CN106884434A - The parameterization design method of circular Double-Wall Steel Boxed Cofferdam - Google Patents

Abstract

The present invention relates to a kind of parameterization design method of circular Double-Wall Steel Boxed Cofferdam, current method for designing is empirical method, during relative configurations dimensions decision scheme is similar to reference to sundry item, then relative dimensions are changed using finite element tentative calculation again, from the overall main points for holding Double-Wall Steel Boxed Cofferdam design calculating process can not be caused complicated, waste of material is big, part cofferdam structure stress is bigger than normal, and safety of structure is low.It is necessary in the case where entirety is considered, design calculation process to Double-Wall Steel Boxed Cofferdam carries out combing, by parameterizing calculation, the unified Rational structure for considering cofferdam, the rational structure and correlation computations formula of circular Double-Wall Steel Boxed Cofferdam design are given, facilitate cofferdam designer tentatively to draft cofferdam structure size；The Double-Wall Steel Boxed Cofferdam designed using the circular Double-Wall Steel Boxed Cofferdam contrast sundry item empirical method of Parametric designing, saves material usage 20%~35%, with great dissemination.

Description

The parameterization design method of circular Double-Wall Steel Boxed Cofferdam

Technical field

The present invention relates to the structure design of Double-Wall Steel Boxed Cofferdam.

Background technology

Double-Wall Steel Boxed Cofferdam is deepwater foundation construction common structure, and in general the Double-Wall Steel Boxed Cofferdam scale of construction is big, and security risk is high, It is the problem that cofferdam designer has to consider that Optimal Structure Designing is carried out while ensuring that double-walled steel cofferdam structure is safe.It is double , to resist based on hydrostatic pressure, flowing pressure and wave force are on the integrally-built influence in cofferdam for the basic force-bearing situation of wall steel cofferdam Relatively small, all kinds of cofferdam structure loads are simply clear and definite, with uniformity.The application is summarizing the basis of conventional sundry item On, it is proposed that the thinking of Parametric designing, and construct evaluation function and carry out bank structure optimization.

The content of the invention

The thinking of Parametric designing of the present invention：For the same problems in concrete structure, when structural load form is fixed, knot Structure size changes, and can carry out the alanysis of the separation of variable, and, structure optimization is only examined by the parameters separated with dimension out Consider configuration and proportionate relationship (dimensionless constant), the optimized design target of structure is determined by constructing evaluation function, so that Draw the optimal design of certain class formation.

The present invention the used technical scheme that solves the above problems is：

Circular Double-Wall Steel Boxed Cofferdam overall structure is as illustrated in fig. 1 and 2.The overall loading characteristic of circular Double-Wall Steel Boxed Cofferdam：Cofferdam Inside and outside wallboard, diagonal brace are pressurized；In horizontal extent, the hydraulic pressure in cofferdam is force self-balanced；Inside and outside cofferdam the thickness of wallboard and the depth of water into Direct ratio, is directly proportional to cofferdam diameter；Cofferdam resistance to overturning is related to cofferdam thickness, the local stability of cofferdam wallboard and central shoring It is related to vertical shifting board spacing.

A kind of parameterization design method of circular Double-Wall Steel Boxed Cofferdam, including

(1) wallboard ribbed stiffener inside and outside cofferdam

Three kinds of materials that the vertical ribbed stiffener of wallboard is typically used inside and outside cofferdam：Angle bar, steel band, flat-bulb steel；From equivalent weight Material is put more energy into from the point of view of effect, and the bigger flat-bulb steel of cross sectional moment of inertia effect of putting more energy into is best.

Effective the ratio between flange plate width and span are b=18%*l (iron Mo Xinke《Elastic theory》The third edition, P244)；

The proportional limit of ribbed stiffener depth-width ratio is h/t≤21 (iron Mo Xinke《Elastic stability theory》The second edition, P458)；Institute Some rolling angle bar and flat-bulb steel all meet proportional limit.

Meet between curved pressure component flange plate effective width b and edge of a wing plate thickness t：(GB50017- 2003《Code for design of steel structures》, P57)；

The spacing of ribbed stiffener generally according to(reference《The 2nd hull 2014 of steel seagoing vessel classification rules》 P2-254)；

The ratio of ring flat-plate and ribbed stiffener height is not less than 2.5 times of (references《The 2nd hull 2014 of steel seagoing vessel classification rules》 P2-112)；

According to《Hot rolling flat-bulb steel》(GB/T 9945-2012) specification, flat-bulb steel has carbon structural steel and high-strength steel, During design can according to stress situation come from different grades of steel, in general, the stress of ribbed stiffener is larger, panel should Power is relatively small, and ribbed stiffener strength of materials grade can a ratio panels specification high when choosing.

