Method for evaluating stability of sheet pile built-in foundation pit by considering unsaturated effect

Abstract

The invention discloses a sheet pile built-in foundation pit stability evaluation method considering an unsaturated effect. Model test and numerical simulation results show that a foundation pit failure slip surface is in a curve and straight line combined form, and the combined form is not applied to the research on the stability of the unsaturated foundation pit at present. Based on the principle of limit analysis and upper limit, the invention provides a horizontal slice halving analytical analysis method, the method is adopted to calculate the external power made by the unsaturated soil gravity, and based on the principle of maximum energy consumption, a display semi-analytical solution of active and passive soil pressure to the moment of a supporting point in the lowermost channel is obtained. And the stability safety coefficient of the sheet pile built-in foundation pit is further obtained. The semi-analytical analysis method constructed by the invention has the advantages of an analytical method and a numerical method, effectively combines the unsaturated soil strength theory with a limit analysis method, can reasonably explain the strengthening mechanism of the suction effect, and has certain practical guiding significance for guiding foundation pit design and excavation under complex conditions.

Description

Technical Field

[0001] The present invention relates to a method for evaluating the stability of geotechnical retaining structures, and particularly to a method for constructing a semi-analytical analysis model for evaluating the stability of sheet pile-embedded foundation pits in unsaturated soils, belonging to the fields of engineering slope stability evaluation and reinforcement, as well as disaster prevention and mitigation. Background Art

[0002] Foundation pits are important components of buildings and structures. With the acceleration of the urbanization process, urban land resources are becoming increasingly scarce, the demand for building space has increased sharply, and foundation pit engineering has also faced new challenges, developing in the direction of 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 buildings, as well as the safety of people's lives and property. Therefore, in the design and construction of foundation pits, multiple analyses and calculations need to be carried out on foundation pit engineering, among which the stability check of the foundation pit is a particularly important link.

[0003] For the stability check of the foundation pit retaining structure, it is necessary to check the embedment depth of the retaining structure, the stability of the foundation pit bottom against heave, and the overall stability of the foundation pit slope, etc. Different forms of foundation pit retaining structures and different check contents lead to differences in the check methods. In addition, the stability checks of foundation pit engineering under different geological conditions are also different.

[0004] In the current "Technical Specification for Building Foundation Pit Support" (JGJ120 - 2012), the stability safety factor of the internal bracing foundation pit retaining structure is calculated using the classical Rankine earth pressure theory. The classical Rankine earth pressure assumes that the angle between the slip surface and the vertical plane is π / 4 ± φ' / 2 (φ' is the internal friction angle of the soil). This linear slip surface has a significant difference from the non-linear slip surface obtained from model tests and numerical simulations, which will inevitably lead to unreasonable analysis results, and the specification does not consider the influence of the foundation pit width on the foundation pit stability. In addition, after the foundation pit is dewatered, the soil around the foundation pit is in an obvious unsaturated state. Conventional foundation pit stability analysis often assumes it to be in a saturated state, ignoring the strengthening effect of soil suction on stability, and inevitably underestimating the stability of the foundation pit.

[0005] So far, there has been relatively little research on the stability of unsaturated foundation pits reinforced with 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 characteristics of the spatio-temporal variability of suction and difficult to construct an energy balance equation for the foundation pit to seek upper and lower bound solutions. The applicant has conducted a series of research in this regard and proposed a semi-analytical method, which can effectively and reasonably consider the influence of matrix suction on the stability of unsaturated foundation pits. Summary of the Invention

[0006] Purpose of the Invention: The purpose of the present invention is to provide a semi - analytical analysis model construction method for the stability of unsaturated foundation pits reinforced by sheet piles, which has a simple calculation principle and reliable calculation results.

[0007] Technical Solution: A method for evaluating the stability of a sheet - pile - embedded foundation pit considering the unsaturated effect. The potential slip surface of the sheet - pile - embedded unsaturated foundation pit is simulated by a combination of a straight line and a logarithmic spiral line to evaluate the stability of the sheet - pile - embedded unsaturated foundation pit, including the following steps:

[0008] S1 Assume that the phreatic surface is horizontally distributed, and divide the soil mass into a saturated zone and an unsaturated zone; the slip surface intersects the bottom and the ground through the pile tip. 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 active earth pressure zone is denoted as ABCE, and the active zone ABCE is divided into soil block ABB'E and soil block BCB'. The soil block in the passive earth pressure zone is denoted as CDD'; among them, a straight - line slip surface is used to simulate the slip surface of soil block ABB'E, and logarithmic spiral line slip surfaces are used to simulate the slip surfaces of soil blocks BCB' and CDD' respectively.

[0009] S2 Calculate the safety factor FOS of the stability of the sheet - pile - embedded foundation pit, which is used to evaluate the stability of the sheet - pile - embedded unsaturated foundation pit.

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

[0011]

[0012] In the formula: M a is the sliding moment, which is generated by the active earth pressure of the soil outside the foundation pit on the sheet pile, and its magnitude is the moment of the active earth pressure about the lowest - level support point; M p is the anti - sliding moment, which is generated by the passive earth pressure of the soil inside the foundation pit on the sheet pile, and its magnitude is the moment of the passive earth pressure about the lowest - level support point.

[0013] Among them, the sliding moment M a is:

[0014]

[0015] In the formula: is the power done by soil block ABB'E, is the power done by soil block BCB', is the energy dissipation of the apparent cohesion of the soil along the straight line AB, the energy consumption of the apparent cohesion of the soil along the logarithmic spiral line BC, ω is the angular velocity;

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

[0017] and The calculation method is as follows: Assume the soil is a rigid body and the energy dissipation within its volume can be ignored. The apparent cohesion of the soil dissipates 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 infinitesimal sliding surface, its corresponding apparent cohesion, and the tangential velocity component. By integrating over the entire sliding surface, the total energy dissipation rate caused by the soil apparent cohesion can be obtained. and

[0018] Among them, the anti - sliding moment M p :

[0019]

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

[0021] The calculation method is as follows: The soil body is discretized to obtain several soil layer units. The unit weight of each soil layer unit is represented by the value at its centroid. The power done by the gravity of the soil layer unit can be expressed as the product of the unit gravity and the velocity component in the gravity direction at its centroid. The unit gravity is the product of the trapezoidal area and its corresponding unit weight. By accumulating the powers done by the gravity of all soil layer units, the total power done by the soil gravity is obtained.

