Calculation method of anti-uplift stability factor considering shear strength of soil above caisson blade

Abstract

The present invention relates to a method for calculating the anti-uplift stability coefficient taking into account the shear strength of the soil above the caisson blade foot, and the method comprises the following steps: (1) determining calculation parameters, which mainly include the thickness, density, internal friction angle, cohesion, ground overload, soil plug height in the well, and geometric dimensions of the caisson; (2) determining the type of the caisson according to the width and sinking depth of the caisson; (3) according to the determined different caisson types, substituting the calculation parameters into a calculation expression to calculate the anti-uplift stability coefficient of the caisson structure; the method for calculating the anti-uplift stability coefficient taking into account the shear strength of the soil above the caisson blade foot proposed by the present invention can quickly and accurately analyze the anti-uplift stability of the caisson in actual engineering, and provide theoretical support for design and construction.

Description

Technical Field

[0001] The present invention relates to the field of geotechnical engineering calculation, and in particular to a method for calculating an anti-uplift stability coefficient taking into account the shear strength of soil above a caisson blade foot. Background Art

[0002] In foundation pit construction, analyzing the anti-uplift stability of the pit can ensure its stability and control its deformation. Caisson structures and foundation pit excavation support share certain characteristics, so an analysis of the anti-uplift stability of the caisson can also be performed to reflect the stability of the caisson construction and the deformation of the surrounding soil, thereby providing guiding parameters for caisson design and construction.

[0003] There are three main methods for studying anti-heave stability: the limit equilibrium method, the limit analysis method, and the finite element method based on strength reduction. The limit equilibrium method performs verification on a preset failure surface. The relationship between the preset failure surface and the actual failure surface cannot be determined, so it is not rigorous in theory. However, due to the clear meaning of its formula parameters, simple form, and rich engineering accumulation, it is difficult to be replaced for a while. The limit analysis method is based on the failure mode of the Prandtl or Terzaghi mechanism, and derives the anti-heave stability coefficient according to the upper limit theorem of plastic limit analysis. It is more rigorous than the limit equilibrium method. The strength reduction finite element method continuously reduces the soil strength until the model is destroyed to obtain the reduction factor, which is the safety factor. There are two main directions of the limit equilibrium method, namely the circular sliding method and the calculation method based on foundation bearing capacity. The current national standard (JGJ120-2012[S]) and Shanghai standard (DG / TJ 08-61-2018[S]) both use the circular sliding method and the foundation bearing capacity method based on the Prandtl formula to calculate the anti-uplift safety stability factor of the foundation pit.

[0004] Caisson structures have high structural rigidity, but before concrete sealing, their rigidity to the soil is only reflected in the horizontal direction. The soil can be squeezed out from under the blade foot, losing vertical balance and being destroyed. The Prandtl formula can reflect the stability of the soil below the blade foot that rises into the well, and is therefore suitable for the anti-uplift stability verification of caissons.

[0005] Prandtl and Terzaghi applied the limit equilibrium theory to a strip shallow foundation on a semi-infinite soil and obtained a similar formula for calculating the foundation bearing capacity. The earliest anti-uplift stability coefficient was provided by Terzaghi. Wang Bingjian and Xia Mingyao (Internal forces and depth of underground continuous walls [J]. Chinese Journal of Geotechnical Engineering, 1983(03):103-114.) took the failure datum plane at the bottom of the retaining wall and proposed a new expression, which is the formula currently adopted by the standard. The main assumptions of this formula are to ignore the gravity effect of the sliding zone below the structure and to ignore the shear strength of the soil above the structure, but only to apply it as a flexible load on the sliding zone. This makes the anti-uplift safety factor independent of the depth of the slip line, and therefore cannot reflect the size effect of the foundation pit and the contribution of the strength of the soil above the pit bottom to safety. This problem is reflected in the caisson structure in that the influence of the strength of the soil above the blade foot is not taken into account. The caisson is a structure that sinks as a whole and sinks at a relatively fast speed. Therefore, the strength of the soil above the blade foot should be considered more when verifying the anti-uplift stability.