Table 1, cofferdam inside and outside wall reinforcing structure optimized dimensions table

Thickness	Recommendation ratio coefficient	Highly	Recommendation ratio coefficient
				Wall panel thickness t0	1t0	Ribbed stiffener height h1	16~20t0
Put more energy into rib thickness t1	1t0	Ring flat-plate height h2	>=2.5h1,50~60t0
				Ring flat-plate thickness t2	1.2~1.4t0	Ring flat-plate edge of a wing height h3	7~9t0
Separation plate thickness t3	1.4~1.6t0	Ribbed stiffener distance s	50~60t0

(2) cofferdam configuration

If circular cofferdam has n V-type to support, circular cofferdam configuration as shown in figure 4,

(3) cofferdam central shoring force analysis

As shown in figure 5, cofferdam wall shrinks prolongs radial direction compatibility of deformation

Outer wall node dynamic balance 2N1sin (φ)+2N3cos (α)=P1 (b)

Inwall node dynamic balance 2N2sin (φ) -2N3cos (β)=P2 (c)

Simultaneous (a), (b), (c) formula solve N1, N2, N3：

(3), (4) formula are investigated, due to φ value very littles, cos (α) ≈ cos (β), it is believed that N1 ≈ N2, the inside and outside wall in cofferdam Stress is basically identical, is unanimously processed according to inside and outside wallboard when cofferdam wall panel thickness is drafted；

(4) wall thickness is drafted inside and outside cofferdam

Wallboard stress is compression inside and outside cofferdam, and both stress are basically identical, it is considered to material factor K1, takes 1.4；

The inside and outside wall plate suqare in cofferdam

Wall panel thickness inside and outside cofferdam

(5) radius-thickness ratio scope in cofferdam is drafted

(5.1) cofferdam minimum radius-thickness ratio m：Cofferdam global stability analysis are as shown in Figure 6Iron Mo Xinke《Bullet Property stable theory》The second edition, P310 (a)

The Double-wall board the moment of inertia I in cofferdam：=2A (0.5mR)²(b)；

Cofferdam stabilization calculates radius r：=(1+0.5m) R (c)；

Cofferdam wallboard area

The hydraulic pressure load of cofferdam outer wall

q：=ρ gH Δs H (e)

Table 2, different specification stability analysis on the first type safety coefficient

Belong to major hazard source in view of steel cofferdam, it is proposed that elastic buckling coefficient of stability selection 4~5, selected within depth of water 10m 4, more than 10m select 5, and it is K2 to define the flexing coefficient of stability；

Then q_cr≥K2·q (f)；

(b), (c), (d), (e) are substituted into (a), and substitute into equation (f), abbreviation obtains below equation, solve the minimum value of m

Will play mould, the strength of materials, material factor, flexing safety coefficient substitute into (8) formula, obtain different materials intensity and Circular cofferdam minimum radius-thickness ratio m under the flexing coefficient of stability；

Circular cofferdam minimum radius-thickness ratio m under table 3, different materials intensity and the flexing coefficient of stability

Play mould E	Strength of materials σ	Material coefficient K1	Buckling coefficient K2	Minimum m values
					200E9	210E6	1.4	4	0.06428513072
200E9	310E6	1.4	4	0.07849940354
					200E9	210E6	1.4	5	0.07210171056
200E9	310E6	1.4	5	0.08800987764

(5.2) the cofferdam minimum thickness that detailing requiments need, unit:mm

The cofferdam minimum thickness of table 4, detailing requiments

(6) the vertical line space design of cofferdam central shoring

Cofferdam central shoring high computational schematic diagram, as shown in Figure 7

Tentatively draft vertical spacing h (n) of n-th layer of central shoring according to load etc. point principle, A1=A2=A3=A4=...= An, now it is considered that each strong point counter-force is basically identical；

q：=ρ gH (b)；

According to the bending rigidity that perpendicular ribbed belt plate is calculated, the positive hogging moment suffered by each perpendicular rib meets intensity requirement, and M/W=σ/ K；

(a), (b), (c) are substituted into formula (d), asks h (n) to obtain：

N=1 is substituted into formula (9), ground floor central shoring spacing is obtained

Remaining each layer meets with the relation of h (1)：

For convenience of processing, the central shoring material in cofferdam selects uniform sizes, while the vertical spacing of central shoring is adjusted into segmentation It is identical.Suggestion carrys out Uniting cofferdam central shoring spacing ratio according to following table：