[0022] The calculation method is as follows: The soil apparent cohesion dissipates along the logarithmic spiral line CD. The energy dissipation on the sliding surface can be expressed as the product of the length of the infinitesimal sliding surface, its corresponding apparent cohesion, and the tangential velocity component. By integrating over the entire sliding surface, the total energy dissipation rate caused by the soil apparent cohesion can be obtained.

[0023] Furthermore, in S2, during the discretization of the soil body, for the soil block ABB'E, it is evenly discretized into n horizontal soil layer units along the height direction. Each soil layer unit is trapezoidal, and the unit thickness is

[0024] For the soil blocks BCB' and CDD', the logarithmic spiral slip surface is evenly discretized into n segments by angles β and θ p The angles corresponding to each segment of the slip surface are β / n and θ / n respectively. The soil mass is discretized into n horizontal soil layer units along the horizontal direction, and each soil layer unit is approximately regarded as a trapezoid. p / n, and the longitudinal width of the soil layer unit is taken as 1, l

[0025] In the above technical solution, in order to effectively evaluate the stability of the unsaturated foundation pit reinforced by sheet piles, based on the upper bound principle of limit analysis, a horizontal slice semi-analytical analysis method is proposed. This method is used to calculate the external power done by the gravity of the unsaturated soil, and based on the principle of maximum energy consumption, the explicit semi-analytical solutions of the moments of the active and passive earth pressures on the lowest internal support point are obtained, and then the stability safety factor of the sheet pile embedded foundation pit is obtained. The semi-analytical analysis method constructed by the present invention has the advantages of the analytical method and the numerical method, effectively combines the unsaturated soil strength theory with 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 as follows:

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

[0028] z i = z 0 + H 2 + H - (i - 0.5)h i = 1...n

[0029] In the formula: H is the depth of the foundation pit, H 1 is the vertical distance from the lowest support point to the bottom of the pit, and H 2 is the embedded depth of the sheet pile.

[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 areas of the upper and lower surfaces of the soil layer unit. The longitudinal width of the soil layer unit is taken as 1, li It can be expressed as:

[0033]

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

[0035]

[0036] By accumulating the power done by the gravity of all soil layer units, the total power done by the soil gravity can be obtained:

[0037]

[0038] For the soil block BCB', the subsidence of the soil outside the lower section of the sheet pile drives the subsidence of the soil outside the upper section of the sheet pile, forming an angle β with the horizontal; the slip surface is evenly discretized into n segments at an angle β, and the angle corresponding to each segment of the slip surface is Δθ = β / n. The soil 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 j (z j ), z j is the vertical distance from the centroid of the soil layer unit to the phreatic surface, which can be expressed as:

[0039] z j = z 0 + H 2 + H 1 -(r j+0.5 cos(n + 0.5 - j)Δθ) j = 1...n

[0040] In the formula: z 0 is the vertical distance from the phreatic surface to the pile tip;

[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. 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 = (H 1 + H 2 )e -(n+1-j)Δθtanφ′

[0046] The polar radius ρ from the centroid of the soil layer element to the moment point O j and the angle θ j are respectively:

[0047]

[0048] By accumulating the power done by the gravity of all soil layer elements, the total power done by the soil gravity can be obtained:

[0049]

[0050] Furthermore, in S2, and The specific calculation methods are:

[0051] 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 slip surface can be expressed as the product of the length of the elemental slip surface and its corresponding apparent cohesion and tangential velocity component. Integrating over the entire slip 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 elemental slip surface is c(z 1 ), z 1 is the vertical distance from the element to the phreatic surface and can be expressed as:

[0052] z 1 = z 0 + H 2 + H 1 - (H 1 + H 2 )e -βtanφ′ (sinα - tanθcosα)

[0053] The length of the elemental slip surface can be expressed as:

[0054]

[0055] The polar radius ρ from the elemental slip surface to the moment point 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 BC, the apparent cohesion on the infinitesimal slip surface is c(z 2 ), where z 2 is the vertical distance from the infinitesimal element to the phreatic surface and can be expressed as:

[0060] z 2 = z 0 + H 1 + H 2 - r(θ)cosθ

[0061] The length of the infinitesimal slip surface can be expressed as:

[0062] ds = (H 1 + H 2 )e -θtanφ′ dθ / cosφ′

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

[0064]

[0065] Furthermore, the specific calculation method of

[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 evenly discretized into n segments by the angle θ p , and the corresponding angle of each slip surface segment is Δθ = θ p / n. The soil mass 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 ), where z k is the vertical distance from the centroid of the soil layer unit to the phreatic surface and can be expressed as:

[0067] z k = z 0 + H 2 + H 1 -(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] Where: l k and lk+1 is the area of the upper and lower surfaces of the soil layer unit, and the longitudinal width of the soil layer unit is taken as 1, l k It can be expressed as:

[0071] l k = r k sin(n + 1 - k)Δθ

[0072] r k = (H 1 + H 2 )e (n+1-k)Δθtanφ ′

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

[0074]

[0075] By accumulating the power done by the gravity of all soil layer units, the total power done by the soil gravity can be obtained:

[0076]

[0077] Furthermore, in S2, The specific calculation method of

[0078] The apparent cohesion of the soil surface 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 micro - element 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 soil apparent cohesion can be obtained. The apparent cohesion on the micro - element sliding surface is c(z 3 ), where z 3 is the vertical distance from the micro - element to the phreatic surface and can be expressed as:

[0079] z 3 = z 0 + H 1 + H 2 - r(θ)cosθ

[0080] The length of the micro - element sliding surface can be expressed as:

[0081] ds = (H 1 + H 2 )e θtanφ′ dθ / cosφ′

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

[0083]

[0084] Furthermore, in S2, the Fredlund-Xing model is adopted to describe the hydraulic and mechanical properties of soil. Based on the assumption of steady-state seepage, the mathematical analytical expression of the fill soil matrix suction can be obtained, and then the distributions of soil unit weight and apparent cohesion can be obtained.

[0085] Furthermore, the specific calculation method for the distributions of soil unit weight and apparent cohesion is as follows:

[0086] The volumetric water content of soil can be expressed as:

[0087]

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

[0089] Based on the assumption of steady-state seepage, the matrix suction distribution expression is:

[0090]

[0091] where: q / k s is the vertical specific discharge, γ w is the unit weight of water, α can be approximated as the reciprocal of the air entry value, z is the vertical distance from a point in the soil to the water table, z 0 is the vertical distance from the water table to the pile tip;

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

[0093] γ′ = γ d + θ w γ w

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

[0095]

[0096] where: θ r and θ s are the residual and saturated soil volumetric water contents respectively; the saturated soil volumetric 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, 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 slip surface.

