CORE WALL-THINNING DESIGN METHOD FOR PRESTRESSED HIGH-PERFORMANCE CONCRETE CYLINDER PIPE

Abstract

A core wall-thinning design method for a prestressed high-performance concrete cylinder pipe is provided. The PCCP uses high-performance concrete, which includes P.O 42.5 or P.O 52.5 portland cement, river sand, mineral powder, fly ash, silica fume, steel fibers, polypropylene fibers, a high-efficiency polycarboxylate superplasticizer, and superabsorbent resin, and which is prepared by: adding all cementitious materials, sand and superabsorbent resin for mixing until uniform dispersion; dissolving the superplasticizer in water, and adding the superplasticizer dissolved in water and evenly stirring; and evenly adding steel fibers and polypropylene fibers and evenly stirring. The compressive strength and the tensile strength of the high-performance concrete are increased. A core wall-thinning design method, includes: establishing an axisymmetric double-layer ring plane strain model, to analyze radial displacement and circumferential stress of an outer ring and an inner ring of the PCCP, and then deriving a calculation formula of the wall-thinning design.

Claims

1. A core wall-thinning design method for a prestressed high-performance concrete cylinder pipe, comprising the following steps: replacing a core concrete of a prestressed concrete cylinder pipe (PCCP) with a high-performance concrete, and using the core wall-thinning design method to achieve wall-thinning of the PCCP.

2. The core wall-thinning design method according to claim 1, wherein in the step of replacing the core concrete of the PCCP with the high-performance concrete, the high-performance concrete comprises P.O 42.5 or P.O 52.5 portland cement, river sand, mineral powder, fly ash, silica fume, steel fibers, polypropylene fibers, a high-efficiency polycarboxylate superplasticizer, and superabsorbent resin.

3. The core wall-thinning design method according to claim 1, wherein in the step of replacing the core concrete of the PCCP with the high-performance concrete, a method for mixing the high-performance concrete comprises: adding cementitious materials, sand and the superabsorbent resin for dry mixing until a uniform dispersion to obtain a first mixture; dissolving the high-efficiency polycarboxylate superplasticizer in water to obtain a dissolved superplasticizer, and adding the dissolved superplasticizer to the first mixture to obtain a second mixture and evenly stirring the second mixture; and evenly adding the steel fibers and the polypropylene fibers to the second mixture to obtain a third mixture and evenly stirring the third mixture.

4. The core wall-thinning design method according to claim 1, wherein in the step of replacing the core concrete of the PCCP with the high-performance concrete, after the high-performance concrete is made, a core mold needs to be first cleaned up, a separator is evenly sprayed, a position of the core mold is fixed, and a cylinder is put into the core mold; the high-performance concrete is cast, a cast surface of an inner concrete is higher than a cast surface of an outer concrete, and a vibrator is turned on when feeding, until a concrete surface is free of bubbles and stops vibrating; after a core is formed, steam curing is performed, and a heating rate of the steam curing is configured to be less than or equal to 25/h; and a cubic test block is reserved in an identical batch during casting, and when a compressive strength of the cubic test block is greater than or equal to 36 MPa, the PCCP is allowed to be demolded and the core concrete is formed.

5. The core wall-thinning design method according to claim 1, wherein in the step of using the wall-thinning design method to achieve the wall-thinning of the PCCP, the core wall-thinning design method comprises the following steps: establishing an axisymmetric double-layer ring plane strain model, to separately analyze radial displacements and circumferential stresses of an outer ring and an inner ring of the PCCP, and deriving a calculation formula of a wall-thinning design of the PCCP.