Table 5, cofferdam designs central shoring spread ratio recommendation tables

(7) shifting board spacing in cofferdam is drafted

Line of deflection is as shown in Figure 10 during the wallboard local buckling of cofferdam, if wallboard warping function is ω (θ) during flexing；Then bend The line differential equation is：

M：=S ω (θ)-Qrsin (θ)； (b)

S：=qr, (c)

The differential equation is solved to obtain：

Investigate boundary condition：

ω ' (0)=0；ω(0)≠0； (d)

ω (α)=ω (- α)=0； (e)

From formula (d)

Below equation group is obtained from condition (e)：(g)

Therefore the condition for meeting above-mentioned equation group is：

Solve

Formula (11) is reduced to：

Table 6, the corresponding Buckling Loads of different shifting board quantity

Cofferdam shifting board quantity n	6	9	12	15	16	18
							Correspondence α angles (°)	30	20	15	12	11.25	10
COEFFICIENT K	8	19.25	35	55.25	63	80

The bending rigidity that I values are calculated for outer or inner ring plate with wallboard effective width band in formula (12), notes local buckling lotus Carry safety coefficient and take K2, K2 takes 4~5；

q_cr≥K₂·q；q：=ρ gH Δs H； (13)

Rigidity I and shifting board quantity n are considered according to formula (12), (13), according to construction proportional sizes above, to not Local buckling analysis tentative calculation is carried out with the cofferdam of depth, has recommended cofferdam shifting board quantity n >=12；

(8) cofferdam wall cabin concrete is highly drafted

Reclaim inconvenience under water in view of Double-Wall Steel Boxed Cofferdam, deduct reclaim after related diving cutting, lifting cost residual value compared with Low, in general concrete height in cofferdam wall cabin is preferably designed into cushion cap top surface；

When wall cabin concrete pouring is used using Double-Wall Steel Boxed Cofferdam, the part steel cofferdam stress in itself can be strongly reduced, phase The central shoring spacing for closing cofferdam can be tuned up, and wall panel thickness can be turned down, it is proposed that be set according to 0.4h (1), corresponding wall panel thickness This section of thickness is can also refer to set；Comprehensive should preferentially consider when cofferdam wall cabin concrete height is analyzed, the steel cofferdam of saving is made Valency is more than increased wall cabin concrete cost.

If cofferdam needs to cut riverbed certain depth, need to consider cofferdam subsidence factor in itself, then to determine cofferdam Highly, correlation computations parameter value refers to the chapters of CECS137-2015 the 6th to the concreting of wall cabin；

Sinking of cofferdam coefficient should meet following equation requirement：

In formula：k_st--- subsidence factor；

G_ik--- cofferdam deadweight standard value (including additional standard value for helping heavy amount, unit kN)；

F_wk--- uplift pressure standard value (unit kN) of sinking watching reclaimed water；

F_fk--- the total frictional resistance standard value (unit kN) in cofferdam；

When subsidence factor is larger, or when meeting soft layer in sinking watching, open caisson should be carried out according to actual conditions Sinking Stability Checking Calculation, and meet following equation requirement, or sinking stability is ensured using lifting measure：

k_{St, s}=0.8~0.9

In formula：Kst, s --- the sinking coefficient of stability；

F′_{Fw, k}--- the uplift pressure standard value (kN) of water under checking computations state；

F′_fw ^---- wall total frictional resistance standard value (kN) in cofferdam under checking computations state；

R_b ^---- cofferdam cutting shoe, partition wall and under bottom girder foundation soil ultimate bearing capacity sum (kN)；

(9) back cover thickness in cofferdam is drafted

The determination of cofferdam back cover thickness considers two factors of aspect；First is to consider that cofferdam whole anti-uplift coefficient is more than 1； Second is to consider that cofferdam back cover thickness resists the moment of flexure of hydraulic pressure；The maximum of both calculating is taken, then adds additional thickness D=300 ~500mm；

(clump of piles pile side friction in the range of G cofferdam+G back cover+back cover)/cofferdam gross buoyancy >=1；Concrete and stake week frictional resistance Power takes 100kPa；

The load that back cover concrete bears under water should be considered by worst situation in construction, i.e., after the back cover of cofferdam, cofferdam Interior water is drained from, and back cover plain concrete will be acted on by issuable upward maximum water pressure, generally with underground flood peak The load of gravity of bottom concrete is highly subtracted as calculated value；Because bottom concrete quality under water is compared with normal concrete Difference, and it is linked to be an entirety with each pile foundation, the two-way slab that should be supported by freely-supported is calculated, when bearing evenly load, mid span moment M1, M2 can be calculated as follows：

A in formula₁、a₂- bending moment coefficients, according to the form below is taken；