[0006] In Rock and Soil Mechanics (2016, 37(S2):433-441), Wang Hongxin published "Size Effect of Foundation Pit and Calculation Method of Anti-Heave Stability Safety Factor Considering Excavation Width". Considering the influence of soil cohesion, overload above the datum surface and foundation width b, assuming that the slip line is exactly connected to the support bottom, the b value is calculated. b Add 0.5N to the calculation formula γ γb, N γ is the Meyehoff foundation bearing capacity coefficient, which reflects the influence of the foundation pit width and the shear strength of the soil outside the support. However, its slip line assumption is based on flexible support and does not consider the different slip line forms for different foundation pit widths. γ The coefficient is also relatively complex and is rarely used in engineering. Tong Lei et al. published "Discussion on the Anti-uplift Stability Calculation of Deep Soft Soil Foundation Wall Bottom" in the Journal of Geotechnical Engineering (2013, 35(S2):707-711). Based on the failure of the soil above the wall bottom, they selected the direct shear failure mode with the highest probability and the smallest safety factor, and used it in K b An item ch, i.e., the cohesion of the direct shear section, is added to the numerator of the calculation formula. The dimension of this item does not match, so the physical meaning is not clear, but its processing method has certain reference significance; Yang Jibao et al. published "Improvement of the Prandtl Calculation Formula for the Anti-uplift Stability of the Bottom of the Foundation Pit Wall in Soft Soil Areas" in the Journal of Engineering Geology (January 14, 2022, 1-9). Taking into account the shear strength of the soil inside and outside the foundation pit above the bottom of the retaining wall, and deducing it based on the limit equilibrium formula, in K b The numerator of the calculation formula increases cN' cz and γHN' qz Two items, of which N'cz and N' qz They are all derived coefficients, and the form is very complicated. The shear strength they consider extends to the ground, and the safety margin is large. The calculation diagram is not set up reasonably, but the derivation method is worth referring to. Summary of the Invention

[0007] The present invention proposes a calculation method for the anti-uplift stability coefficient taking into account the shear strength of the soil above the caisson blade foot, providing a theoretical basis for caisson design and construction.

[0008] In order to achieve the above object, the technical solution of the present invention is: a method for calculating the anti-uplift stability coefficient considering the shear strength of the soil above the caisson blade foot, comprising the following steps:

[0009] The first step is to determine the calculation parameters, including the caisson sinking depth H, caisson width B, soil plug height h, and surrounding soil layer thickness s. i , severe γ i , internal friction angle φ i and cohesion c i , surface overload q k ;

[0010] The second step is to determine the caisson type based on the caisson sinking depth H and caisson width B, where the caisson sinking depth H is the distance from the caisson blade to the ground; if it is a circular caisson, the caisson width B is its diameter; if it is a rectangular caisson, the width is the length of the long side; the method for judging the caisson type is that if B / H is less than 0.5, it is a narrow caisson; if B / H is greater than 0.5 and less than Wide caisson; B / H greater than It is an extra-wide caisson, is the friction angle of the soil at the bottom of the blade foot;

[0011] The third step is to calculate the anti-uplift stability coefficient of the caisson. The load action length b is calculated using different expressions according to different caisson types:

[0012] When the caisson is a narrow caisson,

[0013]

[0014] When the caisson is a wide caisson,

[0015]

[0016] When the caisson is an extra-wide caisson,

[0017] The fourth step is to solve the additional foundation bearing capacity coefficient N′ c as follows,

[0018]

[0019] Among them, h is the height of the soil plug in the well, b is the load acting length, is the friction angle of the soil at the bottom of the blade foot;

[0020] Caisson anti-uplift stability coefficient K b The calculation formula is solved as follows:

[0021]

[0022] Where c' is the weighted cohesion of the soil plug above the caisson blade foot, and the other terms are the original parameters for calculating the anti-heave stability coefficient of the foundation pit based on the classic Prandtl calculation formula. The values ​​of these parameters are also listed below:

[0023]

[0024]

[0025] q=γh

[0026] in, is the internal weighted soil friction angle within the influence range of the blade foot bottom with an approximate thickness b, c is the weighted soil cohesion, γ1 is the weighted degree of soil plug, γ is the weighted degree of soil within the range of the caisson sinking depth H, q k Overload of the ground.

