of the foundation pit to seek upper and lower limit solutions. The applicant has conducted a series of studies in this regard and proposed a semi-analytical method that can effectively and reasonably consider the influence of matrix suction on the stability of unsaturated foundation pits. SUMMARY

[0006] The application aims to provide a semi-analytical analysis model construction method for unsaturated foundation pit stability with sheet pile reinforcement, which is simple in calculation principle and reliable in calculation result.

[0007] The application discloses a sheet pile embedded foundation pit stability evaluation method considering unsaturated effect.

[0008] S1, assuming that the water surface is horizontally distributed, the soil is divided into saturated and unsaturated zones; the sliding surface intersects the pit bottom and the ground through the pile end, the outside of the foundation pit is an active soil pressure zone, and the inside of the foundation pit is a passive soil pressure zone; the active soil pressure zone is marked as ABCE, the active zone ABCE is divided into soil blocks ABB' and BCB', and the soil block of the passive soil pressure zone is marked as CDD'; a straight line sliding surface is used to simulate the sliding surface of the soil block ABB', and a logarithmic spiral sliding surface is used to simulate the sliding surfaces of the soil blocks BCB' and CDD' respectively;

[0009] S2, calculating the stability safety factor FOS of the sheet pile embedded foundation pit, and evaluating the stability of the sheet pile embedded unsaturated foundation pit.

[0010] The stability safety factor FOS of the sheet pile embedded foundation pit can be expressed as follows:

[0011]

[0012] In the formula, M a is a sliding moment generated by the active soil pressure of the soil outside the foundation pit on the sheet pile, and the size is the moment of the active soil pressure on the lowermost support point; M p is an anti-sliding moment generated by the passive soil pressure of the soil inside the foundation pit on the sheet pile, and the size is the moment of the passive soil pressure on the lowermost support point.

[0013] In the formula, M a is:

[0014]

[0015] In the formula, W is the work done by the soil block ABB', is the work done by the soil block BCB', is the energy dissipation of the apparent cohesion of the soil along the straight line AB, is the energy dissipation of the apparent cohesion of the soil along the logarithmic spiral line BC, and omega is an angular velocity.

[0016] and The calculation method of the total power of the soil body gravity is as follows: the soil block ABB'E and the soil block BCB' are discretized respectively to obtain corresponding soil layer units, the unit weight of each soil layer unit is represented by the value at the centroid thereof, the power of the gravity of the soil layer unit can be represented by the product of the unit gravity and the velocity of the gravity direction at the centroid thereof, the unit gravity is the product of the trapezoidal area and the corresponding unit weight, and the total power of the gravity of the soil body is obtained by accumulating the power of the gravity of all the soil layer units and

[0017] and The calculation method of the total power of the soil body gravity is as follows: the soil block ABB'E and the soil block BCB' are discretized respectively to obtain corresponding soil layer units, the unit weight of each soil layer unit is represented by the value at the centroid thereof, the power of the gravity of the soil layer unit can be represented by the product of the unit gravity and the velocity of the gravity direction at the centroid thereof, the unit gravity is the product of the trapezoidal area and the corresponding unit weight, and the total power of the gravity of the soil body is obtained by accumulating the power of the gravity of all the soil layer units and

[0018] wherein the anti-sliding moment M p :

[0019]

[0020] In the formula, is the power of the soil block CDD', is the apparent cohesion of the soil along the logarithmic spiral line CD;

[0021] The calculation method of the total power of the soil body gravity is as follows: the soil block ABB'E and the soil block BCB' are discretized respectively to obtain corresponding soil layer units, the unit weight of each soil layer unit is represented by the value at the centroid thereof, the power of the gravity of the soil layer unit can be represented by the product of the unit gravity and the velocity of the gravity direction at the centroid thereof, the unit gravity is the product of the trapezoidal area and the corresponding unit weight, and the total power of the gravity of the soil body is obtained by accumulating the power of the gravity of all the soil layer units

[0022] The calculation method of the total power of the soil body gravity is as follows: the soil block ABB'E and the soil block BCB' are discretized respectively to obtain corresponding soil layer units, the unit weight of each soil layer unit is represented by the value at the centroid thereof, the power of the gravity of the soil layer unit can be represented by the product of the unit gravity and the velocity of the gravity direction at the centroid thereof, the unit gravity is the product of the trapezoidal area and the corresponding unit weight, and the total power of the gravity of the soil body is obtained by accumulating the power of the gravity of all the soil layer units

[0023] Further, in S2, the soil is discretized, and the soil block ABB'E is discretized into n horizontal soil layer units along the height direction, each soil layer unit is a trapezoid, and the unit thickness is

[0024] For soil blocks BCB' and CDD', the logarithmic spiral slip surface is divided into n segments with equal angle β / n and θ / n p Each segment of slip surface corresponds to an angle of β / n and θ / n respectively, and the soil mass is divided into n horizontal soil layer units along the horizontal direction, and each soil layer unit is approximately regarded as a trapezoid. p / n, the soil mass is divided into n horizontal soil layer units along the horizontal direction, and each soil layer unit is approximately regarded as a trapezoid.

[0025] In the technical scheme, in order to effectively evaluate the stability of the unsaturated foundation pit reinforced by the sheet pile, a horizontal piece half-analytical analysis method is provided based on the upper limit principle of limit analysis, the external work done by the gravity of the unsaturated soil is calculated by using the method, and based on the maximum energy consumption principle, the explicit half-analytical solution of the moment of the point force of the main and passive earth pressure on the lowest support is obtained, and then the stability safety factor of the sheet pile embedded foundation pit is obtained. The half-analytical analysis method constructed by the application has the advantages of analytical method and numerical method, effectively combines the unsaturated soil strength theory and the limit analysis method, can reasonably explain the strengthening mechanism of the suction effect, and has certain practical guiding significance for guiding the sheet pile embedding problem under complex conditions.

[0026] Further, in S2, And The specific calculation method is:

[0027] For the soil block ABB'E, it is divided into n horizontal soil layer units along the height direction, each soil layer unit is a trapezoid, and the thickness is The unit weight of the soil layer unit centroid is γ i (z i ), and z i is the vertical distance from the soil layer unit centroid to the phreatic surface, which can be expressed as:

[0028] z i =z0+H2+H-(i-0.5)hi=i...n

[0029] In the formula, H is the foundation pit depth, H1 is the vertical distance from the lowest support point to the pit bottom, and H2 is the sheet pile embedding depth.

[0030] The area of the soil layer unit can be expressed as:

[0031] S i =0.5h(l i-1 +l i )

[0032] In the formula, l i and l i-1 are the upper and lower surface areas of the soil layer unit, the longitudinal width of the soil layer unit is 1, and l i can be expressed as:

[0033]

[0034] The polar radius of the soil layer unit centroid to the moment point O i and angle θ i are respectively:

[0035]

[0036] The total power of the soil body gravity work is obtained by accumulating the power of all soil layer unit soil body gravity work:

[0037]

[0038] For the soil mass BCB', the sinking of the soil body outside the lower section of the sheet pile drives the sinking of the soil body outside the upper section of the sheet pile, forming an angle with the horizontal, denoted as β; the slip surface is discretized into n sections according to the angle β, and the angle corresponding to each section of the slip surface is Δθ=β / n, and the soil body is discretized into n horizontal soil layer units along the horizontal direction, and each soil layer unit is approximately regarded as a trapezoid, and the unit weight of the soil layer unit centroid is γ j (z j ), z j is the vertical distance from the soil layer unit centroid to the phreatic surface, which can be expressed as:

[0039] z j =z0+H2+H1-(r j+0.5 cos(n+0.5-j)Δθ)j=1...n

[0040] In the formula: z0 is the vertical distance from the phreatic surface to the pile end;