The load (KN/m2) that p- hydrostatic pressures are formed；

l₁The effective span (take minimum across) (m) of-rectangular slab；

Table 7, two-way slab bending moment coefficients table

									0.50	0.0994	0.0335	0.70	0.0732	0.0410	0.90	0.0516	0.0434
0.55	0.0927	0.0359	0.75	0.0673	0.0420	0.95	0.0471	0.0432
									0.60	0.0860	0.0379	0.80	0.0617	0.0426	1.00	0.0429
0.65	0.0795	0.0396	0.85	0.0564	0.0432

The THICKNESS CALCULATION of bottom concrete, is calculated as follows according to the moment M asked：

H- bottoming concrete thickness (mm) in formula；

K- safety coefficients, are 2.65 by the compression of calculation of Tensile Strength, flexural member；

The maximal bending moment (Nmm) of M- plates；

B- plates are wide, and unit length takes 1000mm；

f_ct- concrete tensile strength design load (Nmm2), C20 takes 1.1MPa；

D- considers the increase thickness that underwater concrete may be blended with soil under cofferdam, takes 300~500mm；

(10) cofferdam cutting shoe optimization design

Cofferdam cutting shoe structural map, as shown in figure 11,

Table 8, cofferdam cutting shoe construction computational chart

2nd, a kind of optimizing evaluation function of the circular Double-Wall Steel Boxed Cofferdam Parametric designing based on described in claim 1：For For some project, the height in cofferdam is always consistent, and short transverse can in an optimized fashion mainly by increasing vertical adding Strength rib rigidity, increases horizontal loops tie distance to realize, while can be whole to optimize by pouring the wall cabin concrete of proper height Body cofferdam；

To investigate the overall steel using amount index in cofferdam with the change of relation between radius-thickness ratio and diagonal brace quantity and angle, Lower surface construction one optimizing evaluation function f optimizes the influence of radius-thickness ratio and diagonal brace quantity to cofferdam steel using amount

In formula：

L --- element length (m)；

N --- element force (kN)；

K --- weight coefficient, tension is 1, and it is 2 to be pressurized；

Structure optimization index takes minimum value for f；

It is then 1 by all parameter whole values with dimensional unit by parameter l, N input function f,

Obtain below table：

Table 9, circular cofferdam parameter list

Recommended parameter m	Recommended parameter n	Type coefficient f	From anharmonic ratio
				1/13	96	3.733945419	1.00
1/12	80	3.775509722	1.01
				1/11	72	3.827159366	1.02
1/10	64	3.888713067	1.04
				1/9	60	3.967367385	1.06
1/8	60	4.070541290	1.09

As can be seen from the above table, with the increase of cofferdam radius-thickness ratio, being slowly increased, m values are from 1/13 for bank material quantity ~1/8, material quantity increase about 9%；

While cofferdam economy is considered, cofferdam resistance to overturning, cofferdam transportation by driving and suck sediment subsidence requirement are taken into full account, The cofferdam configuration of recommendation see the table below：

Table 10, cofferdam configuration selection table

Compared with prior art, the advantage of the invention is that：

Herein by the Optimal Structure Designing to circular Double-Wall Steel Boxed Cofferdam, circular Double-Wall Steel Boxed Cofferdam design process is deduced The formula that middle critical feature size is drafted, facilitates cofferdam designer quickly to draft cofferdam structure size in the design starting stage, Ensure that steel cofferdam overall structure meets force request, while ensure that the economy of Double-Wall Steel Boxed Cofferdam, set using above-mentioned formula The steel using amount index of the steel cofferdam of meter is about 52kg/m³Displacement；Contrast sundry item empirical method is designed to saving cofferdam and makes Valency 20%~35%, while ensure that cofferdam reasonable stress is controllable, with great dissemination.

Brief description of the drawings

Fig. 1 is Double-Wall Steel Boxed Cofferdam organigram；

Fig. 2 is the schematic cross-section of Double-Wall Steel Boxed Cofferdam construction；

Fig. 3 is the conventional mode of putting more energy into of cofferdam wallboard；

Fig. 4 is circular cofferdam configuration picture；

Fig. 5 is cofferdam central shoring stressing conditions；

Fig. 6 is cofferdam global stability analysis；

Fig. 7 is cofferdam central shoring high computational schematic diagram；

Fig. 8 is every layer of central shoring height and ground floor proportionate relationship；

Fig. 9 is central shoring total height and ground floor proportionate relationship；

Line of deflection when Figure 10 is cofferdam wallboard local buckling；

Figure 11 is cofferdam cutting shoe structural map.