6. The core wall-thinning design method according to claim 5, wherein the step of establishing the axisymmetric double-layer ring plane strain model comprises: simplifying the PCCP to the axisymmetric double-layer ring plane strain model, comprising converting the inner ring being defined as the core concrete plus a thickness of a cylinder into a cylinder concrete, and converting the outer ring being defined as a protective layer into the core concrete according to a cylinder stiffness contribution, wherein a conversion method is: $\begin{array}{cc}{t}_y^{}=\frac{E_y}{E_c}{t}_y& 1)\end{array}$ $\begin{array}{cc}t=t_y^{}+t_c& 2)\end{array}$ $\begin{array}{cc}t=r_p+r_1& 3)\end{array}$ wherein t.sub.y is the thickness of the cylinder, E.sub.y and E.sub.c are elastic modulus of the cylinder and the high-performance concrete, t.sub.y is a thickness of the cylinder concrete, t.sub.c and t are a concrete core and an effective thickness after a conversion, r.sub.1 is an inner diameter of the inner ring, and r.sub.p is an outer diameter of the inner ring; and the radial displacement of an inner water pressure on the inner ring, a preload pressure on the inner ring, and a contact stress of the outer ring on the inner ring is expressed as: $\begin{array}{cc}{}_{1p}=\frac{\left(1+{}_c\right)}{E_c}\frac{r_1^2{r}_p^2\left(q_1-q_2-q_c\right)}{\left(r_p^2-r_1^2\right)r}+\frac{\left(1-{}_c\right)}{E_c}\frac{q_1{r}_1^2-\left(q_2+q_c\right)r_p^2}{r_p^2-r_1^2}r& 4)\end{array}$ wherein q.sub.1 is the inner water pressure on the inner ring, q.sub.2 is the preload pressure on the inner ring, q.sub.c is the contact stress of the outer ring on the inner ring, .sub.c is a Poisson's ratio of the high-performance concrete, E.sub.c is the elastic modulus of the high-performance concrete, and .sub.1p is the radial displacement of the inner ring under a load; and the outer ring is only subjected to an interlayer contact stress of the inner ring on the outer ring, and the radial displacement of the outer ring under the load is expressed as: $\begin{array}{cc}{}_{2p}=\frac{\left(1+{}_m\right)}{E_m}\frac{r_p^2{r}_2^2{q}_c}{\left(r_2^2-r_p^2\right)r}+\frac{\left(1-{}_m\right)}{E_m}\frac{q_c{r}_p^2}{r_2^2-r_p^2}r& 5)\end{array}$ wherein .sub.m is a Poisson's ratio of the protective layer, E.sub.m is an elastic modulus of the protective layer, and .sub.2p is the radial displacement of the outer ring under the load; when the protective layer is further made of the high-performance concrete, .sub.m=.sub.c; and E.sub.m=E.sub.c; an inner side of the inner ring is a critical calculated cross-section, and the circumferential stress of the inner ring is expressed as: $\begin{array}{cc}{}_{1p}=\frac{r_1^2+r_p^2}{r_p^2-r_1^2}{q}_1-\frac{2r_p^2}{r_p^2-r_1^2}\left(q_2+q_c\right).& 6)\end{array}$

7. The core wall-thinning design method according to claim 5, wherein the core wall-thinning design method needs to take an impact of external loads comprising backfill soil, overburden soil, a pipe structure weight, water, and variable loads on the wall-thinning into consideration, and a circumferential stress generated by the external loads is expressed as: $\begin{array}{cc}{}_{p2t}=\frac{M_{\mathrm{pms}}}{{}_c{w}_p}& 7)\end{array}$ $\begin{array}{cc}{W}_p=\frac{{\mathrm{BT}}^2}{6}& 8)\end{array}$ $\begin{array}{cc}T=t_c+t_y+d_s+t_m& 9)\end{array}$ wherein M.sub.pms is a maximum bending moment of a cross-section caused by the external loads, W.sub.p is an elastic resistance moment of a tensile edge of all sections of a pipe wall without a conversion, and ye is a conversion coefficient of an elastic resistance moment of a tensile edge of an inner cross-section of the pipe wall, wherein a value of .sub.c is 0.9-1.1; B is a calculated cross-sectional width, and a value of B is 1000 mm; Tis a thickness of the pipe wall; and d.sub.s and t.sub.m are a diameter of a steel wire and a thickness of a protective layer.