[0098] Further, in S3, the variable step-size loop algorithm is implemented through MATHEMATICA numerical analysis software to calculate the maximum value of the search safety factor.

[0099] Supplementary description:

[0100] 1. The sliding surface composed of a straight line and a logarithmic spiral is used to simulate the potential sliding surface of the sheet pile-embedded unsaturated foundation pit. The sliding surface intersects the bottom and the ground through the pile tip. The inner side of the foundation pit is the passive earth pressure zone, and the sliding surface is a logarithmic spiral. The outer side of the foundation pit is the active earth pressure zone, and the sliding surface is a combination of a logarithmic spiral and a straight line. For other forms of sliding surfaces, including three-dimensional sliding surfaces, etc., the semi-analytical analysis method proposed by the present invention is still applicable, and the calculation principles are the same. Only specific calculation expressions need to be derived.

[0101] 2. There are many mathematical models for predicting and fitting the soil-water characteristic curve of the soil around the foundation pit, and all of them can be used in this method. By using these models, the volumetric water content of the soil expressed by the matric suction can be obtained, and then the distribution of the unit weight and apparent cohesion in the soil can be obtained.

[0102] 3. The matric suction distribution can be solved according to the Richards equation. Assuming steady-state (such as evaporation) and transient (such as rainfall) seepage conditions, the analytical expressions of the matric suction distribution can be obtained. Under steady-state seepage conditions, the matric suction distribution is only a function of the spatial position and does not change with time. Under transient seepage conditions, the matric suction distribution changes with both the spatial position and time. The matric suction distribution under both steady-state and transient seepage conditions can be solved by the method of the present invention.

[0103] 4. Under one-dimensional seepage conditions, the matric suction in the soil only changes along the depth direction, and is a constant value in the horizontal direction. Under two-dimensional seepage conditions, the matric suction in the soil changes along both the depth direction and the horizontal direction simultaneously. The method of the present invention can not only be used to solve the stability of the foundation pit under one-dimensional seepage conditions, but also the stability of the foundation pit under two-dimensional seepage conditions can be solved by this method.

[0104] 5. There are various foundation pit support methods. In addition to sheet pile support, the backfill earth pressure and its stability problems of support structures such as diaphragm walls and anti-slide piles can all be solved by the method of the present invention.

[0105] 6. To calculate the work done by the soil gravity, the soil needs to be discretized. Under one-dimensional seepage conditions, the unit weight and cohesion of the soil layer unit are constant values, but under two-dimensional conditions, the unit weight and cohesion of the same soil layer unit are different.

[0106] 7. Regarding the unit weight of the soil layer unit as a fixed value, calculate the power done by the gravity of the soil layer unit. The calculation accuracy increases with the increase in the number of soil layer divisions. That is to say, the more the number of soil layer divisions, the closer the calculation result is to the analytical solution. In addition, this assumption is more reasonable for gentle slopes and weakly nonlinear problems, with higher calculation accuracy. For steep slopes and strongly nonlinear problems, the calculation accuracy is slightly weaker, but it can still meet the actual engineering applications.

[0107] 8. In addition to static problems, for the stability problems of foundation pits under dynamic problems (such as seismic action, traffic loads, etc.), the method of the present invention can also be used to solve them. It is necessary to adjust the energy balance equations in the active and passive zones and introduce the power term under the action of dynamic loads.

[0108] 9. There are various methods for describing ground motions. In addition to adopting the pseudo-dynamic assumption, the pseudo-static method and the time-history analysis method can be used. These two methods are also applicable to this method. When using the pseudo-static method, the establishment of the energy balance equation is relatively simple; when using the time-history analysis, it is much more complex.

[0109] 10. Based on the pseudo-dynamic assumption, use a sine wave to describe the dynamic characteristics of seismic waves. The horizontal and vertical seismic accelerations can be expressed as sine functions of time and soil layer depth. The shear wave velocity and compression wave velocity in the soil can be estimated using empirical formulas according to the shear modulus, density, and Poisson's ratio of the soil. For unsaturated soil, its unit weight is non-linearly distributed along the depth, so the shear wave velocity and compression wave velocity increase non-linearly along the soil layer depth.

[0110] 11. For two-dimensional problems, assume that the unsaturated soil is rigid and does not undergo volume change. 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 within its volume. However, the method of the present invention can still be used to solve it.

[0111] 12. This method is more suitable for foundation pits with a single-order regular horizontal ground surface. For partially slope-excavated or multi-order multi-platform foundation pits with two or more slope angles and working platforms, the method of the present invention is also applicable, but the method needs to be improved.

[0112] 13. The present invention assumes that the phreatic surface is located below the pile tip. However, for the stability problems of foundation pits in cases where the groundwater level rises above the pile tip and is affected by pore water pressure, etc., the method proposed by the present invention still has a certain applicability, but further modifications are needed to adapt to the new working conditions.

[0113] 14. For narrow foundation pits, the logarithmic spiral in the passive zone is restricted by the retaining structure and can only be partially developed. The stability problem can also be analyzed using this method. In this case, the reaction force of the retaining structure acting on the soil in the passive zone needs to be considered, and its specific value can be derived through the equilibrium equation of the finite soil width for calculation.

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

[0115] 16. Based on the energy balance equation, the expression of the safety factor of the foundation pit stability is obtained. Using the optimization method based on the random search principle, during the process of searching for the safety factor, the initial and end polar angles corresponding to the sliding soil mass are fixed values. The safety factor is related to the number of layers of soil division. The number of layers when the semi-analytical safety factor and the analytical solution error are less than one-thousandth is selected as the basis for analyzing the number of layers of soil division in the parameter analysis.

[0116] 17. The method for evaluating the stability of sheet pile embedment considering the unsaturated effect proposed by the present invention has the advantages of analytical analysis methods and numerical analysis methods, effectively combines the unsaturated soil strength theory and the limit analysis method, can reasonably explain the action mechanism of the suction effect in the stability problem of the foundation pit with sheet pile embedment, and has certain academic value and practical guiding significance for guiding the design and reinforcement of foundation pits under complex conditions.

