CN102087677A - Method for solving solution of elastic foundation beams and for back analysis of value m - Google Patents
Method for solving solution of elastic foundation beams and for back analysis of value m Download PDFInfo
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Abstract
The invention provides a method for solving solution of elastic foundation beams and for back analysis of value m, belonging to the technical field of geotechnical engineering. The method comprises the following steps of: 1, firstly, converting a fourth order partial differential equation of the elastic foundation beam into a low order partial differential equation set, and setting iteration times and admissible errors; 1, taking a minimum error function of a displacement value sol.y obtained in the step one and an actually-measured displacement value as an objective function, wherein the minimum error function is the sum of squares of difference values; 3, optimizing the objective function in the second step by the application of MATLAB nonlinear optimization algorithm fmincon functions, when reaching the iteration times or the admissible errors set in the first step, stopping iteration, and in this case, the objective function reaching the minimum value; and 4, the parameters corresponding to the minimum value of the objective function being the optimum solution of horizontal resistance factor value m of the to-be-determined soil layer foundation soil. The method provided by the invention is simple in analysis process and easy for programming.
Description
Technical field
The present invention relates to finding the solution and m value inverse analysis method of a kind of beam on elastic foundation, belong to the technical field of Geotechnical Engineering.
Background technology
Along with the development of China's skyscraper and urban underground space, the scale and the quantity of base pit engineering constantly enlarge, and deep big foundation pit is also had higher requirement to supporting construction design simultaneously.Because the city deep big foundation pit is usually located at the prime location, city; the supporting design not only will guarantee the safety and stablization of foundation ditch itself; but also the distortion of wanting effectively to control foundation ditch is with protection neighboring buildings environmentAL safety, and tradition is designed to main mode with strength control and is replaced by the mode based on Deformation Control Design gradually.Elastic foundation method can be considered the equilibrium condition of retaining structure and the interaction of structure and soil, desired parameters is single in the analysis, and can effectively consider excavation of foundation pit, return and to build in the process various Fundamentals and complex situations the influence of supporting construction internal force and distortion, can estimate the distortion of supporting construction preferably, and obtaining structural internal force with the The deformation calculation analysis, result of calculation is also more near actual conditions.So elastic foundation method has become important computing method and the means of retaining structure design, obtain widespread use, for example " building foundation pit supporting technical regulation " (JGJ120-99) (DGTJ08-61-2010) waits all recommendations to adopt elastic foundation method with " Shanghai City base pit engineering technical manual ".
For simple load and Simple Boundary Conditions, beam on elastic foundation has analytic solution at present.But for the foundation pit supporting construction of reality, load and border condition more complicated can't be tried to achieve analytic solution.The means of general at present employing numerical analysis are found the solution beam on elastic foundation, mainly contain leverage finite element method and method of finite difference, but difficulty is all compared in these two kinds of methods programmings.
Key parameter in the beam on elastic foundation is the horizontal resistance coefficient m value of foundation soil, and standard determines that m value method mainly contains single pile horizontal loading test method(s) and experimental formula computing method at present.Single pile horizontal loading test method(s) is the method according to the test of single pile horizontal loading, be actually the method for calculating the used definite m value of stake horizontal bearing capacity in the civil engineering work of using, calculate the m value according to the static test achievement, but there is following subject matter in this method: 1. adopt chance less, specially to carry out the chance of the horizontal static test of single pile few for specific base pit engineering; 2. the stake top displacement of adopting is unreasonable.Because the horizontal shift at the end, hole is generally all bigger than the displacement on stake top; 3. fail layering and determine the m value.The experimental formula computing method is the method that " building foundation pit supporting technical regulation " provides in (JGJ120-99), can determine m value according to the intensive parameter index (cohesive strength and angle of internal friction) and the hole end displacement of soil, and still cheating end displacement defines very big randomness.