[0041] The area of the soil layer unit can be expressed as:

[0042] S i =0.5(l j +l j+1 ){r j+1 cos(n-j)Δθ-r j cos(n+1-j)Δθ}

[0043] In the formula: l j and l j+1 are the upper and lower surface areas of the soil layer unit, and the longitudinal width of the soil layer unit is taken as 1, and l j can be expressed as:

[0044] l j =r j sin(n+1-j)Δθ

[0045] r j =(H1+H2)e -(n+1-j)Δθtanφ′

[0046] The polar radius of the elemental sliding surface to the point of moment O j and the angle θ j are respectively:

[0047]

[0048] The total power dissipated by the soil gravity force is obtained by summing the power dissipated by each soil element:

[0049]

[0050] Further, in S2, the specific calculation method of and is:

[0051] The energy dissipation rate caused by the apparent cohesion of the soil is consumed along the straight line AB and the logarithmic spiral line BC. The energy dissipation on the microelement sliding surface can be expressed as the product of the length of the microelement sliding surface and the corresponding apparent cohesion and tangential velocity component. Integrating over the entire sliding surface, the total energy dissipation rate caused by the apparent cohesion of the soil can be obtained. For the straight line AB, the apparent cohesion on the microelement sliding surface is c(z1), and z1 is the vertical distance of the microelement to the water table, which can be expressed as:

[0052] z1 = z0 + H2 + H1 - (H1 + H2)e -βtanφ′ (sinα - tanθcosα)

[0053] The length of the microelement sliding surface can be expressed as:

[0054]

[0055] The polar radius of the elemental sliding surface to the point of moment O c can be expressed as:

[0056]

[0057] The total energy dissipation rate caused by the apparent cohesion on the straight line AB is:

[0058]

[0059] For the logarithmic spiral line BC, the apparent cohesion on the microelement sliding surface is c(z2), and z2 is the vertical distance of the microelement to the water table, which can be expressed as:

[0060] z2 = z0 + H1 + H2 - r(θ)cosθ

[0061] The length of the microelement sliding surface can be expressed as:

[0062] ds = (H1 + H2)e -θtanφ′ dθ / cosφ'

[0063] The total energy dissipation rate caused by the apparent cohesion on the logarithmic spiral BC is:

[0064]

[0065] Further, The specific calculation method is:

[0066] For the soil block CDD', the angle of the passive zone logarithmic spiral slip surface is denoted as θ p ; the slip surface is discretized into n segments according to the angle θ p , and each segment of the slip surface corresponds to an angle Δθ = θ p / n, and the soil body is discretized into n horizontal soil layer units in the horizontal direction, and each soil layer unit is approximately regarded as a trapezoid, and the unit weight at the centroid of the soil layer unit is γ k (z k ), and z k is the vertical distance from the centroid of the soil layer unit to the phreatic surface, which can be expressed as:

[0067] z k = z0+H2+H1-(r k+0.5 cos(n+0.5-k)Δθ)k=1...n

[0068] The area of the soil layer unit can be expressed as:

[0069] S k =0.5(l k +l k+1 ){r k+1 cos(n-k)Δθ-r k cos(n+1-k)Δθ}

[0070] In the formula, l k and l k+1 are the upper and lower surface areas of the soil layer unit, the longitudinal width of the soil layer unit is taken as 1, and l k can be expressed as:

[0071] l k =r k sin(n+1-k)Δθ

[0072] r k =(H1+H2)e (n+1-k)Δθtanφ ′

[0073] The polar radius ρ k and the angle θ k from the centroid of the soil layer unit to the moment point O are respectively:

[0074]

[0075] The total work done by the gravity of the soil mass is obtained by summing the work done by the gravity of each soil layer unit:

[0076]

[0077] Further, in S2, the Fredlund-Xing model is used to describe the hydraulic and mechanical properties of the soil, and a mathematical expression of the matric suction of the fill is obtained based on the steady-state seepage assumption, and then the distributions of the soil bulk density and the apparent cohesion are obtained. The specific calculation method of the distributions of the soil bulk density and the apparent cohesion is as follows:

[0078] The apparent cohesion of the soil mass is consumed along the logarithmic spiral CD, and the energy dissipation on the micro sliding surface can be represented by the product of the length of the micro sliding surface and the corresponding apparent cohesion and tangential velocity component. The total energy dissipation rate caused by the apparent cohesion of the soil is obtained by integrating the entire sliding surface. The apparent cohesion of the micro sliding surface is c(z3), and z3 is the vertical distance of the micro element to the water table, which can be represented as:

[0079] z3 = z0 + H1 + H2 - r(θ)cosθ

[0080] The length of the micro sliding surface can be represented as:

[0081] ds = (H1 + H2)e θtanφ′ dθ / cosφ′

[0082] The total energy dissipation rate caused by the apparent cohesion on the logarithmic spiral CD is:

[0083]

[0084] Further, in S2, the Fredlund-Xing model is used to describe the hydraulic and mechanical properties of the soil, and a mathematical expression of the matric suction of the fill is obtained based on the steady-state seepage assumption, and then the distributions of the soil bulk density and the apparent cohesion are obtained.

[0085] Further, the specific calculation method of the distributions of the soil bulk density and the apparent cohesion is as follows:

[0086] The volume water content of the soil can be represented as:

[0087]

[0088] In the formula, ψ is the matric suction, ψ r is the matric suction corresponding to the residual water content state, a f is the matric suction corresponding to the inflection point of the soil water characteristic curve, which can be measured by a graphical method, m f and n f are model fitting parameters.

[0089] The expression of the matric suction distribution based on the steady-state seepage assumption is:

[0090]

[0091] In the formula: q / k s is vertical specific discharge, γ w is water unit weight, α can be approximately the inverse of the intake value, z is the vertical distance from a point in the soil to the phreatic surface, and z0 is the vertical distance from the phreatic surface to the pile end;

[0092] The unit weight of the unsaturated soil can be obtained according to the dry unit weight γ d , that is

[0093] γ′=γ d +θ w γ w

[0094] The apparent cohesion of the unsaturated soil can be expressed as:

[0095]

[0096] In the formula: θ r and θ s are the residual and saturated soil volume water contents, respectively; the saturated soil volume water content can be obtained according to the saturated unit weight γ sat and the dry unit weight, that is θ s =(γ sat -γ d ) / γ sat .

[0097] Further, S3 is further included, and the maximum value of the safety factor is calculated by a variable step loop algorithm, and a critical sliding surface corresponding to the maximum value is obtained.

[0098] Further, in S3, the variable step loop algorithm is realized by using the MATHEMATICA numerical analysis software to calculate the maximum value of the safety factor.

[0099] Supplementary explanation:

[0100] 1. The sliding surface simulation plate pile embedded unsaturated foundation potential sliding surface is combined by a straight line and a logarithmic spiral line, the sliding surface intersects the pit bottom and the ground through the pile end, the inside of the foundation pit is a passive earth pressure zone, the sliding surface is a logarithmic spiral line, the outside of the foundation pit is an active earth pressure zone, and the sliding surface is in the form of a logarithmic spiral line and a straight line; for other forms of sliding surfaces, including three-dimensional sliding surfaces, the semi-analytical analysis method proposed in the application is still applicable, and the calculation principles are the same, and only specific calculation expressions need to be derived.

[0101] 2. The mathematical model for predicting and fitting the soil water characteristic curve of the soil around the foundation pit is more, and can be used in the method, by using these models, the soil volume water content represented by the matrix suction can be obtained, and then the unit weight and the apparent cohesion of the soil can be obtained.