[0027] Furthermore, the anti-heave stability coefficient K of the caisson is determined. b Calculation method: The conventional bottom of the blade foot is used as the reference surface. At this time, the soil outside the well and the soil plug inside the well act as the external uniform load Pu and the resistance uniform load q on the isolation body OAGEC respectively; there are soil cohesion c and the resultant force R of normal force and friction force on the segment. Since the segment is a logarithmic spiral The direction of the resultant force R passes through the midpoint A of the logarithmic spiral; and are the active earth pressure of the soil outside the well and the passive earth pressure of the soil inside the well, respectively. Their values ​​are related to Pu and q, respectively, as shown in the following formula:

[0028]

[0029]

[0030] Taking the moment of the isolator OAGEC about the pole A, we should have ∑M A =0, as shown in the following formula:

[0031]

[0032] The length is b / 2. According to the geometric relationship and the equation of the logarithmic spiral, it is easy to know that and Length, M c For arc segments The moment of the upper cohesion c on point A is as follows:

[0033]

[0034] Considering the strength of the soil above the blade foot, it is safe and reasonable to only consider the effect of cohesion for the soil plug inside the well, that is, the resistance of the soil plug inside the well is P1 = c′h, and it acts on point G in a conservative way. For the soil outside the well, the stress situation is more complicated, and the failure surface is often arc-shaped and connected to the well wall, and does not extend to the ground. Its effective resistance range is set to the same as the height of the soil plug, then P2 = c′h, and it acts on point O.

[0035] After considering the two resistances P1 and P2, take the moment of the extreme point A, ∑M A =0, it becomes the following formula:

[0036]

[0037] After sorting, P u =qN q +cN c +c′N′ c , c′ is the cohesion of the upper soil, N′ c is the modified bearing capacity coefficient, as shown below:

[0038]

[0039] Then calculate K b The calculation expression is:

[0040]

[0041] Furthermore, the method of determining different load action lengths b according to different caisson sizes is as follows: when B / H < 0.5, it is a narrow caisson. At this time, the sliding surfaces on both sides of the caisson wall will have a cross-influence. When B = 0, the sliding surfaces completely intersect. When B / H = 0.5, the sliding surfaces become a wide caisson. Assuming that the sliding surface change is linear, the following is derived:

[0042]

[0043] When it is a wide caisson, the sliding surfaces are connected but not intersecting. Then we can get:

[0044]

[0045] When it is an ultra-wide caisson, the main impact range of surface settlement is Can be regarded as width b, when When , the bulges on both sides of the side wall can be considered to be completely independent, and the slip lines do not cross:

[0046]

[0047] At this point, the modified derivation of the anti-heave stability coefficient for application in caissons has been completed. The shear strength of the soil above the blade foot is taken into account. Different caisson types are determined by different caisson widths B and sinking depths H. The load action length b value is then obtained and substituted into the anti-heave coefficient expression to obtain the anti-heave stability coefficient K. b .

[0048] The beneficial effects of the present invention are:

[0049] The present invention proposes a calculation method for the anti-uplift stability coefficient taking into account the shear strength of the soil above the caisson blade foot. The method can consider the influence of the shear strength of the soil above the caisson on the anti-uplift stability coefficient method of the foundation pit derived from the classic calculation formula based on the foundation bearing capacity. The method has the advantages of clear physical meaning, more consistent results with actual conditions, and easy calculation and use. It can quickly and accurately analyze the anti-uplift stability of the caisson in actual engineering and provide theoretical support for design and construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Schematic diagram of the calculation model of the present invention;

[0051] Figure 2 This is a flow chart of a method for calculating the anti-uplift stability coefficient taking into account the shear strength of the soil above the caisson blade foot in a preferred embodiment of the present invention;

[0052] Figure 3 Schematic diagram of the derivation process of the calculation formula of the present invention;

[0053] Figure 4 This is a schematic diagram of the caisson type;

[0054] Figure 5 K is a preferred embodiment of the present invention b Comparison chart of calculated values ​​and values ​​obtained in the current national standard (JGJ120-2012[S]). DETAILED DESCRIPTION

[0055] Specific embodiments of the present invention are described below with reference to the accompanying drawings, but the present invention is not limited to the following embodiments. The advantages and features of the present invention will become more apparent from the following description and claims. It should be noted that the drawings are greatly simplified and use non-precise ratios, and are only used for the purpose of conveniently and clearly illustrating the embodiments of the present invention.