Because m value can't obtain with the shop experiment method, value by rule of thumb often on the present engineering has bigger randomness; What inverse analysis method application at present was more is that positive analysis adopts the leverage Finite Element Method, and unconfined simplicial method is adopted in back analysis.The programming of positive analysis leverage Finite Element Method is complicated, and how back analysis simplicial method in addition calls positive analysis also is a difficult problem that does not have fine solution.
Summary of the invention
It is simple that the object of the invention provides a kind of analytic process, beam on elastic foundation method for solving that is easy to programme and m value inverse analysis method.
Finding the solution and m value inverse analysis method of a kind of beam on elastic foundation comprises the steps:
The first step: at first the quadravalence partial differential equation with beam on elastic foundation is converted to the low order partial differential equations, adopt the function bvp4c that finds the solution boundary value partial differential equations among the MATLAB to find the solution, concrete statement is sol=bvp4c (@odefun, @bcfun, solinit, and iterations and allowable error be set options); Wherein sol is a solving result, wherein sol.y be beam on elastic foundation around song distortion y, odefun is the m documentation function of finding the solution the beam on elastic foundation equation, bcfun is the m documentation function of beam on elastic foundation boundary condition; Solinit is a starting condition; Options is an options;
Second step: the shift value sol.y that the first step is obtained and the smallest error function of measured displacements value be as objective function, smallest error function be squared difference with;
The 3rd step: use MATLAB nonlinear optimization algorithm fmincon function second objective function that goes on foot is optimized, behind the iterations or allowable error that reach first step setting, stop iteration, this moment, objective function reached minimum value;
The 4th step: objective function minimum value, corresponding parameters are the optimum solution of the horizontal resistance coefficient m value of soil ground soil undetermined.
The present invention adopts technique scheme, compared with prior art have following advantage: the present invention is converted to the low order partial differential equations with the quadravalence partial differential equation of beam on elastic foundation, adopt the function bvp4c that separates boundary value partial differential equations among the MATLAB to find the solution this partial differential equations, programming is than being easier to; To be converted to the typical nonlinear optimization problem according to actual measurement distortion inverse m value problem, and adopt the function f mincon that nonlinear programming is found the solution among the MATLAB to find the solution, programming is simple, the efficient height; The MATLAB function is all adopted in positive analysis and back analysis, and positive back analysis slitless connection has solved the traditional elastic grade beam and found the solution the difficult problem that back analysis can't be called the positive analysis result.The present invention obtains realistic m value by displacement back analysis technology, and it can not only reflect the character of the excavation side soil body itself, and is the embodiment of whole some X factor of retaining structure system, has important practical significance.
Description of drawings
Fig. 1 is the comparison synoptic diagram of excavation of foundation pit of the present invention computation optimization value and field measurement value during to 9.5m.
Fig. 2 is the comparison synoptic diagram of excavation of foundation pit of the present invention computation optimization value and field measurement value during to 12.7m.
Fig. 3 is the comparison synoptic diagram of excavation of foundation pit of the present invention computation optimization value and field measurement value during to 15.27m.
Embodiment
Finding the solution and m value inverse analysis method of a kind of beam on elastic foundation comprises the steps:
The first step: at first the quadravalence partial differential equation with beam on elastic foundation is converted to the low order partial differential equations, adopt the function bvp4c that finds the solution boundary value partial differential equations among the MATLAB to find the solution, concrete statement is sol=bvp4c (@odefun, @bcfun, solinit, and iterations and allowable error be set options); Wherein sol is a solving result, wherein sol.y be beam on elastic foundation around song distortion y, odefun is the m documentation function of finding the solution the beam on elastic foundation equation, bcfun is the m documentation function of beam on elastic foundation boundary condition; Solinit is a starting condition; Options is an options;
Second step: the shift value sol.y that the first step is obtained and the smallest error function of measured displacements value be as objective function, smallest error function be squared difference with;
The 3rd step: use MATLAB nonlinear optimization algorithm fmincon function second objective function that goes on foot is optimized, behind the iterations or allowable error that reach first step setting, stop iteration, this moment, objective function reached minimum value;
The 4th step: objective function minimum value, corresponding parameters are the optimum solution of the horizontal resistance coefficient m value of soil ground soil undetermined.