8. The core wall-thinning design method according to claim 5, wherein a wall-thinning design calculation formula established according to the formulas 1-9 in the core wall-thinning design method is expressed as: $\begin{array}{cc}\frac{r_1^2+r_p^2}{r_p^2-r_1^2}{q}_1-\frac{2r_p^2}{r_p^2-r_1^2}\left(q_2+q_c\right)+\frac{M_{\mathrm{pms}}}{{}_c{W}_p}={}_{\mathrm{ct}}{f}_{\mathrm{tk}}& 10)\end{array}$ wherein .sub.ct is a tensile stress restriction factor, value ranges of the high-performance concrete and an ordinary concrete are 1.0-1.5 and 0.3-0.85, wherein the value ranges are selected according to different strengths of materials in a calculation, and f.sub.tk is an axial tensile strength of the high-performance concrete or the ordinary concrete; assuming that .sub.ctf.sub.tkM.sub.pms/(.sub.cW.sub.p)=F, a formula configured for solving a core thickness r.sub.p is obtained by simplifying an equation: $\begin{array}{cc}{a}_0{r}_p^4+b_0{r}_p^3+c_0{r}_p^2+d_0{r}_p+e_{0}0& 11)\end{array}$ $\begin{array}{cc}{a}_0=A_s{f}_{\mathrm{sg}}\left(1-{}_c\right)& 12)\end{array}$ $\begin{array}{cc}{b}_0=\left(r_2^2-r_1^2\right)F-\left(r_2^2+r_1^2\right)q_1& 13)\end{array}$ $\begin{array}{cc}{c}_0=A_s{f}_{\mathrm{sg}}\left[\left(1+{}_c\right)r_2^2+\left({}_c-1\right)r_1^2\right]& 14)\end{array}$ $\begin{array}{cc}{d}_0=\left(q_1+F\right)r_1^4+\left(q_1-F\right)r_1^2{r}_2^2& 15)\end{array}$ $\begin{array}{cc}{e}_0=-A_s{f}_{\mathrm{sg}}{r}_1^2{r}_2^2\left(1+{}_c\right)& 16)\end{array}$ a, b, c, d, eR, a0, and a double root discriminant is =B.sup.2.sub.04A.sub.0C.sub.0, and a formula for determining whether the PCCP is allowed to achieve the wall-thinning is expressed as: $\begin{array}{cc}{A}_0=D_0^2-3F_0& 17)\end{array}$ $\begin{array}{cc}{B}_0=D_0{F}_0-9E_0^2& 18)\end{array}$ $\begin{array}{cc}{C}_0=F_0^2-3D_0{E}_0^2& 19)\end{array}$ $\begin{array}{cc}{D}_0=3b_0^2-8a_0{c}_0& 20)\end{array}$ $\begin{array}{cc}{E}_0=-b_0^3+4a_0{b}_0{c}_0-8a_0^2{d}_0& 21)\end{array}$ $\begin{array}{cc}{F}_0=3b_0^4+16a_0^2{c}_0^2-16a_0{b}_0^2{c}_0+16a_0^2{b}_0{d}_0-64a_0^3{e}_0& 22)\end{array}$ wherein the wall-thinning of the PCCP is allowed to only be achieved when and only when >0, and because a<0, b<0, c>0 are constant, >0 is constant; there are two unequal real roots in the equation; and assuming that intermediate variables y.sub.1, y.sub.2, and y are: $\begin{array}{cc}{y}_1=A_0{D}_0+3\left(\frac{-B_0+\sqrt{B_0^2-4A_0{C}_0}}{2}\right),y_2=A_0{D}_0+3\left(\frac{-B_0-\sqrt{B_0^2-4A_0{C}_0}}{2}\right)& 23)\end{array}$ $\begin{array}{cc}y=D_0^2-D_0\left(\sqrt[3]{y_1}+\sqrt[3]{y_2}\right)+{\left(\sqrt[3]{y_1}+\sqrt[3]{y_2}\right)}^2-3A_0& 24)\end{array}$ and a real solution of a wall thickness r.sub.pd after replacing with the high-performance concrete is expressed as: $\begin{array}{cc}{r}_{\mathrm{pd},1}=\frac{\begin{array}{c}-b_0+\left[a.Math.b.Math.s.Math.\left(E_0\right)/E_0\right]\sqrt{\frac{D_0+\sqrt[3]{y_1}+\sqrt[3]{y_2}}{3}}+\\ \sqrt{\frac{2D_0-\left(\sqrt[3]{y_1}+\sqrt[3]{y_2}\right)+2\sqrt{y}}{3}}\end{array}}{4a_0}& 25)\end{array}$ $r_{\mathrm{pd},2}=\frac{\begin{array}{c}-b_0+\left[a.Math.b.Math.s.Math.\left(E_0\right)/E_0\right]\sqrt{\frac{D_0+\sqrt[3]{y_1}+\sqrt[3]{y_2}}{3}}-\\ \sqrt{\frac{2D_0-\left(\sqrt[3]{y_1}+\sqrt[3]{y_2}\right)+2\sqrt{y}}{3}}\end{array}}{4a_0}.$

9. The core wall-thinning design method according to claim 8, wherein a value of r.sub.pd in the core wall-thinning design method needs to satisfy r.sub.1<r.sub.pd<r.sub.1+t, and a maximum thickness of the wall-thinning is d.sub.p=r.sub.pr.sub.pd.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0029] To more clearly illustrate the technical solution of embodiments of the present invention, the drawings that need to be used in the descriptions of the embodiments are briefly introduced one by one. It is clear that the drawings in the following descriptions are some embodiments of the present invention, and for a person of ordinary skill in the art, other drawings can also be obtained according to the drawings without creative effort.