The cutting shoe of 8 shifting board of rib 5 outer ring plate, 6 diagonal brace, 7 inner ring plate 9 is erected in the outer perpendicular rib 4 of the inwall of 1 exterior panel 2 version 3 The back cover concrete of 10 11 cushion cap concrete of wall cabin concrete 12

Specific embodiment

The present invention is described in further detail below in conjunction with accompanying drawing embodiment.

Circular Double-Wall Steel Boxed Cofferdam Parametric designing application of result

Wuxue City Changjiang River Highway Bridge Bei Ta is deep water foundation, and designing unit and unit in charge of construction set up during basic engineering Computer MSR Information system, the design and construction global optimization for northern tower foundation has done abundant research, and the final cofferdam structure for determining is dumbbell Type Double-Wall Steel Boxed Cofferdam, the physical dimension in cofferdam has been drafted according to circular Double-Wall Steel Boxed Cofferdam Parametric designing, is checked by finite element Simulation, the specific size and result of calculation in cofferdam is as follows, and steel using amount index is 52kg/m³Displacement, it is similar better than other bridges Cofferdam structure.

Table 11, Wuxue City Changjiang River Highway Bridge 15# dumbbell shapes cofferdam size table

Cushion cap internal diameter	Cushion cap length	Cofferdam wall thickness	Cofferdam is highly
				28.8m	58.8m	1.8m	31m
Cofferdam embedded depth	Cofferdam total displacement	Cofferdam gross weight (is free of drilling platform)	Cofferdam steel using amount index
				14m		2705t

Table 12, Wuxue City's Changjiang River Highway Bridge 15# Double-Wall Steel Boxed Cofferdam Load Combination tables

Table 13, Wuxue City's Changjiang River Highway Bridge 15# Double-Wall Steel Boxed Cofferdam result of calculations

Table 14, cofferdam structure steel using amount statistical form

Claims (2)

1. a kind of parameterization design method of circular Double-Wall Steel Boxed Cofferdam, including

(1) wallboard ribbed stiffener inside and outside cofferdam

Three kinds of materials that the vertical ribbed stiffener of wallboard is typically used inside and outside cofferdam：Angle bar, steel band, flat-bulb steel；

Effective the ratio between flange plate width and span are b=18%*l；

The proportional limit of ribbed stiffener depth-width ratio is h/t≤21；All of rolling angle bar and flat-bulb steel all meet proportional limit；

Meet between curved pressure component flange plate effective width b and edge of a wing plate thickness t：

The spacing of ribbed stiffener generally according to

The ratio of ring flat-plate and ribbed stiffener height is not less than 2.5 times；

(2) cofferdam configuration

If circular cofferdam has n V-type to support,

$\mathrm{\φ}:=\frac{\mathrm{\π}}{n},\frac{\sin \left(\mathrm{\φ}\right)}{a}=\frac{sin\left(\mathrm{\α}\right)}{R},\frac{\sin \left(\mathrm{\φ}\right)}{a}=\frac{sin(\mathrm{\π}-\mathrm{\α}-\mathrm{\φ})}{(1+m)\·R}---\left(a\right)$

$a:=\sqrt{-2cos\left(\mathrm{\φ}\right)m+m^2-2cos\left(\mathrm{\φ}\right)+2m+2}R---\left(1\right)$

$\mathrm{\α}:=arcsin\left(\frac{sin\left(\mathrm{\φ}\right)}{\sqrt{2-2cos\left(\mathrm{\φ}\right)m+m^2-2cos\left(\mathrm{\φ}\right)+2m}}\right)---\left(2\right)$

(3) cofferdam central shoring force analysis

Cofferdam wall shrinks and prolongs radial direction compatibility of deformation

Outer wall node dynamic balance 2N1sin (φ)+2N3cos (α)=P1 (b)

Inwall node dynamic balance 2N2sin (φ) -2N3cos (β)=P2 (c)

Simultaneous (a), (b), (c) formula solve N1, N2, N3：

$\begin{array}{c}N1\\ =\frac{1}{2}\left(A1\right(A2\sin \left(\mathrm{\φ}\right)\cos \left(\mathrm{\α}\right)P1l3+A3\cos \left(\mathrm{\β}\right)P1R+A3\cos \left(\mathrm{\α}\right)P2R\left)\right)/\\ \left(\right(A1A2\cos \left(\mathrm{\α}\right)l3\sin \left(\mathrm{\φ}\right)+RA3\cos \left(\mathrm{\α}\right)A2m+R\cos \left(\mathrm{\β}\right)A1A3\\ +RA3\cos \left(\mathrm{\α}\right)A2\left)\sin \left(\mathrm{\φ}\right)\right)\end{array}---\left(3\right)$