[0102] 3、The matrix suction distribution can be solved according to the Richard equation, and the analytical expression of the matrix suction distribution can be obtained under the steady-state (such as evaporation) and transient (such as rainfall) seepage conditions, the matrix suction distribution under the steady-state seepage condition is only a function of the spatial position and does not change with time; the matrix suction distribution under the transient seepage condition changes with the spatial position and time; the matrix suction distribution under the steady-state and transient seepage conditions can be solved by the method.

[0103] 4、Under the one-dimensional seepage condition, the matrix suction in the soil only changes along the depth direction, and the horizontal direction is a constant; under the two-dimensional seepage condition, the matrix suction in the soil changes along the depth direction and the horizontal direction; the method can be used to solve the stability of the foundation pit under the one-dimensional seepage condition, and the stability of the foundation pit under the two-dimensional seepage condition.

[0104] 5、There are various foundation pit support methods, in addition to the sheet pile support, the soil pressure and stability problems of the supporting structures such as the underground continuous wall and the anti-slide pile can be solved by the method.

[0105] 6、The soil body needs to be discretized for the calculation of the gravity work, under the one-dimensional seepage condition, the unit weight and cohesion of the soil layer unit are constants, but under the two-dimensional condition, the unit weight and cohesion of the same soil layer unit are different.

[0106] 7、The unit weight of the soil layer unit is regarded as a constant, the gravity work of the soil layer unit is calculated, and the calculation accuracy increases with the increase of the number of soil body division layers, that is, the more the number of soil body division layers, the closer the calculation result is to the analytical solution; in addition, the assumption is more reasonable for the gentle slope and weak nonlinearity problem, and the calculation accuracy is higher, and the calculation accuracy is slightly weak for the steep slope and strong nonlinearity problem, but it can still meet the engineering practical application.

[0107] 8、In addition to the static problem, the foundation pit stability problem under the action of dynamic problems (such as earthquake action, traffic load, etc.) can also be solved by the method, and the energy balance equation of the active and passive zones needs to be adjusted to introduce the power term under the action of dynamic load.

[0108] 9、There are various methods to describe the ground motion, in addition to the pseudo-dynamic assumption, the pseudo-static method and the time history analysis method can also be used, and the two methods are also applicable to the method, when the pseudo-static method is used, the establishment of the energy balance equation is relatively simple; when the time history analysis is used, it is relatively complex.

[0109] 10、Based on the pseudo-dynamic assumption, the dynamic characteristics of seismic waves are described by sinusoidal waves, and the horizontal and vertical seismic accelerations can be expressed as sinusoidal functions of time and soil depth. The shear wave velocity and compression wave velocity in soil can be estimated by empirical formula according to the shear modulus, density and Poisson's ratio of soil. For unsaturated soil, the unit weight is nonlinearly distributed along the depth, so the shear wave velocity and compression wave velocity nonlinearly increase along the soil depth.

[0110] 11、For two-dimensional problems, the unsaturated soil is assumed to be rigid and not to change in volume, and the power dissipation rate caused by the apparent cohesion only occurs on the velocity discontinuity surface; but for three-dimensional problems, the power dissipation rate caused by the apparent cohesion not only occurs on the velocity discontinuity surface, but also occurs in the volume thereof, but the method of the present application can still be used for solving.

[0111] 12、The method is more suitable for single-stage regular ground horizontal foundation pits, and for part of the slope excavation or multi-stage multi-platform foundation pits with more than two slope angles and working platforms, the method of the present application is also applicable, but needs to be improved.

[0112] 13、The present application assumes that the phreatic surface is located below the pile end, but for the stability problems of foundation pits under the conditions of rising groundwater level, exceeding the pile end and being affected by pore water pressure, the method proposed by the present application still has certain applicability, but needs to be further modified to adapt to new working conditions.

[0113] 14、For narrow foundation pits, the logarithmic spiral of the passive zone is limited by the retaining structure and can only partially expand, and the stability problem thereof can also be analyzed by using the method; at this time, the reaction force of the retaining structure acting on the soil body of the passive zone needs to be considered, and the specific value thereof can be derived by the balance equation of the finite soil body width to calculate.

[0114] 15、In addition to the stability checking of sheet pile embedded foundation pits, the anti-heave stability checking of foundation pits can also be analyzed by using the method, and the soil body is also discretized, the unit weight of the soil layer unit is regarded as a constant value, the power done by the gravity of the soil layer unit and the dissipation rate of the apparent cohesion are calculated, and then the energy balance equation is established to obtain the anti-heave stability safety factor.

[0115] 16、The expression of the stability safety factor of the foundation pit is obtained based on the energy balance equation, and the optimization method based on the random search principle is used, in the process of searching for the safety factor, the initial and ending polar angles corresponding to the sliding soil body are constant values, the safety factor is related to the division number of the soil body, the number of layers selected when the error between the semi-analytical safety factor and the analytical solution is less than one thousandth is taken as the basis for analyzing the division of the number of layers of the soil body.

[0116] 17、The plate pile embedded stability evaluation method considering unsaturated effect provided by the application has the advantages of analytical analysis method and numerical analysis method, effectively combines unsaturated soil strength theory and limit analysis method, can reasonably explain the action mechanism of suction effect in the stability problem of the plate pile embedded foundation pit, and has certain academic value and practical guiding significance for guiding the foundation pit design and reinforcement under complex conditions.

[0117] Beneficial effects: Compared with the prior art, the application has the following remarkable advantages:

[0118] 1、The analysis method disclosed by the application can effectively evaluate the stability of the plate pile embedded foundation pit, reveal the influence mechanism of the suction effect on the stability of the supporting structure, the analysis result is more reasonable, more truly reflects the actual situation, and more accurately judges the safety reserve of the supporting structure, and can save materials for secondary buildings and structures.

[0119] 2、The method disclosed by the application can effectively deal with the non-linear problem of rock and soil materials, and can evaluate the stability problem under two seepage conditions according to the analytical expression of the matrix suction distribution under the two seepage conditions and in combination with the method.

[0120] 3、The analysis method disclosed by the application can effectively reveal the stability problem of the unsaturated foundation pit, and the related research work is less, and has higher academic value and theoretical significance.

[0121] 4、The application is based on the energy balance equation, and adopts a random search method to optimize the design of the foundation pit stability problem, has the advantages of simple calculation principle, high operability, high calculation efficiency and high calculation accuracy, and the comparative analysis result shows that the semi-analytical calculation result obtained by the method has high consistency with the theoretical analysis result. BRIEF DESCRIPTION OF DRAWINGS

[0122] Figure 1 It is a schematic view of the plate pile embedded unsaturated foundation pit of the application;

[0123] Figure 2 It is a calculation sketch of the soil gravity work level piece method of the application;

[0124] Figure 3 It is a calculation sketch of the apparent cohesion dissipation rate of the application;

[0125] Figure 4 It is a change of the foundation pit safety factor with cohesion under different seepage conditions of the application;

[0126] Figure 5 It is a change of the foundation pit safety factor with friction angle under different seepage conditions of the application. DETAILED DESCRIPTION

[0127] The analysis method in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative analysis are within the protection scope of the present application.