[0056] Please refer to Figure 1 and Figure 2The steps for calculating the anti-uplift stability coefficient of the present invention taking into account the shear strength of the soil above the caisson blade foot are as follows:

[0057] The first step is to determine the calculation parameters, including the caisson sinking depth H, caisson width B, soil plug height h, and surrounding soil layer thickness s. i , severe γ i , internal friction angle φ i and cohesion c i , surface overload q k .

[0058] The second step is to determine the caisson type based on the sinking depth H and the caisson width B. The sinking depth H is the distance from the caisson blade to the ground. If it is a circular caisson, the caisson width B is its diameter; if it is a rectangular caisson, the width is the length of the long side. The method for judging the caisson type is that if B / H is less than 0.5, it is a narrow caisson; if B / H is greater than 0.5 and less than 0.5, it is a wide caisson. Wide caisson; B / H greater than For extra wide caisson, see Figure 4 ,in is the friction angle of the soil at the bottom of the blade foot.

[0059] The third step is a method for calculating the anti-uplift stability coefficient considering the shear strength of the soil above the caisson blade according to claim 1, characterized in that the load action length b adopts different calculation expressions according to different caisson types.

[0060] When the caisson is a narrow caisson,

[0061]

[0062] When the caisson is a wide caisson,

[0063]

[0064] When the caisson is an extra-wide caisson,

[0065] The fourth step is to solve the additional foundation bearing capacity coefficient N′ c as follows,

[0066]

[0067] Among them, h is the height of the soil plug in the well, b is the load acting length, is the friction angle of the soil at the bottom of the blade foot.

[0068] Caisson anti-uplift stability coefficient K b The calculation formula is solved as follows:

[0069]

[0070] Where c' is the weighted cohesion of the soil plug above the caisson blade foot, and the other terms are the original parameters for calculating the anti-heave stability coefficient of the foundation pit based on the classic Prandtl calculation formula. The values ​​of these parameters are also listed below:

[0071]

[0072]

[0073] q=γh

[0074] in, is the weighted soil internal friction angle within the influence range of the blade foot bottom (approximate thickness is b), c is the weighted soil cohesion, γ1 is the weighted degree of soil plug, γ is the weighted degree of soil within the sinking depth H of the caisson, q k Overload of the ground.

[0075] Combine Figure 3 , 4, shows the derivation process of the present invention.

[0076] The conventional bottom of the blade foot is used as the reference surface. At this time, the soil outside the well and the soil plug inside the well act as the external uniform load Pu and the resistance uniform load q on the isolation body OAGEC respectively; there are soil cohesion c and the resultant force R of normal force and friction force on the segment. Since the segment is a logarithmic spiral The direction of the resultant force R passes through the midpoint A of the logarithmic spiral; and are the active earth pressure of the soil outside the well and the passive earth pressure of the soil inside the well, respectively. Their values ​​are related to Pu and q, respectively, as shown in the following formula:

[0077]

[0078]

[0079] Taking the moment of the isolator OAGEC about the pole A, we should have ∑M A =0, as shown in the following formula:

[0080]

[0081] The length is b / 2. According to the geometric relationship and the equation of the logarithmic spiral, it is easy to know that and Length, M c For arc segments The moment of the upper cohesion c on point A is as follows:

[0082]

[0083] The present invention considers the strength of the soil above the blade foot. For the soil plug inside the well, since it is not high and is significantly disturbed during sinking, resulting in a low stress level and less friction, it is safe and reasonable to assume direct shear failure with the shortest path and consider only the influence of cohesion. That is, the resistance of the soil plug inside the well, P1 = c′h, is conservatively applied to point G. For the soil outside the well, the stress conditions are more complex, and the failure surface often arcs onto the well wall and does not extend to the ground. The present invention sets the effective resistance range to the same as the soil plug height, so P2 = c′h, and acts at point O, which is also on the safe side.