$\begin{array}{c}N2=\frac{1}{2}\left(A2\right(A1\sin \left(\mathrm{\φ}\right)\cos \left(\mathrm{\α}\right)P2l3+A3\cos \left(\mathrm{\β}\right)P1Rm+A3\cos \left(\mathrm{\α}\right)P2Rm\\ +A3\cos \left(\mathrm{\β}\right)P1R+A3\cos \left(\mathrm{\α}\right)P2R\left)\right)/\left(A1A2\cos \right(\mathrm{\α})l3\sin \left(\mathrm{\φ}\right)+RA3\cos \left(\mathrm{\α}\right)A2m\\ +R\cos \left(\mathrm{\β}\right)A1A3+RA3\cos \left(\mathrm{\α}\right)A2\left)\sin \left(\mathrm{\φ}\right)\right)\end{array}---\left(4\right)$

$N3=-\frac{1}{2}\frac{RA3(-A2P1m+A1P2-A2P1)}{A1A2\cos \left(\mathrm{\α}\right)l3\sin \left(\mathrm{\φ}\right)+RA3\cos \left(\mathrm{\α}\right)A2m+R\cos \left(\mathrm{\β}\right)A1A3+RA3\cos \left(\mathrm{\α}\right)A2}---\left(5\right)$

Investigate (3), (4) formula, due to φ value very littles, cos (α) ≈ cos (β), it is believed that N1 ≈ N2, the inside and outside wall stress in cofferdam It is basically identical, unanimously processed according to inside and outside wallboard when cofferdam wall panel thickness is drafted；

(4) wall thickness is drafted inside and outside cofferdam

Wallboard stress is compression inside and outside cofferdam, and both stress are basically identical, it is considered to material factor K1, takes 1.4；

The inside and outside wall plate suqare in cofferdam

Wall panel thickness inside and outside cofferdam

(5) radius-thickness ratio scope in cofferdam is drafted

(5.1) cofferdam minimum radius-thickness ratio m：

$q_{cr}:=\frac{3\·E\·I}{r^3}---\left(a\right)$

The Double-wall board the moment of inertia I in cofferdam：=2A (0.5mR)²(b)；

Cofferdam stabilization calculates radius r：=(1+0.5m) R (c)；

Cofferdam wallboard area

The hydraulic pressure load of cofferdam outer wall

q：=ρ gH Δs H (e)

Belong to major hazard source in view of steel cofferdam, it is proposed that elastic buckling coefficient of stability selection 4~5,4 selected within depth of water 10m, More than 10m selects 5, and it is K2 to define the flexing coefficient of stability；

Then q_cr≥K2·q (f)；

(b), (c), (d), (e) are substituted into (a), and substitute into equation (f), abbreviation obtains below equation, solve the minimum value of m

$(\frac{3}{4}\·K1\·E-\frac{1}{8}\·K2\·\mathrm{\σ})\·m^3+(\frac{3}{4}\·K1\·E-\frac{5}{4}\·K2\·\mathrm{\σ})\·m^2-1.5\·K2\·\mathrm{\σ}\·m-K2\·\mathrm{\σ}=0;---\left(8\right)$

Mould, the strength of materials, material factor, flexing safety coefficient will be played and substitute into (8) formula, obtain different materials intensity and flexing Circular cofferdam minimum radius-thickness ratio m under the coefficient of stability；

(5.2) the cofferdam minimum thickness that detailing requiments need, unit:mm

(6) the vertical line space design of cofferdam central shoring

Tentatively draft vertical spacing h (n) of n-th layer of central shoring according to load etc. point principle, A1=A2=A3=A4=...=An, this When can consider that each strong point counter-force is basically identical；

$H:=\frac{h\left(n\right)\·\left(\sqrt{n}\right)}{\sqrt{n}-\sqrt{n-1}}---\left(a\right);$

q：=ρ gH (b)；

According to the bending rigidity that perpendicular ribbed belt plate is calculated, the positive hogging moment suffered by each perpendicular rib meets intensity requirement, M/W=σ/K；

$M:=\frac{1}{12}\·q\·b\·h{\left(n\right)}^2---\left(c\right);$

$\frac{M}{W}\·K\≤\mathrm{\σ}---\left(d\right);$

(a), (b), (c) are substituted into formula (d), asks h (n) to obtain：

$h\left(n\right)={12}^{1/3}{\left(\frac{\mathrm{\σ}(\sqrt{n}-\sqrt{n-1})W}{\mathrm{\ρ}g\sqrt{n}bK}\right)}^{1/3}---\left(9\right);$

N=1 is substituted into formula (9), ground floor central shoring spacing is obtained