[0128] In an embodiment, a method for evaluating the stability of a sheet pile embedded foundation considering the unsaturated effect is provided, a straight line and a logarithmic spiral line are combined to simulate the potential sliding surface of the unsaturated foundation, and the stability of the unsaturated foundation is evaluated, including the following steps:

[0129] S1: soil body division: the water table is assumed to be horizontally distributed, and the soil body is divided into a saturated zone and an unsaturated zone; the sliding surface intersects the pit bottom and the ground through the pile end, the outside of the foundation pit is an active earth pressure zone, and the inside of the foundation pit is a passive earth pressure zone; the active earth pressure zone is denoted as active zone ABCE, which is divided into soil block ABB' and soil block BCB'; the soil block in the passive earth pressure zone is denoted as soil block CDD'; the sliding surface of soil block ABB' is simulated by a straight line, and the sliding surfaces of soil block BCB' and soil block CDD' are simulated by logarithmic spiral lines;

[0130] S2: calculating the stability safety factor FOS of the sheet pile embedded foundation, which is used for the stability evaluation of the unsaturated foundation; the stability safety factor FOS of the sheet pile embedded foundation can be expressed as the ratio of the sliding moment M p and the sliding moment M a ; the sliding moment M a is generated by the active earth pressure of the soil body outside the foundation pit on the sheet pile, and the size is the moment of the active earth pressure on the lowest support point, that is, the earth pressure of active zone ABCE; the sliding moment M p is generated by the passive earth pressure of the soil body inside the foundation pit on the retaining structure, and the size is the moment of the passive earth pressure on the lowest support point, that is, the earth pressure of passive zone CDD';

[0131] The stability safety factor FOS of the sheet pile embedded foundation can be expressed as:

[0132]

[0133] In the formula, M a is the sliding moment, which is generated by the active earth pressure of the soil body outside the foundation pit on the sheet pile, and the size is the moment of the active earth pressure on the lowest support point; M p is the sliding moment, which is generated by the passive earth pressure of the soil body inside the foundation pit on the sheet pile, and the size is the moment of the passive earth pressure on the lowest support point.

[0134] In an embodiment, in the S1 soil body division, the sliding surface form of the combination of straight line and logarithmic spiral is adopted to analyze the embedded depth stability of the unsaturated foundation pit sheet pile, the foundation pit depth is H, the vertical distance from the lowest support point to the pit bottom is H1, the sheet pile embedded depth is H2, after the foundation pit dewatering is stable, the phreatic surface is horizontally distributed, the vertical distance to the pile end is z0, the soil body is divided into saturated area and unsaturated area, the inside and outside of the foundation pit are passive area and active area, θ p is the angle of the logarithmic spiral sliding surface of the passive area;

[0135] Under the action of the inner and outer earth pressure, the sheet pile rotates along the lowest support point to the inside of the foundation pit, the angular velocity is ω, which drives the peripheral soil body of the lower section of the sheet pile to move, forming a logarithmic spiral sliding surface with the lowest support point O as the center and passing through the lowest end of the sheet pile; the inside soil body of the lower section of the sheet pile is uplifted, the outside soil body is subsided, the upper section of the outside of the sheet pile is an inclined sliding surface with the horizontal angle being β (β = π / 4 + φ' / 2), and the lower section of the outside of the sheet pile is a logarithmic spiral; the continuity of the soil body movement must make the straight line and the logarithmic spiral sliding surface continuous and smooth;

[0136] A horizontal piece half analytic analysis method is proposed, the soil body is discretized, and the active area ABCE is divided into soil block ABB'E and soil block BCB'; for the soil block ABB'E, it is discretized into n horizontal soil layer units along the height direction, each soil layer unit is a trapezoid, for the soil block BCB', it is discretized into n soil layer units according to the angle β, and each soil layer unit is approximately regarded as a trapezoid; similarly, the soil block CDD' is discretized into n soil layer units according to the angle θ p , and each soil layer unit is also approximately regarded as a trapezoid.

[0137] In an embodiment, in the S2 calculation of the sheet pile embedded foundation pit stability safety factor FOS, the sheet pile embedded foundation pit stability safety factor FOS can be expressed as the ratio of the anti-sliding moment M p to the sliding moment M a ; the sliding moment M a is generated by the active earth pressure of the soil body outside the foundation pit on the sheet pile, and the size is the moment of the active earth pressure on the lowest support point, that is, the earth pressure of the active area ABCE; the anti-sliding moment M p is generated by the passive earth pressure of the soil body inside the foundation pit on the retaining structure, and the size is the moment of the passive earth pressure on the lowest support point, that is, the earth pressure of the active area CDD'.

[0138] S2 specifically includes the following steps:

[0139] The hydraulic and mechanical parameters of S201 unsaturated soil were determined by using the Fredlund-Xing model to describe the hydraulic and mechanical properties of the soil. Based on the steady-state seepage assumption, the mathematical analytical expression of the suction of the fill matrix can be obtained, and then the distribution of soil weight and apparent cohesion can be obtained.

[0140] S202 Calculates the sliding torque M a The external forces acting on the soil include the reaction forces σ and τ from the sheet piles, and the soil's weight G. The normal stress σ is distributed horizontally to the right, the shear stress τ is distributed vertically upward along EC, and the weight G is uniformly distributed on the soil. At the instant of foundation pit failure, the work done by the normal stress σ is W. σ The shear stress τ passes through the moment point O, and the work done is W. τ =0; The work done by gravity on the soil is calculated by zone, representing the work done by gravity in zone ABB'E. Work done by gravity in the BCB' region The sum of the apparent cohesion of the soil, c cap Consumption along the straight line AB and the logarithmic spiral BC are respectively and

[0141] S203 calculates the power exerted by soil gravity in the active zone. The unit weight of each soil element is represented by the value at its centroid. The power exerted by soil element gravity can be expressed as the product of the element's weight and the velocity in the direction of gravity at its centroid. The element's weight is the product of the trapezoidal area and its corresponding unit weight. The total power exerted by soil gravity is obtained by summing the power exerted by soil gravity in all soil elements. and

[0142] S204 calculates the power dissipation rate caused by apparent cohesion in the active zone, assuming the soil is a rigid body and its internal energy dissipation is negligible. The apparent cohesion of the soil, c... cap The energy dissipation on the sliding surface can be expressed as the product of the length of the infinitesimal sliding surface and its corresponding apparent cohesion and tangential velocity components. By integrating along the entire sliding surface, the total energy dissipation rate caused by the apparent cohesion of the soil can be obtained.

[0143] At the instant S205 soil fails, according to the energy balance equation, the work done by the external force equals the power consumed. The sliding torque M can then be obtained. a ;

[0144] S206 Calculation of anti-slip moment M p The forces acting on the soil in the passive zone include the reaction forces of the retaining structure on the soil, including the normal stress σ and the downward shear stress τ, as well as the weight of the soil G; at the instant of foundation pit failure, the work done by the normal stress σ is W. σ The shear stress τ passes through the moment point O, and the work done is W.τ = 0; the soil gravity work The soil apparent cohesion c cap Logarithmic spiral CD consumption

[0145] S207, the passive zone soil gravity work, the unit weight of each soil layer unit is represented by its centroid value, the soil layer unit gravity work can be represented as the product of the trapezoidal area and its corresponding unit weight, and the gravity direction velocity at the centroid, the total gravity work of the soil is obtained by accumulating the gravity work of all soil layer units

[0146] S208, the passive zone soil apparent cohesion power dissipation rate is calculated, the soil apparent cohesion c cap Along the logarithmic spiral CD consumption, the energy dissipation on the sliding surface can be represented as the product of the length of the micro sliding surface and its corresponding apparent cohesion and tangential velocity component, and the total energy dissipation rate caused by the soil apparent cohesion can be obtained by integrating the entire sliding surface;

[0147] S209, at the moment when the soil fails, according to the energy balance equation, i.e. the external force work is equal to the consumed power The anti-dynamic moment M p ;

[0148] S210, the safety factor of the sheet pile embedded foundation pit stability is calculated, based on the upper bound method of limit analysis and the straight-line-logarithmic spiral sliding surface, the safety factor of the sheet pile embedded foundation pit stability can be represented as FOS = M p / M a .

[0149] In an embodiment, S3 is further included, a variable step size loop algorithm calculation code is developed based on the random search principle to search for the maximum value of the safety factor and give the corresponding critical sliding surface by means of the MATHEMATICA numerical analysis software. Specifically, a variable step size loop algorithm calculation code is developed based on the random search principle to search for the maximum value of the safety factor and give the corresponding critical sliding surface by means of the MATHEMATICA numerical analysis software.