[0084] like Figure 3 As shown, after considering the two resistances P1 and P2, take the moment of the extreme point A, ∑M A =0, it becomes the following formula:

[0085]

[0086] After sorting, P u =qN q +cN c +c′N′ c , c′ is the cohesion of the upper soil, N′ c is the modified bearing capacity coefficient, as shown below:

[0087]

[0088] Then calculate K b The calculation expression is:

[0089]

[0090] The load action length b is related to the type of caisson. The following describes how to determine the load action length b according to different caisson sizes. The specific diagram is as follows: Figure 3 shown.

[0091] When B / H is less than 0.5, the caisson is narrow. In this case, the sliding surfaces on both sides of the caisson wall will have a cross-influence. When B=0, the sliding surfaces completely intersect. When B / H=0.5, the sliding surfaces become wide caisson. Assuming that the sliding surface change is linear, the following is derived:

[0092]

[0093] When it is a wide caisson, the sliding surfaces are connected but not intersecting. Then we can get:

[0094]

[0095] When it is an ultra-wide caisson, the main impact range of surface settlement is Can be regarded as width b, when When , the bulges on both sides of the side wall can be considered to be completely independent, and the slip lines do not cross:

[0096]

[0097] At this point, the modified derivation of the anti-heave stability coefficient for application in caissons has been completed. The shear strength of the soil above the blade foot is taken into account. Different caisson types are determined by different caisson widths B and sinking depths H. The load action length b value is then obtained and substituted into the anti-heave coefficient expression to obtain the anti-heave stability coefficient K. b .

[0098] This revised formula is based on a formula widely used in the industry. It has a clear physical meaning and calculation process. It takes into account the shear strength of the soil inside and outside the caisson, and can reflect the higher anti-uplift stability of narrow caissons than wide caissons, and the results are better.

[0099] In order to verify the rationality of the formula of the present invention, an example is assumed: the sinking depth of the caisson is H = 20m, the height of the soil plug is h = 4m, the cohesion of the soil above and below the blade foot is c = c' = 5kpa, and the internal friction angle is Soil weighting γ=18kN / m 3 , different caisson width B, the calculation method of the present invention is compared with the current industry standard results. Figure 5 The calculation method of the present invention can better reflect the size effect of improved stability when the caisson width becomes narrower, and when the B value increases, it can gradually coincide with the standard method, indicating that the method of the present invention has greater rationality and practical applicability.

[0100] In summary, the present invention improves the anti-uplift stability coefficient based on the Prandtl calculation formula, takes into account the shear strength of the soil above the blade foot, and assumes the form of slip lines based on different caisson types. It not only inherits the limit equilibrium idea, but also can reflect the influence of caisson size changes on anti-uplift stability. The results perform well under ideal engineering assumptions, but its applicability needs to be verified in actual engineering.