Remaining each layer meets with the relation of h (1)：

(7) shifting board spacing in cofferdam is drafted

If wallboard warping function is ω (θ) during flexing；Then deflection differential equation is：

${\mathrm{\ω}}^{\′\′}\left(\mathrm{\θ}\right)+\mathrm{\ω}\left(\mathrm{\θ}\right)=-\frac{r^2}{EI}\·M;---\left(a\right)$

M：=S ω (θ)-Qrsin (θ)； (b)

S：=qr, (c)

The differential equation is solved to obtain：

$\mathrm{\ω}\left(\mathrm{\θ}\right):=\sin \left(\frac{\sqrt{{\mathrm{Sr}}^2+EI}\mathrm{\θ}}{\sqrt{EI}}\right)\_C2+cos\left(\frac{\sqrt{{\mathrm{Sr}}^2+EI}\mathrm{\θ}}{\sqrt{EI}}\right)\_C1+\frac{\sin \left(\mathrm{\θ}\right)Qr}{s};---\left(10\right)$

Investigate boundary condition：

ω ' (0)=0；ω(0)≠0； (d)

ω (α)=ω (- α)=0； (e)

From formula (d)

Below equation group is obtained from condition (e)：(g)

$\frac{\sin \left(\frac{\sqrt{{\mathrm{Sr}}^2+EI}\mathrm{\α}}{\sqrt{EI}}\right)Qr\sqrt{EI}}{\sqrt{{\mathrm{Sr}}^2+EI}S}+\cos \left(\frac{\sqrt{{\mathrm{Sr}}^2+EI}\mathrm{\α}}{\sqrt{EI}}\right)\_C1-\frac{\sin \left(\mathrm{\α}\right)Qr}{S}=0$

$-\frac{\sin \left(\frac{\sqrt{{\mathrm{Sr}}^2+EI}\mathrm{\α}}{\sqrt{EI}}\right)Qr\sqrt{EI}}{\sqrt{{\mathrm{Sr}}^2+EI}S}+\cos \left(\frac{\sqrt{{\mathrm{Sr}}^2+EI}\mathrm{\α}}{\sqrt{EI}}\right)\_C1+\frac{\sin \left(\mathrm{\α}\right)Qr}{S}=0$

Therefore the condition for meeting above-mentioned equation group is：

Solve

$qcr:=\frac{1}{4}\frac{EI({\mathrm{\π}}^2-4{\mathrm{\α}}^2)}{{\mathrm{\α}}^2{r}^3};---\left(11\right)$

Formula (11) is reduced to：

The bending rigidity that I values are calculated for outer or inner ring plate with wallboard effective width band in formula (12), notices that local buckling load is pacified Overall coefficient takes K2, and K2 takes 4~5；

q_cr≥K₂·q；q：=ρ gH Δs H； (13)

Rigidity I and shifting board quantity n are considered according to formula (12), (13), according to construction proportional sizes above, to different depths The cofferdam of degree has carried out local buckling analysis tentative calculation, recommends cofferdam shifting board quantity n >=12；

(8) cofferdam wall cabin concrete is highly drafted

Inconvenience is reclaimed under water in view of Double-Wall Steel Boxed Cofferdam, and recovery residual value is relatively low after deducting related diving cutting, lifting cost, one As for cofferdam wall cabin concrete height be preferably designed into cushion cap top surface；

When wall cabin concrete pouring is used using Double-Wall Steel Boxed Cofferdam, the part steel cofferdam stress in itself can be strongly reduced, and correlation is enclosed The central shoring spacing on weir can be tuned up, and wall panel thickness can be turned down, it is proposed that be set according to 0.4h (1), and corresponding wall panel thickness also may be used Set with reference to this section of thickness；

If cofferdam needs to cut riverbed certain depth, need to consider cofferdam subsidence factor in itself, then to determine cofferdam wall cabin Highly, correlation computations parameter value refers to the chapters of CECS137-2015 the 6th for concreting；

Sinking of cofferdam coefficient should meet following equation requirement：

$k_{st}\≥1.05;k_{st}:=\frac{G_{ik}-F_{wk}}{F_{fk}};---\left(14\right)$

In formula：k_st--- subsidence factor；

G_ik--- cofferdam deadweight standard value (including additional standard value for helping heavy amount, unit kN)；

F_wk--- uplift pressure standard value (unit kN) of sinking watching reclaimed water；

F_fk--- the total frictional resistance standard value (unit kN) in cofferdam；

When subsidence factor is larger, or when meeting soft layer in sinking watching, the sinking of open caisson should be carried out according to actual conditions Stability Checking Calculation, and meet following equation requirement, or sinking stability is ensured using lifting measure：

k_{St, s}=0.8~0.9

$k_{st,s}=\frac{G_{ik}-{F^{\′}}_{fw,k}}{{F^{\′}}_{fw}+R_b}---\left(15\right)$

In formula：Kst, s --- the sinking coefficient of stability；

F′_{Fw, k}--- the uplift pressure standard value (kN) of water under checking computations state；