[0150] In an embodiment, a sheet pile embedded foundation pit stability evaluation method considering unsaturated effect is provided, and the specific implementation is described in Figures 2-3 , the foundation pit depth is H, the vertical distance from the lowest support point to the pit bottom is H1, the sheet pile embedded depth is H2, after the foundation pit is dewatered, the phreatic surface is assumed to be horizontally distributed, the soil is divided into saturated and unsaturated zones, the vertical distance from the phreatic surface to the pile end is z0, the inside and outside of the foundation pit are the passive zone and the active zone, θ p is the angle of the logarithmic spiral sliding surface in the passive zone.

[0151] Under the action of inner and outer earth pressure, the sheet pile rotates along the lowermost support point to the inside of the foundation pit, with angular velocity ω, driving the peripheral soil mass of the lower section of the sheet pile to move, forming a logarithmic spiral sliding surface with the lowermost support point O as the center and passing through the lowermost end of the sheet pile; the inner soil mass of the lower section of the sheet pile is uplifted, and the outer soil mass is subsided, and the upper section of the outer side of the sheet pile is an inclined sliding surface with a horizontal angle of β (β = π / 4 + φ' / 2), and the lower section of the outer side is a logarithmic spiral sliding surface; the continuity of soil mass movement must make the straight line and the logarithmic spiral sliding surface continuous and smooth.

[0152] The soil strength is described by using the generalized Mohr-Coulomb failure criterion, and the strength indexes are effective internal cohesion c' and effective internal friction angle φ', and the influence of suction on the stability of the sheet pile can be realized by regarding it as an apparent cohesion. The hydraulic and mechanical properties of the fill are described by using the Fredlund-Xing model, and for the unsaturated foundation pit, the mathematical analytical expression of the matric suction of the soil can be obtained based on the steady-state seepage assumption, and then the distribution of the unit weight and apparent cohesion of the soil is obtained.

[0153] The embodiment of the present application is based on the upper limit principle of limit analysis, and proposes a horizontal slice half analytic analysis method, Figure 1 It is a schematic diagram of the sheet pile embedded unsaturated foundation pit of the present application, Figure 2 It is a calculation diagram of the horizontal slice half method for soil gravity work, Figure 3 It is a calculation diagram of the apparent cohesion dissipation rate.

[0154] The specific calculation steps are as follows:

[0155] S1 soil division: the water table is assumed to be horizontally distributed, and the soil is divided into saturated and unsaturated zones; the sliding surface intersects the pit bottom and the ground through the pile end, the outside of the foundation pit is the active earth pressure zone, and the inside of the foundation pit is the passive earth pressure zone; the soil is discretely processed, and the active zone ABCE is divided into soil blocks ABB'E and soil block BCB'; the passive zone soil block is recorded as soil block CDD'; for soil block ABB'E, it is discretely divided into n horizontal soil layer units along the height direction, and each soil layer unit is a trapezoid; for soil block BCB', it is discretely divided into n soil layer units according to angle β, and each soil layer unit is approximately regarded as a trapezoid; similarly, soil block CDD' is discretely divided into n soil layer units according to angle θp, and each soil layer unit is also approximately regarded as a trapezoid; specifically,

[0156] S2 calculate the stability safety factor FOS of the sheet pile embedded foundation pit, which is used for the stability evaluation of the unsaturated foundation pit sheet pile embedded foundation pit;

[0157]

[0158] S201 Determination of hydraulic and mechanical parameters of unsaturated soil, the Fredlund-Xing model is used to describe the hydraulic and mechanical properties of soil, and the mathematical expression of matric suction of fill soil is obtained based on the steady seepage assumption, and then the distribution of soil bulk density and apparent cohesion is obtained;

[0159] Specifically, the Fredlund-Xing model is used to describe the hydraulic and mechanical properties of soil, and based on the model, the soil volume moisture content can be expressed as:

[0160]

[0161] In the formula: ψ is the matric suction, ψ r is the matric suction corresponding to the residual moisture state, a f is the matric suction corresponding to the inflection point of the soil water characteristic curve, which can be measured by a f and n f are model fitting parameters.

[0162] Based on the steady seepage assumption, the matric suction distribution expression is obtained as:

[0163]

[0164] In the formula: q / k s is the vertical specific flow, γ w is the water unit weight, α can be approximately the reciprocal of the air entry value, z is the vertical distance from a point in the soil to the phreatic surface, and z0 is the vertical distance from the phreatic surface to the pile end.

[0165] The unit weight of unsaturated soil can be obtained according to the dry bulk density of the soil γ d , that is

[0166] γ′=γ d +θ w γ w

[0167] The apparent cohesion of unsaturated soil can be expressed as:

[0168]

[0169] In the formula: θ r and θ s are the residual and saturated soil volume moisture contents, respectively. The saturated soil volume moisture content can be obtained according to the saturated unit weight γ sat and the dry bulk density, that is θ s =(γ sat -γ d ) / γ sat .

[0170] S202 Calculate the sliding torque M a, the external force acting on the soil body has the reaction force of the sheet pile σ and τ, and the gravity of the soil body G. The normal stress σ is horizontally distributed to the right, the shear stress τ is vertically distributed upwards along EC, and the gravity G is uniformly distributed on the soil body. The foundation pit is destroyed instantaneously, and the normal stress σ does work W σ , the shear stress τ passes through the moment point O, and does work W τ = 0; the gravity of the soil body does work in the ABB'E area and the BCB' area , and the apparent cohesion c of the soil body is consumed along the straight line AB and the logarithmic spiral line BC, respectively cap and and

[0171] The sliding torque M a of the active area can be obtained according to the energy balance equation of the active area, that is:

[0172]

[0173] In the formula: W σ is the work done by the normal stress, W τ is the work done by the shear stress, the shear stress passes through the moment point O, W τ = 0, is the work done by the gravity in the ABB'E area, is the work done by the gravity in the BCB' area, is the energy dissipation of the apparent cohesion along the straight line AB, is the energy dissipation of the apparent cohesion along the logarithmic spiral line BC.

[0174] S203 calculates the work done by the gravity of the active area. The unit weight of each soil layer unit at its centroid is represented by its value, and the work done by the gravity of the soil layer unit can be represented as the product of the unit weight at the centroid and the gravity direction velocity. The unit weight of the soil layer unit is the product of the trapezoidal area and its corresponding unit weight. The total work done by the gravity of the soil body is obtained by accumulating the work done by the gravity of all soil layer units and

[0175] The work done by the gravity of the active area is calculated. For the soil block ABB'E, the unit weight at the centroid of the soil layer unit is γ i (z i ), and z i is the vertical distance from the centroid of the soil layer unit to the phreatic surface, which can be represented as:

[0176] z i = z0+H2+H-(i-0.5)h i=1...n

[0177] The area of the soil layer unit can be represented as:

[0178] Si = 0.5h(l i-1 + l i )

[0179] where: l i and l i-1 are the upper and lower surface areas of the soil element, the longitudinal width of the soil element is taken as 1, l i can be expressed as:

[0180]

[0181] The polar radius ρ i and the angle θ i of the centroid of the soil element to the point of moment O are respectively:

[0182]

[0183] The total power done by the gravity of the soil body can be obtained by accumulating the power done by the gravity of all soil elements:

[0184]

[0185] For the soil mass BCB', the slip surface is discretized into n segments with equal angles β, and the angle of each segment of the slip surface is Δθ = β / n. The soil body is discretized into n horizontal soil elements along the horizontal direction, and each soil element is approximately regarded as a trapezoid. The unit weight of the centroid of the soil element is γ j (z j ), and the vertical distance z j from the centroid of the soil element to the phreatic surface can be expressed as:

