A calculation method for preventing upheaval in a long and narrow foundation pit

Abstract

A calculation method for anti-heave of narrow and long foundation pits, based on the traditional theoretical calculation of foundation pit heave, introduces the catastrophe theory and fully considers the strain energy effect of the water-resistant clay layer. The present invention specifically analyzes the heave failure model occurring in the instability failure of the water-resistant clay layer at the bottom of the foundation pit. According to the cusp catastrophe theory and the model characteristics, an energy balance method is introduced to establish a heave catastrophe model for the key layer at the bottom of the pit. In the analysis and calculation, not only the self-weight of the soil at the bottom of the pit is considered, but also the bending elastic strain energy effect of the clay water-resistant layer itself is fully considered. As a supplement to the calculation theory of anti-heave of narrow and long foundation pits, the present invention makes full use of the bending elastic strain capacity of the clay water-resistant layer itself to improve the deficiency of being too conservative in the conventional calculation of anti-heave of foundation pits. The theoretical model of the present invention conforms to the actual situation and is consistent with the on-site results of actual engineering projects. It not only makes a reasonable supplement theoretically, but also significantly reduces the cost of anti-heave measures for foundation pits and improves the implementation progress of the project.

Description

Technical Field

[0001] The present invention studies the anti-heave stability of long and narrow foundation pits based on catastrophe theory, specifically a calculation method for the anti-heave of long and narrow foundation pits, and is particularly suitable for the anti-heave analysis of long and narrow foundation pits with an impermeable clay layer at the bottom of the pit. Background Technique

[0002] In recent years, the domestic municipal engineering construction has developed rapidly, accompanied by increasing construction investment. However, since the municipal engineering foundation pits are generally long and narrow, the current commonly used specification method for the anti-heave analysis of such foundation pits ignores the shape characteristics of the long and narrow foundation pits. Especially in the coastal soft clay areas, according to a large number of engineering practices, the calculation by the specification method is too conservative because the spatial shape effect of the excavation unloading of the foundation pit is not fully considered, and an economically reasonable calculation and analysis result cannot be obtained, and the favorable effect of the soft clay at the bottom of the pit is not fully recognized.

[0003] The traditional calculation of the anti-heave at the bottom of a long and narrow foundation pit only considers the self-weight of the soil body and does not fully consider the shape characteristics of the long and narrow foundation pit. The purpose of the present invention is to provide a theoretical calculation method. The calculation method proposed in this patent fully considers the shape characteristics of the long and narrow foundation pit, significantly highlighting the economic principle of engineering costs; secondly, the method has a clear intention and is basically consistent with the actual engineering monitoring situation, facilitating the popularization and application of similar projects. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the existing design methods and provide a calculation method for the anti-heave of long and narrow foundation pits based on catastrophe theory, which is particularly suitable for the anti-heave calculation and analysis of municipal long and narrow foundation pits in soft clay areas.

[0005] The purpose of the present invention can be achieved by the following method: a calculation method for the anti-heave of long and narrow foundation pits, characterized in that the method comprises the following steps:

[0006] A. Establish a fixed-end beam model based on the standard potential function form of the cusp catastrophe theory;

[0007] V(x) = x 4 + ux 2 + vx

[0008] The partial differential equation on the control variable plane:

[0009] 8u 3 + 27v 2 = 0

[0010] Obtain the total potential energy function of the rock beam bending;

[0011]

[0012] B. Establish a bursting force model for the foundation pit in combination with the characteristics of the long and narrow foundation pit project:

[0013] According to the force balance, it can be known that

[0014]

[0015] In the formula: F s —Horizontal extrusion force; F r —Vertical upward extrusion force; λ—Lateral pressure coefficient; —Equivalent comprehensive internal friction angle; γ—Soil unit weight; h—Foundation pit depth; L—Foundation pit width;

[0016] Assume the deflection curve equation of the beam bending:

[0017]