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

[0118] 1. The analysis method disclosed by the present invention can effectively evaluate the stability of the sheet pile embedded foundation pit, reveal the influence mechanism of the suction effect on the stability of the support structure, the analysis results are more reasonable, more truly reflect the actual situation, and more accurately judge the safety reserve of the support structure. For secondary buildings and structures, etc., it can achieve the purpose of saving materials.

[0119] 2. The method disclosed by the present invention can effectively handle the nonlinear problems of geotechnical materials. For the stability problems under steady-state (such as evaporation) and transient (such as rainfall) seepage conditions, according to the analytical expressions of the matrix suction distribution under the two seepage conditions and combined with the method of the present invention, the stability problems under the two seepage conditions can be evaluated.

[0120] 3. The analysis method disclosed by the present invention can effectively reveal the stability problems of unsaturated foundation pits. There is relatively little research work in related aspects, and it has high academic value and theoretical significance.

[0121] 4. Based on the energy balance equation, the present invention uses a random search method to optimize the design of the foundation pit stability problem, which has the advantages of simple calculation principle, high operability, high calculation efficiency and high calculation accuracy. The comparative analysis results show that the semi-analytical calculation results obtained by this method are highly consistent with the theoretical analysis results. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] Figure 1 It is a schematic diagram of a sheet pile embedded non-saturated foundation pit of the present invention;

[0123] Figure 2 It is a calculation sketch of the method for dividing horizontal slices of the work done by the soil gravity of the present invention;

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

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

[0126] Figure 5 It is the change of the foundation pit safety factor with the friction angle under different seepage conditions of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0127] Next, the analysis method in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative analysis methods belong to the scope of protection of the present invention.

[0128] In one embodiment, a method for evaluating the stability of a sheet pile embedded foundation pit considering the non-saturated effect is provided. A potential slip surface of the sheet pile embedded non-saturated foundation pit is simulated by a combination of a straight line and a logarithmic spiral line, and the stability of the sheet pile embedded foundation pit of the non-saturated foundation pit is evaluated, including the following steps:

[0129] S1 Soil division: Assuming that the phreatic surface is horizontally distributed, the soil body is divided into a saturated zone and a non-saturated zone; the slip surface intersects the bottom and the ground through the pile tip. 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 active earth pressure zone is denoted as the active zone ABCE, and the active zone ABCE is divided into soil block ABB'E and soil block BCB'. The soil block in the passive earth pressure zone is denoted as soil block CDD'; among them, the slip surface of soil block ABB'E is simulated by a straight line slip surface, and the slip surfaces of soil block BCB' and soil block CDD' are respectively simulated by a logarithmic spiral slip surface;

[0130] S2 calculates the safety factor of foundation pit stability FOS for the embedded sheet pile, which is used for the stability evaluation of the embedded sheet pile foundation pit in unsaturated foundation pit; the safety factor of foundation pit stability FOS for the embedded sheet pile can be expressed as the anti-sliding moment M p and the sliding moment M a ratio. The sliding moment M a is generated by the active earth pressure of the soil outside the foundation pit on the sheet pile, and its magnitude is the moment of the active earth pressure on the lowest support point, that is, the earth pressure in the active area ABCE; the anti-sliding moment M p is generated by the passive earth pressure of the soil inside the foundation pit on the retaining structure, and its magnitude is the moment of the passive earth pressure on the lowest support point, that is, the earth pressure in the active area CDD';

[0131] The safety factor of foundation pit stability FOS for the embedded sheet pile 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 outside the foundation pit on the sheet pile, and its magnitude is the moment of the active earth pressure on the lowest support point; M p is the anti-sliding moment, which is generated by the passive earth pressure of the soil inside the foundation pit on the sheet pile, and its magnitude is the moment of the passive earth pressure on the lowest support point.

[0134] In an embodiment, in the S1 soil division, the sliding surface form combined with a straight line and a logarithmic spiral is used to analyze the stability of the embedded depth of the sheet pile in the unsaturated foundation pit. The depth of the foundation pit is H, and the vertical distance from the lowest support point to the bottom of the pit is H 1 , the embedded depth of the sheet pile is H 2 , after the foundation pit dewatering is stable, the phreatic surface is horizontally distributed, and the vertical distance to the pile tip is z 0 , the soil body is divided into a saturated area and an unsaturated area. The inside and outside of the foundation pit are passive areas and active areas, and θ p is the angle of the logarithmic spiral sliding surface in the passive area;

[0135] Under the action of the internal and external earth pressures, the sheet pile rotates inward to the foundation pit along the lowest support point, with an angular velocity of ω, driving the soil around the lower section of the sheet pile to move, forming a logarithmic spiral sliding surface centered on the lowest support point O and passing through the lowest end of the sheet pile; the soil inside the lower section of the sheet pile bulges, and the soil outside sinks. The upper section outside the sheet pile is an inclined sliding surface with an angle of β (β = π / 4 + φ' / 2) with the horizontal, and the lower section outside sliding surface is a logarithmic spiral; the continuity of the soil movement must make the straight line and the logarithmic spiral sliding surface continuous and smooth;

[0136] A horizontal slice semi - analytical analysis method is proposed to discretize the soil mass. The active area ABCE is divided into soil block ABB'E and soil block BCB'. For soil block ABB'E, it is evenly discretized into n horizontal soil layer units along the height direction, and each soil layer unit is trapezoidal. For soil block BCB', it is evenly discretized into n soil layer units at an angle β, and each soil layer unit is approximately regarded as trapezoidal. Similarly, soil block CDD' is evenly discretized into n soil layer units at an angle θ p and each soil layer unit is also approximately regarded as trapezoidal.

[0137] In one embodiment, in S2 for calculating the safety factor FOS of the stability of the sheet - pile - embedded foundation pit, the safety factor FOS of the stability of the sheet - pile - embedded foundation pit 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 outside the foundation pit on the sheet pile, and its magnitude is the moment of the active earth pressure about the lowest support point, that is, the earth pressure in the active area ABCE. The anti - sliding moment M p is generated by the passive earth pressure of the soil inside the foundation pit on the retaining structure, and its magnitude is the moment of the passive earth pressure about the lowest support point, that is, the earth pressure in the active area CDD'.