[0186] z j = z0+ H2+ H1- (r j+0.5 cos(n+0.5-j)Δθ)j = 1...n

[0187] The area of the soil element can be expressed as:

[0188] S i = 0.5(l j + l j+1 ){r j+1 cos(n-j)Δθ-r j cos(n+1-j)Δθ}

[0189] where: l j and l j+1 are the upper and lower surface areas of the soil element, the longitudinal width of the soil element is taken as 1, l j can be expressed as:

[0190] l j = r j sin(n+1-j)Δθ

[0191] r j = (H1+H2)e -(n+1-j)Δθtanφ ′

[0192] The polar radius ρ of the centroid of the soil element to the point O of the moment j and the angle θ are respectively: j

[0193]

[0194] The total power done by the gravity of the soil mass is obtained by summing the power done by the gravity of all the soil elements:

[0195]

[0196] S204 calculates the power dissipation rate caused by the apparent cohesion of the soil at the active zone. Assuming that the soil is rigid, the energy dissipation within the volume of the soil can be ignored. The apparent cohesion of the soil is consumed along the straight line AB and the logarithmic spiral line BC. The energy dissipation on the sliding surface can be expressed as the product of the length of the micro sliding surface and the corresponding apparent cohesion and the tangential velocity component. The total energy dissipation rate caused by the apparent cohesion is obtained by integrating the product over the entire sliding surface.

[0197] The power dissipation rate of the apparent cohesion is generated along the straight line AB and the logarithmic spiral line BC. The energy dissipation on the sliding surface can be expressed as the product of the length of the micro sliding surface and the corresponding apparent cohesion and the tangential velocity component. The total energy dissipation rate caused by the apparent cohesion is obtained by integrating the product over the entire sliding surface. For the straight line AB, the apparent cohesion of the micro sliding surface is c(z1), and z1 is the vertical distance of the micro element to the water table, which can be expressed as:

[0198] z1 = z0 + H2 + H1 - (H1+H2)e -βtanφ′ (sinα-tanθcosα)

[0199] The length of the micro sliding surface can be expressed as:

[0200]

[0201] The polar radius ρ of the micro sliding surface to the point O of the moment c can be expressed as:

[0202]

[0203] The total energy dissipation rate caused by the apparent cohesion on the straight line AB is:

[0204]

[0205] ​For logarithmic spiral BC, the apparent cohesion on the infinitesimal sliding surface is c(z2), z2 is the vertical distance from the infinitesimal to the water surface, which can be expressed as:

[0206] z2 = z0 + H1 + H2 - r(θ)cosθ

[0207] The length of the infinitesimal sliding surface can be expressed as:

[0208] ds = (H1 + H2)e -θtanφ′ dθ / cosφ'

[0209] The total energy dissipation rate caused by the apparent cohesion on the logarithmic spiral BC is:

[0210]

[0211] S205 At the moment of soil failure, according to the energy balance equation, i.e. the work done by external force is equal to the power consumed The sliding torque M can be obtained a ; according to the active zone energy balance equation, the sliding torque M can be expressed as: a

[0212]

[0213] S206 Calculate the anti-sliding torque M p , the force acting on the passive zone soil has the reaction force of the retaining structure on the soil, including normal stress σ and downward shear stress τ, and the gravity of the soil G; at the moment of foundation failure, the normal stress σ does work W σ , the shear stress τ passes through the torque point O, and does work W τ = 0; the gravity of the soil does work The apparent cohesion of the soil c cap consumed by the logarithmic spiral CD

[0214] The anti-sliding torque M p can be obtained according to the passive zone energy balance equation, i.e.:

[0215]

[0216] In the formula: W σ is the work done by normal stress, W τ is the work done by shear stress, the shear stress passes through the torque point O, W τ = 0; is the work done by the gravity of the soil, is the apparent cohesion consumed along the logarithmic spiral CD.

[0217] ​S207 Calculate the work done by the passive zone soil gravity, the unit weight of each soil layer unit is represented by its centroid value, the work done by the gravity of the soil layer unit can be represented as the product of the unit gravity and the velocity of the gravity direction at its centroid, the unit gravity is the product of the trapezoidal area and its corresponding unit weight, accumulate the work done by the gravity of all soil layer units to obtain the total work done by the gravity of the soil body

[0218] For passive zone CDD', the slip surface is divided into n segments according to angle θ p , each segment of the slip surface corresponds to an angle of Δθ = θ p / n, and the soil body is discretized into n horizontal soil layer units along the horizontal direction, each soil layer unit is approximately regarded as a trapezoid, and the unit weight at the centroid of the soil layer unit is γ k (z k ), z k is the vertical distance from the centroid of the soil layer unit to the phreatic surface, which can be represented as:

[0219] z k = z0+H2+H1-(r k+0.5 cos(n+0.5-k)Δθ)k=1...n

[0220] The area of the soil layer unit can be represented as:

[0221] S k =0.5(l k +l k+1 ){r k+1 cos(n-k)Δθ-r k cos(n+1-k)Δθ}

[0222] In the formula: l k and l k+1 are the upper and lower surface areas of the soil layer unit, the longitudinal width of the soil layer unit is taken as 1, and l k can be represented as:

[0223] l k =r k sin(n+1-k)Δθ

[0224] r k =(H1+H2)e (n+1-k)Δθtanφ′

[0225] The polar radius ρ k and the angle θ k from the centroid of the soil layer unit to the moment point O are respectively:

[0226]

[0227] The total work done by the gravity of the soil body can be obtained by accumulating the work done by the gravity of all soil layer units.

[0228]

[0229] S208 The power dissipation rate caused by the apparent cohesion of the passive zone is calculated, and the apparent cohesion of the soil body is consumed along the logarithmic spiral CD. The energy dissipation on the sliding surface can be represented as the product of the length of the microelement sliding surface and its corresponding apparent cohesion and tangential velocity component. Integrating over the entire sliding surface, the total energy dissipation rate caused by the apparent cohesion of the soil can be obtained.

[0230] The apparent cohesion is consumed along the logarithmic spiral CD. The energy dissipation on the sliding surface can be represented as the product of the length of the microelement sliding surface and its corresponding apparent cohesion and tangential velocity component. Integrating over the entire sliding surface, the total energy dissipation rate caused by the apparent cohesion of the soil can be obtained. The apparent cohesion of the microelement sliding surface is c(z3), and z3 is the vertical distance from the microelement to the water table, which can be represented as:

[0231] z3 = z0 + H1 + H2 - r(θ)cosθ

[0232] The length of the microelement sliding surface can be represented as:

[0233] ds = (H1 + H2)e θtanφ′ dθ / cosφ′

[0234] The total energy dissipation rate caused by the apparent cohesion on the logarithmic spiral CD is:

[0235]

[0236] S209 At the moment when the soil body fails, the energy balance equation is used, i.e. the work done by external forces is equal to the dissipated power The anti-dynamic moment M p can be obtained.

[0237] According to the energy balance equation of the passive zone, the anti-sliding moment M p can be represented as:

[0238]

[0239] S210 Based on the upper bound method of limit analysis and the straight line-logarithmic spiral sliding surface, the stability safety factor of the sheet pile embedded foundation pit can be represented as:

[0240] FOS = M p / M a .

[0241] S3 uses the numerical analysis software MATHEMATICA to develop a variable step cycle algorithm to calculate the maximum value of the safety factor of code search, and gives the corresponding critical sliding surface. With the geometric parameters of the sliding soil as the independent variable, the safety factor is calculated and compared with the preset value, and the larger safety factor is stored; the size of the above-mentioned independent variable is changed in turn, each independent variable is changed in turn according to the specified increment size in a single calculation cycle, the new safety factor is calculated and compared with the stored value, and the cycle is repeated until the maximum value is searched, and finally the maximum safety factor and the corresponding sliding soil geometric parameters are output, and the critical sliding surface is obtained.