[0018] In the formula: δ—Deflection at x = L / 2;

[0019] The work done by the uniformly distributed load q is:

[0020]

[0021] In the formula: γ w —Unit weight of water; γ1—Unit weight of sandy soil; γ2—Unit weight of cohesive soil; h w —Head difference between inside and outside the foundation pit of the confined aquifer; h1—Thickness of the sandy soil layer; h2—Thickness of the cohesive soil layer;

[0022] C. Derive the potential energy function of the equivalent beam of the impermeable cohesive soil layer at the bottom of the pit according to the total potential energy function of the beam bending:

[0023]

[0024] Thus, it is obtained that:

[0025]

[0026] The sufficient condition for the initial fracture of the cohesive soil impermeable layer is:

[0027]

[0028] Let:

[0029]

[0030] That is When

[0031] The critical head difference between the inside and outside the foundation pit for the foundation pit to resist bursting is obtained:

[0032]

[0033] The present invention studies the anti-heave stability of long and narrow foundation pits based on catastrophe theory. This method mainly introduces catastrophe theory on the basis of the traditional theoretical calculation of foundation pit heave, and fully considers the strain energy effect of the water-resistant clay layer. The present invention specifically analyzes the heave failure model of the water-resistant clay layer at the bottom of the foundation pit. According to the cusp catastrophe theory and the model characteristics, an energy balance method is introduced to establish a heave catastrophe model for the key layer at the bottom of the pit. In the analysis and calculation, not only the self-weight of the soil at the bottom of the pit is considered, but also the bending elastic strain energy effect of the clay water-resistant layer itself is fully considered. The total potential energy function of the bending of the clay equivalent beam is established, and the sufficient condition for the initial fracture of the key layer is obtained by combining with the cusp catastrophe function equation, and then the calculation formula for the critical water head difference of the foundation pit against heave is fitted. The present invention uses the clay water-resistant layer to establish a fixed-end beam model. On the basis of considering mechanical equilibrium, the potential energy effect of the clay fixed-end beam is fully utilized. In the analysis of the anti-heave of long and narrow foundation pits, the critical water head difference of the foundation pit against heave can be reasonably calculated, and the engineering measure cost can be effectively reduced. The present invention is also applicable to wide foundation pits, and its anti-heave calculation results are consistent with the traditional calculation results, verifying that the anti-heave calculation of wide foundation pits is a special case simplification method of this method. The present invention is mainly used as a supplement to the anti-heave calculation theory of long and narrow foundation pits, and fully utilizes the bending elastic strain capacity of the clay water-resistant layer itself to improve the deficiency of being too conservative in the conventional anti-heave calculation of foundation pits. Compared with the conventional calculation method, the theoretical model of the present invention fits the actual situation and is consistent with the results of the actual engineering project site. It not only makes a reasonable supplement theoretically, but also significantly reduces the cost of foundation pit anti-heave measures and improves the implementation progress of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a typical sectional view of a long and narrow foundation pit.

[0035] Figure 2 It is a diagram of the fixed-end beam model.

[0036] Figure 3 It is the relationship between the critical water head difference of foundation pit heave and the foundation pit size. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] The following is a detailed description of the present invention according to specific embodiments of the present invention.

[0038] The present invention studies the anti-heave stability of long and narrow foundation pits based on catastrophe theory. This method mainly introduces catastrophe theory on the basis of the traditional theoretical calculation of foundation pit heave, and fully considers the strain energy effect of the water-resistant clay layer. The anti-heave calculation method for long and narrow foundation pits of the present invention specifically includes the following steps:

[0039] 1. Yu Qiuge (in 2017) established a fixed-end beam model based on the standard potential function form of the cusp catastrophe theory:

[0040] V(x) = x 4 + ux 2+vx (Equation 1)

[0041] Difference equation on the control variable plane:

[0042] 8u 3 +27v 2 =0 (Equation 2)

[0043] Find the total potential energy function of the rock beam bending:

[0044]

[0045] Where: V - potential function; x, u, v - potential function variable parameters; U - beam bending strain energy; W1 - work done by the horizontal extrusion force; W2 - work done by the vertical upward support force; W q — work done by the uniformly distributed load; EI - flexural rigidity / kN·m 2 ; L - beam length / m; δ - deflection; F s — horizontal extrusion force / kN; γ - average unit weight of the rock layer above the hard rock layer / (kN·m -3 ); H0 - depth at the hard rock layer m.