[0138] S2 specifically includes the following steps:

[0139] S201 Determination of the hydraulic and mechanical parameters of unsaturated soil. The Fredlund - Xing model is used to describe the hydraulic and mechanical properties of the soil. Based on the assumption of steady - state seepage, the mathematical analytical expression of the soil matrix suction of the fill can be obtained, and then the distributions of the soil unit weight and apparent cohesion can be obtained;

[0140] S202 Calculate the sliding moment M a . The external forces acting on the soil mass are the reaction forces σ and τ of the sheet pile, and the soil gravity G. The normal stress σ is distributed horizontally to the right, the shear stress τ is distributed vertically upward along EC, and the gravity G is evenly distributed on the soil mass. 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 W τ = 0; The work done by the soil gravity is calculated by partition, which is the sum of the work done by the gravity in the ABB'E area and the work done by the gravity in the BCB' area . The apparent cohesion c cap of the soil is consumed along the straight line AB and the logarithmic spiral line BC, which are respectively and

[0141] S203 calculates the power done by the gravity of the soil in the active zone. 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 gravity and the velocity component in the gravity direction at its centroid. The element gravity is the product of the trapezoidal area and its corresponding unit weight. Summing up the powers done by the gravities of all soil layer elements, the total power done by the soil gravity is obtained. and

[0142] S204 calculates the power dissipation rate caused by the apparent cohesion of the soil in the active zone. Assuming the soil is a rigid body, the energy dissipation within its volume can be ignored. The apparent cohesion c of the soil cap 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, its corresponding apparent cohesion, and the 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;

[0143] S205 At the moment when the soil fails, according to the energy balance equation, that is, the work done by the external force is equal to the consumed power the sliding moment M can be obtained a ;

[0144] S206 calculates the anti-sliding moment M p , and the forces acting on the soil in the passive zone include the reaction force of the retaining structure on the soil, including the normal stress σ and the downward shear stress τ, as well as the soil gravity 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 does work W τ = 0; the work done by the soil gravity is the apparent cohesion c of the soil cap is consumed along the logarithmic spiral CD

[0145] S207 calculates the power done by the gravity of the soil in the passive zone. 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 gravity and the velocity component in the gravity direction at its centroid. The element gravity is the product of the trapezoidal area and its corresponding unit weight. Summing up the powers done by the gravities of all soil layer elements, the total power done by the soil gravity is obtained.

[0146] S208 calculates the power dissipation rate caused by the apparent cohesion of the soil in the passive zone. The apparent cohesion c of the soil cap 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, its corresponding apparent cohesion, and the 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;

[0147] At the moment when the soil mass fails, according to the energy balance equation, that is, the work done by the external force is equal to the power consumed the anti-dynamic moment M can be obtained p ;

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

[0149] In one embodiment, it further includes S3. With the help of MATHEMATICA numerical analysis software, a variable-step cyclic algorithm calculation code is developed based on the random search principle to search for the maximum value of the safety factor and give its corresponding critical slip surface. Specifically, with the help of MATHEMATICA numerical analysis software, a variable-step cyclic algorithm calculation code is developed to search for the maximum value of the safety factor and give its corresponding critical slip surface

[0150] In one embodiment, a method for evaluating the stability of a sheet pile embedded foundation pit considering the unsaturated effect is provided. For the specific implementation manner, see Figure 2-3 , the depth of the foundation pit is H, the vertical distance from the lowest support point to the bottom of the pit is H 1 , the embedded depth of the sheet pile is H 2 , after the foundation pit dewatering is stable, the phreatic surface is assumed to be horizontally distributed, and the soil mass is divided into a saturated zone and an unsaturated zone. The vertical distance from the phreatic surface to the pile tip is z 0 , the inside and outside of the foundation pit are the passive zone and the active zone, and θ p is the angle of the logarithmic spiral slip surface in the passive zone

[0151] Under the action of the internal and external earth pressures, the sheet pile rotates inward to the foundation pit along the lowest support point with an angular velocity of ω, driving the surrounding soil mass of the lower section of the sheet pile to move, forming a logarithmic spiral slip surface centered on the lowest support point O and passing through the lowest end of the sheet pile; the soil mass inside the lower section of the sheet pile bulges, and the soil mass outside sinks. The upper section outside the sheet pile is an inclined slip surface with an angle of β (β = π / 4 + φ' / 2) with the horizontal, and the lower section outside slip surface is a logarithmic spiral; the continuity of the soil mass movement necessarily makes the straight-line and logarithmic spiral slip surfaces continuous and smooth

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

[0153] Based on the upper bound principle of limit analysis, an embodiment of the present invention proposes a horizontal slice semi-analytical analysis method. Figure 1 It is a schematic diagram of a sheet pile embedded non-saturated foundation pit of the present invention. Figure 2 It is a simplified calculation diagram of the horizontal slice method for the work done by soil gravity. Figure 3 It is a simplified calculation diagram for the calculation of the apparent cohesion dissipation rate.

[0154] The specific calculation steps are as follows:

[0155] S1 Soil division: Assuming that the phreatic surface is horizontally distributed, the soil body is divided into a saturated zone and an unsaturated zone; the slip surface intersects the bottom and the ground through the pile tip, 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 body is discretized, and the active zone ABCE is divided into soil block ABB'E and soil block BCB'; the passive zone soil block is denoted as soil block CDD'; for soil block ABB'E, it is evenly discretized into n horizontal soil layer units along the height direction, and each soil layer unit is trapezoidal. For soil block BCB', it is evenly discretized into n soil layer units according to the angle β, and each soil layer unit is approximately regarded as trapezoidal; similarly, soil block CDD' is evenly discretized into n soil layer units according to the angle θp, and each soil layer unit is also approximately regarded as trapezoidal; specifically,

[0156] S2 Calculate the stability safety factor FOS of the sheet pile embedded foundation pit for the stability evaluation of the non-saturated foundation pit sheet pile embedded foundation pit.

[0157]

[0158] S201 Determination of the hydraulic and mechanical parameters of unsaturated soil. 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 fill matrix suction can be obtained, and then the distribution of soil unit weight and apparent cohesion can be obtained.

[0159] Specifically, the Fredlund-Xing model is used to describe the hydraulic and mechanical properties of the soil. Based on this model, the volumetric water content of the soil can be expressed as:

[0160]

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

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

[0163]

[0164] Where: q / k s is the vertical specific discharge, γ w is the unit weight of water, α can be approximated as the reciprocal of the air entry value, z is the vertical distance from a point in the soil to the water table, z 0 is the vertical distance from the water table to the pile tip.