[0030] FIG. 1 is a diagram of a structure of a prestressed high-performance concrete cylinder pipe; and

[0031] FIGS. 2A-2C are schematic diagrams of stress analysis for calculating a wall-thinning thickness of a prestressed high-performance concrete cylinder pipe according to Embodiment 1.

[0032] In the figures, 1: inner core; 2: cylinder; 3: outer core; 4: prestressed steel wire; and 5: protective layer.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] To understand the objective, features, and advantages of the present invention more clearly, the present invention is further described below with reference to the accompanying drawings and embodiments. It should be noted that, without conflict, the embodiments of the present application and features in the embodiments may be combined with each other.

[0034] Many specific details are described in the following descriptions to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from the descriptions herein. Therefore, the present invention is not limited to the specific embodiments of the following disclosed specification.

[0035] Embodiment 1: This embodiment is designed to resolve a problem of unclear mix proportions of high-performance concrete as a replacement material. In view of this, recommended dosage ranges of cementitious materials and aggregates per cubic meter of the high-performance concrete according to this embodiment is shown in Table 1, and recommended volume dosage ranges of other materials per cubic meter of the high-performance concrete is shown in Table 2. A method for the preparation of the high-performance concrete includes: [0036] 1. Adding all cementitious materials, sand and superabsorbent resin for dry mixing until uniform dispersion; [0037] 2. Dissolving the superplasticizer in water, and adding the superplasticizer dissolved in the water to mixture and evenly stirring the mixture; and [0038] 3. Evenly adding steel fibers and polypropylene fibers to the mixture and evenly stirring the mixture, where a compulsory mixer for stirring is suggested.

[0039] To ensure the mechanical properties of the material, the high-performance concrete preparation process needs to strictly follow the mixing sequence as required above, and even stirring needs to be ensured at all links.

TABLE-US-00001 TABLE 1 Recommended Dosage Ranges of Cementitious Materials and Aggregates Per Cubic Meter of High-performance Concrete Ratio of Ratio of cementi- water and tious cementi- Mineral Silica materials tious Cement powder Fly ash fume and sand materials 40%-55% 10%-20% 10%-20% 15%-25% 0.8-1.2 0.18-0.22

TABLE-US-00002 TABLE 2 Recommended Volume Dosage Ranges of Other Materials Per Cubic Meter of High-performance Concrete Steel Polypropylene Superabsorbent fiber fiber resin Superplasticizer 0.5%-1.5% 0.5%-1.2% 0.3%-0.6% 1.5%-3%

[0040] The replacement of the high-performance concrete with the core significantly improves the mechanical properties and durability of the material, and improves the stress distribution of the core under external loads. The interplay of a plurality of factors provides optimization potential for lightweight pipe design.

[0041] Embodiment 2: This embodiment provides an example of wall-thinning calculation of a DN2000 prestressed high-performance concrete cylinder pipe.

[0042] Based on the DN2000 PCCP in the project, a core is replaced with high-performance concrete and the wall-thinning design is achieved. The basic geometric dimensioning of the pipe before the replacement is shown in Table 3.

TABLE-US-00003 TABLE 3 Geometric Dimensioning of DN2000 Prestressed High-performance Concrete Cylinder Pipe Pipe Steel Protective Steel inner Cylinder wire Core layer wire diameter thickness diameter thickness thickness area 2000 mm 1.5 mm 6 mm 125 mm 50 mm 1557 mm.sup.2

[0043] In addition, a covering depth of the pipe is 3 m, working internal pressure is 0.8 MPa, and designed internal water pressure is 1.12 Mpa. Sizes of each load under external loads is shown in Table 4.

TABLE-US-00004 TABLE 4 External Loads Action Values Vertical soil Lateral soil pressure pressure Pipe weight Fluid weight Variable loads 156.07 kN/m 24.91 kN/m.sup.2 24.59 kN/m 31.42 kN/m 10 kN/m.sup.2

[0044] The compressive strength of the high-performance concrete prepared by the foregoing mix ratio is 90 MPa, the tensile strength is 6.4 MPa, and a core wall-thinning thickness is about 22 mm through calculation. The thickness of the core after wall-thinning is 103 mm.

[0045] The foregoing descriptions are only better embodiments of the present invention and are not construed as any limitation on the present invention in other forms. Any person skilled in the art may change or modify the disclosed technical solutions into equivalent embodiments of equivalent changes for applications in other fields. Any simple modification, equivalent changes, and modifications made to the foregoing embodiments according to the technical essence of the present invention shall still fall within the protection scope of the technical solutions of the present invention without departing from the technical solutions of the present invention.