[0046] 2. Establish a bursting force model for the foundation pit in combination with the characteristics of the long and narrow foundation pit project, as shown in Figure 1 and Figure 2 .

[0047] According to the force balance, it can be known that

[0048]

[0049] Where: F s — horizontal extrusion force / kN; F r — vertical upward extrusion force / kN; λ - lateral pressure coefficient; — equivalent comprehensive internal friction angle; γ - soil unit weight / (kN·m -3 ); h - foundation pit depth / m; L - foundation pit width / m; h1 - thickness of the sandy soil layer / m; h2 - thickness of the clay soil layer / m.

[0050] Assume the deflection curve equation of the beam bending:

[0051]

[0052] Where: δ - deflection at x = L / 2.

[0053] The work done by the uniformly distributed load q is:

[0054]

[0055] Where: γ w — unit weight of water / (kN·m -3);γ1—Unit weight of sandy soil / (kN·m -3 );γ2—Unit weight of cohesive soil / (kN·m -3 );h w —Head difference between inside and outside of the pit in the confined aquifer layer / m; h1—Thickness of sandy soil layer / m; h2—Thickness of cohesive soil layer / m.

[0056] 3. Derive the potential energy function of the equivalent beam of the impermeable cohesive soil layer at the bottom of the pit from the total potential energy function of beam bending:

[0057]

[0058] In the cusp catastrophe theory, the potential energy function of the equivalent beam of the impermeable cohesive soil layer satisfies (Formula 1), thus obtaining:

[0059]

[0060] The sufficient condition for the initial fracture of the cohesive soil impermeable layer is obtained from (Formula 2):

[0061]

[0062] Let:

[0063]

[0064] That is When

[0065] Obtain the critical head difference between the inside and outside of the pit for the anti-heave of the foundation pit:

[0066]

[0067] Calculation and analysis of engineering examples

[0068] Taking the actual engineering data summarized by Liang Yongran (in 1996) as an example, see the following table for details:

[0069] Table 1 Comparison between traditional analysis and on-site actual situation of heave in actual excavated foundation pits

[0070]

[0071] Note: 1. L—Width of the foundation pit, h2—Thickness of the cohesive soil layer, H w —Actual head difference between inside and outside of the pit, h cra —Critical head difference obtained by traditional calculation method;

[0072] 2. The heave of the No. 4 foundation pit occurred after the workers inserted steel rods into the holes during the construction process. Otherwise, it might also be stable.

[0073] (1) Take the cross-section of a single-width foundation pit for calculation, and the specific calculation results are compared as shown in the following table:

[0074] Table 2 Comparison Table of Foundation Pit Heaving Analysis Based on Catastrophe Theory and Field Practice

[0075]

[0076] Note: 1. h1—Here, it is considered that there is no sandy soil above the upper part of the clay aquitard, and h crb —Critical head difference obtained by the calculation method based on catastrophe theory;

[0077] 2. In the table, the value of h crb is “—”, indicating that the value here is much larger than the value of H w .

[0078] It can be seen from Table 2 that the analysis of foundation pit heaving based on catastrophe theory is consistent with the actual on-site monitoring results. The heaving of Foundation Pit ④ occurred after the workers inserted steel rods into the holes during the construction process. If human factors are not considered, the foundation pit is also stable, which is consistent with the settlement results here. Furthermore, it is concluded that when the foundation pit width is very narrow relative to the foundation pit excavation depth, the foundation pit will not have the problem of heaving instability.