F′_fw- --- wall total frictional resistance standard value (kN) in cofferdam under checking computations state；

R_b- --- cofferdam cutting shoe, partition wall and under bottom girder foundation soil ultimate bearing capacity sum (kN)；

(9) back cover thickness in cofferdam is drafted

The determination of cofferdam back cover thickness considers two factors of aspect；First is to consider that cofferdam whole anti-uplift coefficient is more than 1；Second It is to consider that cofferdam back cover thickness resists the moment of flexure of hydraulic pressure；The maximum of both calculating is taken, then plus additional thickness D=300~ 500mm；

(clump of piles pile side friction in the range of G cofferdam+G back cover+back cover)/cofferdam gross buoyancy >=1；Concrete takes with pile perimeter resistance 100kPa；

The load that back cover concrete bears under water should be considered by worst situation in construction, i.e., after the back cover of cofferdam, in cofferdam Water is drained from, and back cover plain concrete will be acted on by issuable upward maximum water pressure, generally with underground flood peak highly The load of gravity of bottom concrete is subtracted as calculated value；Because bottom concrete quality is poor compared with normal concrete under water, and It is linked to be an entirety with each pile foundation, the two-way slab that should be supported by freely-supported is calculated, and when bearing evenly load, mid span moment M1, M2 can It is calculated as follows：

$\begin{array}{cc}{M}_1=a_1{\mathrm{pl}}_1^2& M_2=a_2{\mathrm{pl}}_2^2\end{array}$

A in formula₁、a₂- bending moment coefficients, according to the form below is taken；

The load (KN/m2) that p- hydrostatic pressures are formed；

l₁The effective span (take minimum across) (m) of-rectangular slab；

Two-way slab bending moment coefficients table

The THICKNESS CALCULATION of bottom concrete, is calculated as follows according to the moment M asked：

$h=\sqrt{\frac{3.5K\·M}{b\·f_{ct}}}+D$

H- bottoming concrete thickness (mm) in formula；

K- safety coefficients, are 2.65 by the compression of calculation of Tensile Strength, flexural member；

The maximal bending moment (Nmm) of M- plates；

B- plates are wide, and unit length takes 1000mm；

f_ct- concrete tensile strength design load (Nmm2), C20 takes 1.1MPa；

D- considers the increase thickness that underwater concrete may be blended with soil under cofferdam, takes 300~500mm；

(10) cofferdam cutting shoe optimization design

Cofferdam cutting shoe structural map,

Cofferdam cutting shoe construction computational chart

2. a kind of optimizing evaluation function of the circular Double-Wall Steel Boxed Cofferdam Parametric designing based on described in claim 1：For specific Project for, the height in cofferdam is always consistent, and short transverse can in an optimized fashion mainly by increasing vertical ribbed stiffener Rigidity, increases horizontal loops tie distance to realize, while overall enclosing can be optimized by pouring the wall cabin concrete of proper height Weir；

To investigate the overall steel using amount index in cofferdam with the change of relation between radius-thickness ratio and diagonal brace quantity and angle, below An optimizing evaluation function f is constructed to optimize the influence of radius-thickness ratio and diagonal brace quantity to cofferdam steel using amount

$f:=\underset{i=1}{\overset{n}{\Σ}}{l}_i{N}_i{K}_i---\left(16\right)$

In formula：

L --- element length (m)；

N --- element force (kN)；

K --- weight coefficient, tension is 1, and it is 2 to be pressurized；

Structure optimization index takes minimum value for f；

It is then 1 by all parameter whole values with dimensional unit by parameter l, N input function f,

Obtain below table：

Circular cofferdam parameter list

Recommended parameter m Recommended parameter n Type coefficient f From anharmonic ratio 1/13 96 3.733945419 1.00 1/12 80 3.775509722 1.01 1/11 72 3.827159366 1.02 1/10 64 3.888713067 1.04 1/9 60 3.967367385 1.06 1/8 60 4.070541290 1.09

As can be seen from the above table, with the increase of cofferdam radius-thickness ratio, being slowly increased, m values are from 1/13~1/ for bank material quantity 8, it is consequently increased 9% from anharmonic ratio；

While cofferdam economy is considered, cofferdam resistance to overturning, cofferdam transportation by driving and suck sediment subsidence requirement are taken into full account, recommended Cofferdam configuration see the table below：

Cofferdam configuration selection table