[0242] Effect comparison

[0243] Figure 4 And Figure 5 The calculation results of the present application are compared with the calculation results of other scholars, and the data are quoted from: Zhang Zhaohui, Analysis of Narrow Foundation Embedment Depth and Anti-heave Stability Based on Energy Method[D]. Lanzhou University of Technology, 2023.

[0244] The relevant parameters are: the excavation depth of the foundation pit H = 10.27m, the width of the foundation pit L = 10.5m, the embedded depth of the sheet pile H2 = 23.4m, the distance from the bottom of the pit to the support point H1 = 4.27m, the saturated unit weight of the soil γ sat = 19.63kN / m 3 , the dry unit weight of the soil γ sat = 17.7kN / m 3 , the assumed cohesion range is 0-50kPa, and the internal friction angle range is 0-20°; the relevant parameters of the typical unsaturated soil are: a f = 100kPa, n f = 2, m f = 1, ψ r = 1000kPa, α = 0.02kPa -1 , θ r = 0.078.

[0245] It can be found that, without considering the suction effect, the calculation results of the present application have high consistency with the theoretical calculation results, verifying the rationality of the calculation method of the present application; when considering the suction effect, the traditional analysis method significantly underestimates the stability of the sheet pile embedded foundation pit, and under the stable infiltration condition, the matric suction in the soil gradually decreases and tends to be saturated, therefore, the safety of the foundation pit gradually decreases with the increase of the infiltration rate, and tends to be the safety factor under the saturated state.

[0246] In summary, the application creatively proposes a sheet pile embedded foundation pit stability evaluation method considering unsaturated effect, combines unsaturated soil strength theory and limit analysis method, creatively proposes a horizontal sheet half analytical analysis method, can reasonably explain the strengthening mechanism of soil suction effect, more truly reflects the safety reserve of the foundation pit, and has certain academic value and reference significance for guiding the design and reinforcement of the foundation pit under complex conditions.

[0247] The above examples are merely illustrative of the present application and are not meant to limit the embodiments of the present application. Other variations and modifications of the above embodiments can be made by those skilled in the art without departing from the scope of the present application. It is also to be understood that not all of the examples herein are mutually exclusive, and that the present application encompasses all such variations and modifications. Obviously, many modifications and changes can be made thereto without departing from the essence of the application. It is therefore desired that such modifications and changes be understood as being within the scope of the application as set forth in the appended claims, without undue experimentation.

Claims

1. A method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects, characterized in that, The potential slip surface of an unsaturated sheet pile-embedded foundation pit is simulated using a combination of linear and logarithmic spiral slip surfaces. The stability of the unsaturated sheet pile-embedded foundation pit is evaluated, including the following steps: The S1 water table is assumed to be horizontally distributed, dividing the soil into saturated and unsaturated zones. The slip surface intersects the pit bottom and ground surface through the pile tip. The outer side of the pit is the active earth pressure zone, and the inner side is the passive earth pressure zone. The active earth pressure zone is denoted as ABCE, which is divided into soil block ABB'E and soil block BCB'. The soil block in the passive earth pressure zone is denoted as CDD'. A straight slip surface is used to simulate the slip surface of soil block ABB'E, and a spiral slip surface is used to simulate the slip surfaces of soil blocks BCB' and CDD' respectively. S2 calculates the safety factor FOS for the stability of sheet pile embedded foundation pits, which is used to evaluate the stability of unsaturated foundation pits with sheet pile embedded foundation pits. The stability safety factor (FOS) of a sheet pile embedded foundation pit can be expressed as: Where: M a The sliding moment is generated by the active earth pressure exerted by the soil outside the foundation pit on the sheet pile, and its magnitude is the moment of the active earth pressure about the lowest support point; M p The anti-sliding moment is generated by the passive earth pressure on the sheet piles from the soil inside the pit, and its magnitude is the moment of the passive earth pressure on the lowest support point. Wherein, sliding torque M a for: In the formula: Power applied to the soil block ABB'E Power applied to the soil block BCB' This represents the energy dissipation of the apparent cohesion of the soil along the straight line AB. The energy consumption of apparent cohesion of soil along the logarithmic spiral BC, where ω is the angular velocity; Among them, the anti-slip moment M p : In the formula: Power applied to the soil block CDD' The apparent cohesion of the soil is consumed along the logarithmic spiral CD.

2. The method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects according to claim 1, characterized in that, In S2, during the discretization of the soil mass, for the soil block ABB'E, it is discretized equally along the height direction into n horizontal soil layer elements. Each soil layer element is trapezoidal, and the element thickness is... For soil blocks BCB' and CDD', the logarithmic spiral slip surface is calculated using angles β and θ. p The sliding surface is equally discretized into n segments, with the angles corresponding to each segment being β / n and θ, respectively. p / n, the soil is discretized into n horizontal soil units along the horizontal direction, and each soil unit is approximately regarded as a trapezoid.

3. The method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects according to claim 1, characterized in that, S2 and The calculation method is as follows: Soil blocks ABB'E and BCB' are discretized to obtain corresponding soil element units. The unit weight of each soil element is represented by the value at its centroid. The power exerted by gravity on a soil element can be expressed as the product of the element's gravity and the velocity in the direction of gravity at its centroid. The element's gravity is the product of the trapezoidal area and its corresponding unit weight. The total power exerted by gravity on all soil elements is obtained by summing these total powers. and and The calculation method is as follows: Assuming the soil is a rigid body, the energy dissipation within its volume can be ignored. The apparent cohesion of the soil is consumed along the straight line AB and the logarithmic spiral BC. The energy dissipation on the sliding surface can be expressed as the product of the length of the infinitesimal sliding surface and its corresponding apparent cohesion and tangential velocity components. Integrating over the entire sliding surface, the total energy dissipation rate caused by the apparent cohesion of the soil can be obtained. and The calculation method is as follows: The soil mass is discretized to obtain several soil layer elements. The unit weight of each soil layer element is represented by the value at its centroid. The power done by the gravity of the soil layer element can be expressed as the product of the element weight and the velocity in the direction of gravity at its centroid. The element weight is the product of the area of ​​the trapezoid and its corresponding unit weight. The total power done by the gravity of the soil is obtained by summing the power done by the gravity of all soil layer elements. The calculation method is as follows: the apparent cohesion of the soil is consumed along the logarithmic spiral CD. The energy dissipation on the sliding surface can be expressed as the product of the length of the infinitesimal sliding surface and its corresponding apparent cohesion and tangential velocity components. Integrating over the entire sliding surface yields the total energy dissipation rate caused by the apparent cohesion of the soil.