[0079] (2) Taking the above Foundation Pits ① and ② as examples, the thickness of the clay layer at the bottom of Foundation Pit ① is 1.7 m, and the foundation pit widths considered are 8.5 m, 10.2, 11.9, 13.6, 15.3, 17 m, 25.5 m, 34 m, 51 m respectively. The thickness of the clay layer at the bottom of Foundation Pit ② is 1.1 m, and the foundation pit widths considered are 5.5 m, 6.6, 7.7, 8.8, 9.9, 11 m, 16.5 m, 22 m, 33 m respectively. The ratios of these to the thickness of the clay aquitard are L / h2 = 5, 6, 7, 8, 9, 10, 15, 20, 30 respectively. For details, see Figure 3 .

[0080] From Figure 3 it can be seen that when L / h2 ≥ 10, the calculation results by the calculation method provided by the present invention are consistent with those of the traditional code method, indicating that the traditional code method is a simplified method of the method of the present invention; when L / h2 ≤ 6, the critical head difference of heaving is much larger than the head difference in the actual project, indicating that when the foundation pit width is relatively narrow and there is a relatively thick clay layer at the bottom of the pit, there will be no problem of the stability of the bottom of the pit against heaving; in the actual engineering application, when 6 < L / h2 < 10, the calculation method of the present invention can effectively calculate and analyze the stability of the bottom of the long and narrow foundation pit against heaving, and thus can provide an effective theoretical calculation tool.

[0081] Conclusion

[0082] (1) In view of the booming development of the current municipal long and narrow foundation pit construction, the present invention establishes a stress model of the key layer of viscous soil for foundation pit heaving based on the mutation theory, breaks through the overly conservative calculation method of the traditional code method in this field, and provides a feasible theoretical calculation method.

[0083] (2) The present invention is verified by combining specific engineering examples. The results show that it is feasible to use the calculation method of the present invention for the analysis of the anti-heaving of the foundation pit bottom, and the calculated judgment data obtained by the analysis is also consistent with the actual situation on site. Compared with the traditional method, it has obvious advantages, has a certain feasibility in the practical application of engineering construction, and can produce certain economic effects, especially for the long and narrow municipal engineering foundation pit, it is particularly effective, targeted and reasonable.

Claims

1. A calculation method for preventing upwelling in a long and narrow foundation pit, characterized in that The method includes the following steps: A. Establish a fixed-ended beam model based on the standard potential function form of the cusp catastrophe theory; V(x) = x 4 + ux 2 + vx The partial difference equation on the control variable plane: 8u 3 +27v 2 =0 Obtain the total potential energy function of the rock beam bending; B. Establish a force-bearing model for the foundation pit heave in combination with the characteristics of the long and narrow foundation pit project: According to the force balance, it can be known that Where: F s — Horizontal extrusion force; F r — Vertical upward extrusion force; λ— Lateral pressure coefficient; — Equivalent comprehensive internal friction angle; γ— Unit weight of soil; h— Foundation pit depth; L— Foundation pit width; Assume the deflection curve equation of the beam bending: Where: δ—the deflection at x = L / 2; The work done by the uniform load q is: Where: γ w — unit weight of water; γ1— unit weight of sandy soil; γ2— unit weight of cohesive soil; h w — head difference of confined aquifer inside and outside the pit; h1— thickness of sandy soil layer; h2— thickness of cohesive soil layer; C. Derive the potential energy function of the equivalent beam of the water-resistant cohesive soil layer at the bottom of the pit from the total potential energy function of the beam bending: Thus, it can be obtained that The sufficient condition for the initial fracture of the cohesive soil water-resistant layer is obtained as: Let: i.e. when Obtain the critical water head difference between the confined aquifers inside and outside the foundation pit for anti-heave:

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