The core thinking of finding the solution the beam on elastic foundation equation based on MATLAB is: according to " building foundation pit supporting technical regulation " (JGJ120-99), as the perpendicular beam on elastic foundation that places soil, its Flexural Equation is described by the beam on elastic foundation equation with support pile:
In the formula: EI is the bendind rigidity of supporting construction, and unit is kN * m2; b
0Be the supporting construction molded breadth, unit is m; M is the horizontal resistance coefficient of foundation soil, and unit is kN/m4; b
sBe outside active load action width, campshed is got pile spacing, and diaphram wall is got unit width, and unit is m; H is the excavation of foundation pit degree of depth, and unit is m; e
AikBe active earth pressure intensity, unit is kPa; Z is a coordinate; D is the partial differential symbol; Y is the horizontal deflection distortion of waiting to ask supporting construction.
The grade beam up and down constraint condition at two ends is the boundary condition of beam on elastic foundation equation, mainly divide stiff end (
,
), simply supported end (
,
) and free end (
,
) three kinds of boundary conditions.
The ordinary differential equation boundary value problem that beam on elastic foundation equation and boundary condition constitute together its essence is a partial differential equation of higher order, with the derivative depression of order of the differential equation, even
,
,
,
, then the beam on elastic foundation equation becomes:
（2a）；
Equation (2a)-(2d2) and boundary condition promptly constitute an ordinary differential equation boundary value problem together, can adopt the function bvp4c that finds the solution boundary value partial differential equations among the MATLAB to find the solution.
Embodiment
Track traffic line Cang Jie station in Suzhou is underground two floor island formulas, station structure top board absolute altitude is about 0.00m(1985 country height datum), station structure base plate absolute altitude is about-11.29m, effectively platform central track top mark is high is-10.033m, main body is about 122m, wide about 20m.The station agent structure adopts the continuous underground wall structure of 800mm, and the ground-connecting-wall degree of depth is 28m, and first road supports the reinforced concrete that adopts 800mm * 800mm and supports, and support stiffness is 340MN/m
2; Two～four roads employing φ 609mm(t=16mm) steel supports, and the rigidity of support is 174MN/m
2
The supposition underground water table is 0.5m in the calculating, the soil pressure that adopts water and soil to divide the calculation pattern to calculate supporting construction, and the ground overload is 20kN/m
2, the following active region soil pressure of excavation of foundation pit face is a rectangular distribution.The soil layer physical mechanical property index sees Table 1.
Table 1 Cang Jie station soil mass of foundation pit physical parameter
| The soil body number and title | Severe (KN/m 3） | Thickness (m) | Cohesive strength KPa | Angle of internal friction ( 0） |
| 1. 1 plain fill | 18 | 0.7 | 6 | 12 |
| 1. 2 plain fills | 19 | 1.7 | 12 | 12 |
| 3. 1 silty clay | 19.7 | 2.2 | 35 | 15.6 |
| 3. 2 silty claies | 19.3 | 2.8 | 15 | 16.5 |
| 4. 1a silty clay | 19.2 | 2.2 | 9 | 18.5 |
| 4. 1 silt | 18.9 | 1.6 | 9.2 | 25.6 |
| 4. 2 flour sands, silt | 19 | 6.6 | 8.4 | 27.5 |
| 5. silty clay | 19 | 5.3 | 9 | 17.5 |
| 6. 1 silty clay | 20.2 | 5.8 | 36.6 | 16.5 |
The excavation of foundation pit operating mode is as follows:
Operating mode one: excavation 1.5m;
Operating mode two: add the first road reinforced concrete at the 1.0m place and support;
Operating mode three: be excavated to 5.9m;
Operating mode four: add the brace pre axial force that the second road steel supported and applied 720KN at the 5.4m place;
Operating mode five: be excavated to 9.5m;
Operating mode six: add the brace pre axial force that the 3rd road steel supported and applied 800KN at the 9.0m place;
Operating mode seven: be excavated to 12.7m;
Operating mode eight: add the brace pre axial force that the 4th road steel supported and applied 720KN at the 12.2m place;
Operating mode nine: be excavated to 15.27m.