4. The method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects according to claim 1, characterized in that, In S2, and The specific calculation method is as follows: For the soil block ABB'E, it is discretized into n horizontal soil elements equally along the height direction. Each soil element is trapezoidal and has a thickness of [missing information]. The unit weight at the centroid of the soil layer unit is γ i (z i ), z i The vertical distance from the centroid of the soil unit to the water table can be expressed as: mm i =z0+H2+H-(i-0.5)hi=1...n In the formula: z0 is the vertical distance from the water level to the pile tip, H2 is the sheet pile embedment depth, and H is the foundation pit depth; The area of ​​a soil layer unit can be expressed as: S i =0.5h(l i-1 +l i ) In the formula: l i and l i-1 Let l be the area of ​​the upper and lower surfaces of the soil layer element, and let l be the longitudinal width of the soil layer element. i It can be represented as: In the formula: φ′ is the internal friction angle of the soil; The polar radius ρ from the centroid of the soil element to the moment point O i and angle θ i They are respectively: By summing up the power exerted by the weight of the soil in all soil units, we can obtain the total power exerted by the weight of the soil. For the soil block BCB', the settlement of the soil on the outer side of the lower section of the sheet pile causes the soil on the outer side of the upper section of the sheet pile to settle, forming an angle β with the horizontal. The slip surface is discretized into n segments with equal angle β, and the angle corresponding to each slip surface segment is Δθ = β / n. The soil is discretized into n horizontal soil layer units along the horizontal direction. Each soil layer unit is approximately considered as a trapezoid, and the unit weight at the centroid of the soil layer unit is γ. j (z j ), z j The vertical distance from the centroid of the soil unit to the water table can be expressed as: z j =z0+H2+H1-(r j+0.5 cos(n+0.5-j)Δθ) j=1...n In the formula: H1 is the vertical distance from the lowest support point to the bottom of the pit; The area of ​​a soil unit can be expressed as: S j =0.5(l j +l j+1 ){r j+1 cos(n-j)Δθ-r j cos(n+1-j)Δθ} In the formula: l j and l j+1 Let l be the area of ​​the upper and lower surfaces of the soil layer element, and let l be the longitudinal width of the soil layer element. j It can be represented as: l j =r j sin(n+1-j)Δθ r j =(H1+H2)e -(n+1-j)Δθtanφ′ The polar radius ρ from the centroid of the soil element to the moment point O j and angle θ j They are respectively: By summing up the power exerted by the weight of the soil in all soil units, we can obtain the total power exerted by the weight of the soil.

5. The method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects according to claim 1, characterized in that, In S2, and The specific calculation method is as follows: The power dissipation rate caused by the apparent cohesion of the soil occurs along the straight line AB and the logarithmic spiral BC. The energy dissipation on the sliding surface can be expressed as the product of the length of the infinitesimal sliding surface and its corresponding apparent cohesion and tangential velocity components. Integrating over the entire sliding surface, the total energy dissipation rate caused by the apparent cohesion of the soil can be obtained. For the straight line AB, the apparent cohesion on the infinitesimal sliding surface is c(z1), where z1 is the vertical distance from the infinitesimal element to the water table, which can be expressed as: z1=z0+H2+H1-(H1+H2)e -βtanφ′ (sinα-tanθcosα) In the formula: z0 is the vertical distance from the water level to the pile tip, H2 is the sheet pile embedment depth, H1 is the vertical distance from the lowest support point to the bottom of the pit, and φ′ is the internal friction angle of the soil. The length of the sliding surface of the infinitesimal element can be expressed as: The extreme radius ρ from the sliding surface of the infinitesimal element to the torque point O c It can be represented as: The total energy dissipation rate caused by apparent cohesion on line AB is: For a logarithmic spiral BC, the apparent cohesion on the sliding surface of the infinitesimal element is c(z2), where z2 is the vertical distance from the infinitesimal element to the water table, which can be expressed as: z2=z0+H1+H2-r(θ)cosθ The length of the sliding surface of the infinitesimal element can be expressed as: ds=(H1+H2)e -θtanφ′ dθ / cosφ′ The total energy dissipation caused by apparent cohesion on the logarithmic spiral BC is:

6. The method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects according to claim 1, characterized in that, In S2, The specific calculation method is as follows: For the soil block CDD', the angle of the passive region's logarithmic spiral slip plane is denoted as θ. p ; Adjust the sliding surface at an angle θ p The sliding surface is equally discretized into n segments, and the angle corresponding to each segment is Δθ = θ. p / n, the soil mass is discretized into n horizontal soil elements along the horizontal direction. Each soil element is approximately considered as a trapezoid, and the unit weight at the centroid of the soil element is γ. k (z k ), z k The vertical distance from the centroid of the soil unit to the water table can be expressed as: z k =z0+H2+H1-(r k+0.5 cos(n+0.5-k)Δθ) k=1...n In the formula: z0 is the vertical distance from the water level to the pile tip, H2 is the sheet pile embedment depth, and H1 is the vertical distance from the lowest support point to the bottom of the pit. The area of ​​a soil unit can be expressed as: S k =0.5(l k +l k+1 ){r k+1 cos(n-k)Δθ-r k cos(n+1-k)Δθ} In the formula: l k and l k+1 Let l be the area of ​​the upper and lower surfaces of the soil layer element, and let l be the longitudinal width of the soil layer element. k It can be represented as: l k =r k sin(n+1-k)Δθ r k =(H1+H2)e (n+1-k)Δθtanφ′ In the formula: φ′ is the internal friction angle of the soil; The polar radius ρ from the centroid of the soil element to the moment point O k and angle θ k They are respectively: By summing up the power exerted by the weight of the soil in all soil units, we can obtain the total power exerted by the weight of the soil.

7. The method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects according to claim 1, characterized in that, In S2, The specific calculation method is as follows The apparent cohesion of the soil is consumed along the logarithmic spiral CD. The energy dissipation on the sliding surface can be expressed as the product of the length of the infinitesimal sliding surface and its corresponding apparent cohesion and tangential velocity components. Integrating over the entire sliding surface yields the total energy dissipation rate caused by the apparent cohesion of the soil. The apparent cohesion on the infinitesimal sliding surface is c(z3), where z3 is the vertical distance from the infinitesimal element to the water table, which can be expressed as: z3=z0+H1+H2-r(θ)cosθ In the formula: z0 is the vertical distance from the water level to the pile tip, H2 is the sheet pile embedment depth, and H1 is the vertical distance from the lowest support point to the bottom of the pit. The length of the sliding surface of the infinitesimal element can be expressed as: ds=(H1+H2)e θtanφ′ dθ / cosφ′ In the formula: φ′ is the internal friction angle of the soil; The total energy dissipation caused by apparent cohesion on the logarithmic spiral CD is: In the formula: θ p This represents the polar angle range of the logarithmic spiral CD.

8. The method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects according to claim 1, characterized in that, In S2, the Fredlund-Xing model is used to describe the hydraulic and mechanical properties of the soil. Based on the steady-state seepage assumption, the mathematical analytical expression of the suction of the fill matrix can be obtained, and then the distribution of soil weight and apparent cohesion can be obtained.

9. The method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects according to claim 7, characterized in that, The specific calculation methods for the distribution of soil weight and apparent cohesion are as follows: The volumetric water content of soil can be expressed as: In the formula: ψ is the matrix suction force, ψ r a represents the matrix suction corresponding to the residual moisture content state. f The matrix suction corresponding to the inflection point of the soil-water characteristic curve can be measured graphically, m. f and n f Parameters for model fitting; Based on the steady-state seepage assumption, the expression for the matrix suction distribution is as follows: Where: q / k s For vertical specific flow rate, γ w For water, α s It can be approximated as the reciprocal of the air intake value, z is the vertical distance from a point in the soil to the water table, and z0 is the vertical distance from the water table to the pile tip. The unit weight of unsaturated soil can be determined based on the dry unit weight γ of the soil. d To obtain, that is γ′=γ d +θ w c w The apparent cohesion of unsaturated soil can be expressed as: In the formula: θ r and θ s These are the residual and saturated soil volumetric water contents, respectively; the saturated soil volumetric water content can be determined based on the saturated unit weight γ. sat The dry weight is obtained, i.e., θ s =(γ) sat -γ d ) / γ sat .

10. The method for evaluating the stability of sheet pile embedded foundation pits considering unsaturation effects according to claim 1, characterized in that, It also includes S3, which calculates the maximum value of the code search safety factor through a variable step-size loop algorithm and obtains its corresponding critical sliding surface.

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