[0165] The unit weight of unsaturated soil can be obtained from the dry unit weight γ d of the soil, that is

[0166] γ′ = γ d + θ w γ w

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

[0168]

[0169] Where: θ r and θ s are the residual and saturated soil volume water contents respectively. The saturated soil volume water content can be obtained from the saturated unit weight γ sat and the dry unit weight, that is θ s = (γ sat - γ d ) / γ sat .

[0170] S202 calculates the sliding moment M a , the external forces acting on the soil mass are the reaction forces σ and τ of the sheet pile, and the soil weight G. The normal stress σ is distributed horizontally to the right, the shear stress τ is distributed vertically upward along EC, and the gravity G is uniformly distributed on the soil mass. 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 does work W τ = 0; the work done by the soil weight is calculated in sections, which is the sum of the work done by the soil weight in the ABB'E area and the work done by the soil weight in the BCB' area . The apparent cohesion c cap of the soil is consumed along the straight line AB and the logarithmic spiral BC, which are respectively and

[0171] The sliding moment M a in the active area can be obtained from the energy balance equation in the active area, that is:

[0172]

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

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

[0175] Calculating the power done by the gravity of the soil in the active area. For the soil mass ABB'E, the unit weight at the centroid of the soil layer unit is γ i (z i ), z i is the vertical distance from the centroid of the soil layer unit to the phreatic surface and can be expressed as:

[0176] z i = z 0 + H 2 + H - (i - 0.5)h i = 1...n

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

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

[0179] Where: l i and l i-1 are the areas of the upper and lower surfaces of the soil layer unit. The longitudinal width of the soil layer unit is taken as 1. l i can be expressed as:

[0180]

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

[0182]

[0183] Summing up the power done by the gravity of all soil layer units, the total power done by the soil gravity can be obtained:

[0184]

[0185] For the soil mass BCB', the slip surface is evenly discretized into n segments at an angle β, and the angle corresponding to each slip surface segment is Δθ = β / n. 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 j (z j ), z j is the vertical distance from the centroid of the soil layer unit to the phreatic surface and can be expressed as:

[0186] z j = z 0 + H 2 + H 1 -(r j+0.5 cos(n + 0.5 - j)Δθ) j = 1...n

[0187] The area of the soil layer unit 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] In the formula: l j and l j+1 are the areas of the upper and lower surfaces of the soil layer unit. The longitudinal width of the soil layer unit is taken as 1. l j can be expressed as:

[0190] l j = r j sin(n + 1 - j)Δθ

[0191] r j = (H 1 + H 2 )e -(n+1-j)Δθtanφ ′

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

[0193]

[0194] By accumulating the power done by the gravity of all soil layer units, the total power done by the soil body gravity can be obtained:

[0195]

[0196] S204 calculates the power dissipation rate caused by the apparent cohesion of the soil in the active zone. Assuming the soil is a rigid body, the energy dissipation within its volume can be neglected. 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, its corresponding apparent cohesion, and the tangential velocity component. Integrating over the entire sliding surface can obtain the total energy dissipation rate caused by the apparent cohesion of the soil.

[0197] The power dissipation rate of the apparent cohesion is generated 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, its corresponding apparent cohesion, and the tangential velocity component. Integrating over the entire sliding surface can obtain the total energy dissipation rate generated by the apparent cohesion. For the straight line AB, the apparent cohesion on the infinitesimal sliding surface is c(z 1 ), z 1 is the vertical distance from the infinitesimal element to the phreatic surface and can be expressed as:

[0198] z 1 = z 0 + H 2 + H 1 -(H 1 + H 2 )e -βtanφ′ (sinα - tanθcosα)

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

[0200]

[0201] The polar radius ρ c of the infinitesimal sliding surface to the moment point O 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 the logarithmic spiral BC, the apparent cohesion on the infinitesimal sliding surface is c(z 2 ), z 2 is the vertical distance from the infinitesimal element to the phreatic surface and can be expressed as:

[0206] z 2 = z 0 + H 1 + H 2 - r(θ)cosθ

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

[0208] ds = (H1 +H 2 )e -θtanφ′ dθ / cosφ′

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

[0210]

[0211] At the moment when the soil mass fails, according to the energy balance equation, that is, the work done by the external force is equal to the power consumption the sliding moment M can be obtained a ; According to the energy balance equation in the active zone, the sliding moment M a can be expressed as:

[0212]

[0213] S206 Calculate the anti-sliding moment M p , the forces acting on the soil mass in the passive zone include the reaction force of the retaining structure on the soil mass, including the normal stress σ and the downward shear stress τ, as well as the soil gravity G; at the moment 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 does work W τ = 0; the work done by the soil gravity is the apparent cohesion c of the soil cap consumed by the logarithmic spiral CD

[0214] the anti-sliding moment M p can be obtained according to the energy balance equation in the passive zone, that is:

[0215]

[0216] 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 soil gravity, is the consumption of the apparent cohesion along the logarithmic spiral CD.

[0217] S207 Calculate the power done by the soil gravity in the passive zone. The unit weight of each soil layer unit is represented by the value at its centroid. The power done by the soil layer unit gravity can be expressed as the product of the unit gravity and the velocity in the direction of the gravity at its centroid. The unit gravity is the product of the trapezoidal area and its corresponding unit weight. Accumulate the power done by the soil gravity of all soil layer units to obtain the total power done by the soil gravity

[0218] For the passive zone CDD', the slip surface is divided by the angle θ pEvenly discretized into n segments, the angle corresponding to each slip surface is Δθ = θ p / n. The soil mass 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 ) where z k is the vertical distance from the centroid of the soil layer unit to the phreatic surface and can be expressed as:

[0219] z k = z 0 + H 2 + H 1 -(r k+0.5 cos(n + 0.5 - k)Δθ) for k = 1...n

[0220] The area of the soil layer unit can be expressed 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 areas of the upper and lower surfaces of the soil layer unit. The longitudinal width of the soil layer unit is taken as 1. l k can be expressed as:

[0223] l k = r k sin(n + 1 - k)Δθ

[0224] r k = (H 1 + H 2 )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] By accumulating the power done by the gravity of all soil layer units, the total power done by the soil gravity can be obtained:

[0228]

[0229] S208 Calculate the power dissipation rate caused by the apparent cohesion of the soil in the passive zone. The apparent cohesion of the soil dissipates 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, its corresponding apparent cohesion, and the tangential velocity component. Integrating over the entire sliding surface can obtain the total energy dissipation rate caused by the apparent cohesion of the soil.