[0101] While the present invention has been disclosed above with reference to preferred embodiments, this is not intended to limit the present invention. Persons skilled in the art will readily appreciate that various modifications and variations can be made without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for calculating the anti-uplift stability coefficient considering the shear strength of the soil above the caisson blade foot, characterized in that: The following steps are involved: The first step is to determine the calculation parameters, including the caisson sinking depth H, caisson width B, soil plug height h, and surrounding soil layer thickness s. i , severe γ i , internal friction angle φ i and cohesion c i , surface overload q k ; The second step is to determine the caisson type based on the caisson sinking depth H and caisson width B, where the caisson sinking depth H is the distance from the caisson blade to the ground; if it is a circular caisson, the caisson width B is its diameter; If it is a rectangular caisson, the width is the length of the long side; the method for judging the type of caisson is that if B / H is less than 0.5, it is a narrow caisson; if B / H is greater than 0.5 and less than Wide caisson; B / H greater than It is an extra-wide caisson, is the internal friction angle of the soil at the bottom of the blade foot; The third step is to calculate the anti-uplift stability coefficient of the caisson. The load action length b is calculated using different expressions according to different caisson types: When the caisson is a narrow caisson, When the caisson is a wide caisson, When the caisson is an extra-wide caisson, The fourth step is to solve the additional foundation bearing capacity coefficient N c 'as follows, Among them, h is the height of the soil plug in the well, b is the load acting length, is the internal friction angle of the soil at the bottom of the blade foot; the anti-heave stability coefficient K of the caisson b The calculation formula is solved as follows: Where c' is the weighted cohesion of the soil plug above the caisson blade foot, and the other terms are the original parameters for calculating the anti-heave stability coefficient of the foundation pit based on the classic Prandtl calculation formula. The values ​​of these parameters are also listed below: q=γh in, is the internal weighted soil friction angle within the influence range of the blade foot bottom with an approximate thickness b, c is the weighted soil cohesion, γ1 is the weighted degree of soil plug, γ is the weighted degree of soil within the range of the caisson sinking depth H, q k Overload of the ground.

2. The method for calculating the anti-uplift stability coefficient considering the shear strength of the soil above the caisson blade according to claim 1 is characterized by: Determine the anti-heave stability coefficient K of the caisson b Calculation method: The conventional bottom of the blade foot is used as the reference surface. At this time, the soil outside the well and the soil plug inside the well act as the external uniformly distributed load Pu and the resistance uniformly distributed load q on the isolation body OAGEC respectively; On the segment, there are soil cohesion c and the resultant force R of normal force and friction force. Since the segment is a logarithmic spiral The direction of the resultant force R passes through the midpoint A of the logarithmic spiral; and are the active earth pressure of the soil outside the well and the passive earth pressure of the soil inside the well, respectively. Their values ​​are related to Pu and q, respectively, as shown in the following formula: Taking the moment of the isolator OAGEC about the pole A, we should have ∑M A =0, as shown in the following formula: The length is b / 2. According to the geometric relationship and the equation of the logarithmic spiral, it is easy to know that and Length, M c For arc segments The moment of the upper cohesion c on point A is as follows: Considering the strength of the soil above the blade foot, it is safe and reasonable to only consider the effect of cohesion for the soil plug inside the well, that is, the resistance of the soil plug inside the well is P1 = c′h, and it acts on point G in a conservative way. For the soil outside the well, the stress situation is more complicated, and the failure surface is often arc-shaped and connected to the well wall, and does not extend to the ground. Its effective resistance range is set to the same as the height of the soil plug, then P2 = c′h, and it acts on point O. After considering the two resistances P1 and P2, take the moment of the extreme point A, ∑M A =0, it becomes the following formula: After sorting, P u =qN q +cN c +c'N′ c , c' is the cohesion of the upper soil, N' c is the modified bearing capacity coefficient, as shown below: Then calculate K b The calculation expression is:

3. The method for calculating the anti-uplift stability coefficient considering the shear strength of the soil above the caisson blade foot according to claim 1 is characterized in that: The method of determining the load action length b according to different caisson sizes is as follows: when B / H < 0.5, it is a narrow caisson. At this time, the sliding surfaces on both sides of the caisson wall will have a cross-influence. When B = 0, the sliding surfaces completely intersect. When B / H = 0.5, the sliding surfaces become a wide caisson. Assuming that the sliding surface change is linear, the following is derived: When it is a wide caisson, the sliding surfaces are connected but not intersecting. Then we can get: When it is an ultra-wide caisson, the main impact range of surface settlement is Can be regarded as width b, when When , the bulges on both sides of the side wall can be considered to be completely independent, and the slip lines do not cross: At this point, the modified derivation of the anti-heave stability coefficient for application in caissons has been completed. The shear strength of the soil above the blade foot is taken into account. Different caisson types are determined by different caisson widths B and sinking depths H. The load action length b value is then obtained and substituted into the anti-heave coefficient expression to obtain the anti-heave stability coefficient K. b .

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