With reference to " Shanghai City base pit engineering technical manual " (DGTJ08-61-2010) span of the m in the table 2.6, determine the scope of m according to the liquidity index in the prospecting data.For inverting more near the Suzhou geological condition, can suitably enlarge the span of m a bit.The beam on elastic foundation that adopts patent to propose is found the solution and m value inverse analysis method.The minimum value that objective function is obtained in above each operating mode is respectively
, its iterations 259 times,
, its iterations 71 times,
, its iterations is 26 times.Owing in the actual measurement deformation data 56 measuring points are arranged, so the minimum value of objective function can meet the demands.
From the optimization result of the m value of last table as can be seen, 4. the m value of 2 layers of soil is at 1500～3090KN/m
4Between, from the comparison diagram of following field measurement value and computation optimization value as can be seen, optimization effect is fine.The body of wall horizontal shift that obtains by the m optimal value and comparison such as Fig. 1～Fig. 3 of measured displacements.
Table 2 Cang Jie station foundation soil m value inverting optimal value (KN/m
4)
Claims (2)
1. finding the solution and m value inverse analysis method of a beam on elastic foundation is characterized in that comprising the steps:
The first step: at first the quadravalence partial differential equation with beam on elastic foundation is converted to the low order partial differential equations, adopt the function bvp4c that finds the solution boundary value partial differential equations among the MATLAB to find the solution, concrete statement is sol=bvp4c (@odefun, @bcfun, solinit, and iterations and allowable error be set options); Wherein sol is a solving result, wherein sol.y be beam on elastic foundation around song distortion y, odefun is the m documentation function of finding the solution the beam on elastic foundation equation, bcfun is the m documentation function of beam on elastic foundation boundary condition; Solinit is a starting condition; Options is an options;
Second step: the shift value sol.y that the first step is obtained and the smallest error function of measured displacements value be as objective function, smallest error function be squared difference with;
The 3rd step: use MATLAB nonlinear optimization algorithm fmincon function second objective function that goes on foot is optimized, behind the iterations or allowable error that reach first step setting, stop iteration, this moment, objective function reached minimum value;
The 4th step: objective function minimum value, corresponding parameters are the optimum solution of the horizontal resistance coefficient m value of soil ground soil undetermined.
2. finding the solution and m value inverse analysis method of beam on elastic foundation according to claim 1 is characterized in that the Flexural Equation of beam on elastic foundation in the above-mentioned first step is:
In the formula: EI is the bendind rigidity of supporting construction; b
0Be the supporting construction molded breadth; M is the horizontal resistance coefficient of foundation soil; b
sBe outside active load action width, campshed is got pile spacing, and diaphram wall is got unit width; H is the excavation of foundation pit degree of depth; e
AikBe active earth pressure intensity; Z is a coordinate; D is the partial differential symbol; Y is the horizontal deflection distortion of waiting to ask supporting construction;
The grade beam up and down constraint condition at two ends is the boundary condition of beam on elastic foundation equation, be divided into stiff end (
,
), simply supported end (
,
) and free end (
,
) three kinds of boundary conditions;
The ordinary differential equation boundary value problem that beam on elastic foundation equation and boundary condition constitute together is a partial differential equation of higher order, with the derivative depression of order of the differential equation, even
,
,
,
, then the beam on elastic foundation equation becomes:
Equation (2a)-(2d2) and boundary condition constitute an ordinary differential equation together, adopt the function bvp4c that finds the solution boundary value partial differential equations among the MATLAB to find the solution.
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| CN108763833A (en) * | 2018-07-05 | 2018-11-06 | 中国矿业大学(北京) | A kind of computational methods for the foundation pit supporting pile amount of deflection considering earth resistance mutation |
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Application publication date: 20110608 |