[0230] The apparent cohesion dissipates 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, its corresponding apparent cohesion, and the tangential velocity component. Integrating over the entire sliding surface can obtain the total energy dissipation rate caused by the apparent cohesion of the soil. The apparent cohesion on the infinitesimal sliding surface is c(z 3 ), z 3 is the vertical distance from the infinitesimal to the phreatic surface and can be expressed as:

[0231] z 3 = z 0 + H 1 + H 2 - r(θ)cosθ

[0232] The length of the infinitesimal sliding surface can be expressed as:

[0233] ds = (H 1 + H 2 )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 fails, according to the energy balance equation, that is, the work done by the external force is equal to the power consumption 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 expressed as:

[0238]

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

[0240] FOS = M p / M a .

[0241] Using the MATHEMATICA numerical analysis software, develop a variable-step cyclic algorithm to calculate the maximum value of the code search safety factor and give its corresponding critical slip surface. Taking the geometric parameters of the sliding soil mass as independent variables, calculate the safety factor and compare it with the preset value, and store the larger safety factor; sequentially change the magnitudes of the above independent variables, and each independent variable is sequentially changed in a single calculation cycle according to the specified increment, repeat the calculation, obtain the new safety factor, and compare it with the stored value, and repeat the cycle until the maximum value is searched. Finally, output the maximum safety factor and the corresponding geometric parameters of the sliding soil mass to obtain the critical slip surface.

[0242] Effect comparison

[0243] Figure 4 and Figure 5 This is the comparison between the calculation results of the present invention and the calculation results of other scholars. The data is cited from: Zhang Zhao, Research on the Embedded Depth and Anti-Heave Stability Analysis of Narrow Foundation Pits Based on the 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 H 2 = 23.4m, the distance from the lowest support point to the bottom of the pit H 1 = 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 , assuming that the cohesion varies in the range of 0 - 50kPa and the internal friction angle varies in the range of 0 - 20°; the relevant parameters of 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 from the comparison that when the suction effect is not considered, the calculation results of the present invention are highly consistent with the theoretical calculation results, verifying the rationality of the calculation method of the present invention; when the suction effect is considered, the traditional analysis method significantly underestimates the stability of the sheet pile-embedded foundation pit. Under the condition of stable infiltration, the matrix 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 approaches the safety factor under the saturated state.

[0246] In summary, the present invention creatively proposes a method for evaluating the stability of sheet pile-embedded foundation pits considering the unsaturated effect. Combining the strength theory of unsaturated soils and the limit analysis method, a horizontal slice semi-analytical method is creatively proposed, which can reasonably explain the strengthening mechanism of the suction effect in soils and more realistically reflect the safety reserve of foundation pits, having certain academic value and reference significance for guiding the design and reinforcement of foundation pits under complex conditions.

[0247] The above embodiments are merely examples clearly illustrating the present invention and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. And the obvious changes or modifications derived therefrom still fall within the protection scope of the present invention.

Claims

1. A method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated effects, characterized in that: The potential sliding surface of the sheet pile embedded unsaturated foundation pit is simulated by using the sliding surface composed of straight lines and logarithmic spiral lines to evaluate the stability of the sheet pile embedded unsaturated foundation pit, including the following steps: The S1 water table is assumed to be distributed horizontally, and the soil is divided into a saturated zone and an unsaturated zone; the slip surface intersects the pit bottom and the ground through the pile end, the outer side of the foundation pit is the active earth pressure zone, and the inner side of the foundation pit is the passive earth pressure zone; the active earth pressure zone is recorded as ABCE, and the active zone ABCE is divided into soil blocks ABB'E and soil blocks BCB', and the soil blocks in the passive earth pressure zone are recorded as CDD'; the linear slip surface is used to simulate the slip surface of soil block ABB'E, and the spiral slip surface is used to simulate the slip surfaces of soil blocks BCB' and soil blocks CDD' respectively; S2 calculates the safety factor FOS of the stability of the sheet pile embedded foundation pit, which is used to evaluate the stability of the sheet pile embedded unsaturated foundation pit; The stability safety factor FOS of the sheet pile embedded foundation pit can be expressed as: Where: M a is the sliding moment, which is generated by the active earth pressure of the soil outside the foundation pit on the sheet pile, and its magnitude is the moment of the active earth pressure on the lowest support point; M p It is the anti-sliding moment, generated by the passive earth pressure of the soil inside the foundation pit on the sheet pile, and its magnitude is the moment of the passive earth pressure on the lowest support point; Among them, the sliding moment M a for: Where: Power made by ABB'E for soil blocks, Power for the clod BCB', is the energy dissipated by the apparent cohesion of the soil along the line AB, Energy consumption of apparent cohesion of soil along the logarithmic spiral line BC, ω is the angular velocity; Among them, the anti-slip moment M p : Where: Power for the clod CDD', It is the apparent cohesion of soil consumed along the logarithmic spiral CD.

2. A method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated effects according to claim 1, characterized in that: In S2, when the soil is discretized, for the soil block ABB'E, it is evenly discretized into n horizontal soil layer units along the height direction. Each soil layer unit is trapezoidal and the unit thickness is For soil blocks BCB' and CDD', the logarithmic spiral slip surface is divided into two parts according to the angles β and θ. p The discretization is equally divided into n segments, and the corresponding angles of each slip surface are β / n and θ respectively. p / n, the soil is discretized into n horizontal soil layer units along the horizontal direction, and each soil layer unit is approximately regarded as a trapezoid.

3. A method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated effects according to claim 1, characterized in that: S2 and The calculation method is to discretize the soil blocks ABB'E and BCB' respectively to obtain the corresponding soil layer units. The unit weight of each soil layer unit is represented by the value at its centroid. The power done by the gravity of the soil layer unit can be expressed as the product of the unit gravity and the velocity in the gravity direction at its centroid. The unit gravity is the product of the trapezoid area and its corresponding unit weight. The power done by the soil gravity of all soil layer units is accumulated to obtain the total power done by the soil gravity. and and The calculation method is as follows: Assuming that the soil is a rigid body, the energy dissipation in 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 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. and The calculation method is as follows: discretize the soil to obtain several soil layer units. The unit weight of each soil layer unit is represented by the value at its centroid. The power done by the gravity of the soil layer unit can be expressed as the product of the unit gravity and the velocity in the gravity direction at its centroid. The unit gravity is the product of the trapezoid area and its corresponding unit weight. The power done by the gravity of all soil layer units is accumulated to obtain the total power done by the gravity of the soil. 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 microelement sliding surface and its corresponding apparent cohesion and tangential velocity component. By integrating over the entire sliding surface, the total energy dissipation rate caused by the apparent cohesion of the soil can be obtained.

4. The method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated effects according to claim 1, characterized in that: In S2, and The specific calculation method is: For the soil block ABB'E, it is evenly discretized into n horizontal soil layer units along the height direction. Each soil layer unit is trapezoidal with a thickness of The unit weight at the centroid of the soil layer unit is γ i (z i ), z i is the vertical distance from the centroid of the soil layer unit to the water table, which can be expressed as: z i =z0+H2+H-(i-0.5)hi=1...n Where: H is the depth of the foundation pit, H1 is the vertical distance from the lowest support point to the bottom of the pit, and H2 is the embedding depth of the sheet pile. The area of ​​a soil layer unit can be expressed as: S i =0.5h(l i-1 +l i ) Where: l i and l i-1 is the upper and lower surface area of ​​the soil layer unit, and the longitudinal width of the soil layer unit is taken as 1, l i It can be expressed as: The polar diameter ρ from the centroid of the soil layer unit to the moment point O i and angle θ i They are: By adding up the power done by the soil weight of all soil layer units, the total power done by the soil weight can be obtained: For the soil block BCB', the sinking of the soil outside the lower section of the sheet pile drives the soil outside the upper section of the sheet pile to sink, forming an angle with the horizontal recorded as β; the slip surface is discretized into n sections at an angle β, and the angle corresponding to each slip surface is Δθ=β / n. The soil 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 at the centroid of the soil layer unit is γ j (z j ), z j is the vertical distance from the centroid of the soil layer unit to the water table, which can be expressed as: z j =z0+H2+H1-(r j+0.5 cos(n+0.5-j)Δθ) j=1...n Where: z0 is the vertical distance from the diving surface to the pile end; The unit area of ​​the soil layer can be expressed as: S i =0.5(l j +l j+1 ){r j+1 cos(n-j)Δθ-r j cos(n+1-j)Δθ} Where: l j and l j+1 is the upper and lower surface area of ​​the soil layer unit, and the longitudinal width of the soil layer unit is taken as 1, l j It can be expressed as: l j =r j sin(n+1-j)Δθ r j =(H1+H2)and -(n+1-j)Δθtanφ′ The polar diameter ρ from the centroid of the soil layer unit to the moment point O j and angle θ j They are: By adding up the power done by the soil weight of all soil layer units, the total power done by the soil weight can be obtained:

5. The method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated effects according to claim 1, characterized in that: In S2, and The specific calculation method is: 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 micro-element sliding surface and its corresponding apparent cohesion and tangential velocity component. By 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 micro-element sliding surface is c(z1), where z1 is the vertical distance from the micro-element to the water table, which can be expressed as: z1=z0+H2+H1-(H1+H2)e -βtanφ′ (sinα-tanθcosα) The length of the microelement sliding surface can be expressed as: The polar diameter ρ from the infinitesimal sliding surface to the moment point O c It can be expressed as: The total energy dissipation rate caused by the apparent cohesion on line AB is: For the logarithmic spiral BC, the apparent cohesion on the microelement sliding surface is c(z2), where z2 is the vertical distance from the microelement to the diving surface, which can be expressed as: z2=z0+H1+H2-r(θ)cosθ The length of the microelement sliding surface can be expressed as: ds=(H1+H2)e -θtanφ′ dθ / cosφ′ The total energy dissipation rate caused by the apparent cohesion on the logarithmic spiral BC is:

6. A method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated effects according to claim 1, characterized in that: In S2, The specific calculation method is: For soil block CDD', the angle of the logarithmic spiral slip surface in the passive zone is denoted by θ p ; The sliding surface is shifted by an angle θ p The discretization is equally divided into n segments, and the angle corresponding to each slip surface is Δθ=θ p / n, the soil is discretized into n horizontal soil layer units in 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 water table, which can be expressed as: z k =z0+H2+H1-(r k+0.5 cos(n+0.5-k)Δθ)k=1...n The unit area of ​​the soil layer 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} Where: l k and l k+1 is the upper and lower surface area of ​​the soil layer unit, and the longitudinal width of the soil layer unit is taken as 1, l k It can be expressed as: l k =r k sin(n+1-k)Δθ r k =(H1+H2)and (n+1-k)Δθtanφ′ The polar diameter ρ from the centroid of the soil layer unit to the moment point O k and angle θ k They are: By adding up the power done by the soil weight of all soil layer units, the total power done by the soil weight can be obtained:

7. The method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated effects according to claim 1, characterized in that: In S2, The specific calculation method is 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 micro-element sliding surface and its corresponding apparent cohesion and tangential velocity component. By 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 on the micro-element sliding surface is c(z3), where z3 is the vertical distance from the micro-element to the water table, which can be expressed as: z3=z0+H1+H2-r(θ)cosθ The length of the microelement sliding surface can be expressed as: ds=(H1+H2)eθ tanφ′ dθ / cosφ′ The total energy dissipation rate caused by the apparent cohesion on the logarithmic spiral CD is:

8. The method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated 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 fill matrix suction can be obtained, and then the distribution of soil weight and apparent cohesion can be obtained.

9. The method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated effects according to claim 7, characterized in that: The specific calculation method for the distribution of soil weight and apparent cohesion is: The volumetric moisture content of soil can be expressed as: Where: ψ is the matrix suction, ψ r is the matrix suction corresponding to the residual water content state, a f is the matrix suction corresponding to the inflection point of the soil-water characteristic curve, which can be measured by graphical method, m f and n f are the model fitting parameters; Based on the steady-state seepage assumption, the matrix suction distribution expression is: Where: q / k s is the vertical specific flow rate, γ w is the unit weight of water, α can be approximated as the inverse 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 end; The unit weight of unsaturated soil can be calculated based on the dry weight of soil γ d Get, that is γ′=γ d +θ w c w The apparent cohesion of unsaturated soil can be expressed as: Where: θ r and θ s are the residual and saturated soil volume moisture contents respectively; the saturated soil volume moisture content can be calculated based on the saturated unit weight γ sat and dry weight, that is, θ s =(γ sat -γ d ) / γ sat .

10. The method for evaluating the stability of a sheet pile embedded foundation pit considering unsaturated 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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