CN104077451A - Deep soft soil metro foundation pit soil body parameter inversion analyzing method - Google Patents

Abstract

The invention relates to the technical field of rock tunnel construction and earthwork parameter calculation, in particular to a deep soft soil metro foundation pit soil body parameter inversion analyzing method. The method includes multiplying a least square function of a difference value between a finite element numerical calculation result and an actually monitored value by a specific weighting coefficient to obtain the function which serves as a target function, utilizing an improved Gaussian-Newton method to conduct optimal solution on the target function, and conducting repeated iterative computation to enable the finite element numerical calculation result to gradually approach the actually monitored value to determine an optimal solution of a parameter to be confirmed and build the relation between the monitored value and the foundation pit soil body parameter basic characteristic value. By means of the method, the actual observation value is combined to conduct constant soil body parameter inversion and correction to further predict the soil body deformation of the next stage, a prediction result is more and more accurate with the number increase of the monitored value, a very good monitoring and early warning method is provided for deep soft soil metro foundation pit project construction, and the method has high application value in the soil body parameter determination process.

Description

A kind of method for Deep Thick Soft Ground subway foundation pit Soil Parameters back analysis

[technical field]

The present invention relates to rock constructing tunnel and geotechnological journey calculation of parameter technical field, be specifically related to a kind of method for Deep Thick Soft Ground subway foundation pit Soil Parameters back analysis.

[background technology]

Base pit engineering is as a Geotechnical Engineering, be characterized in very strong systematicness and uncertain, if excavation of foundation pit is improper, can cause safety and the stable problem of base pit engineering self, surrounding building, underground pipe network etc. is impacted, especially, when geologic media is Deep Thick Soft Ground, potential destruction risk is higher.Therefore can the distortion of Accurate Prediction foundation ditch in work progress, the safe construction of base pit engineering is had to great importance.Finite element method, due to its powerful applicability, becomes the powerful tool of predicting foundation pit deformation in deep-foundation pit engineering just day by day.Finite element analysis is to utilize the method for mathematical approach to simulate actual physical system, utilizes simple and interactional element, just can remove to approach with the unknown quantity of limited quantity the real system of unlimited unknown quantity.

This structure of soil body material during existing finite element analysis adopts revises Cambridge constitutive model (Modified Cam-Clay Model), this this structure has all been illustrated the elastic-plastic deformation characteristic of the soil body theoretically with in test preferably, is one of weak soil constitutive model being most widely used.And determine there are at present three kinds of methods: theoretical method, test method and parametric inversion method for Parameters of constitutive model.Theoretical method carries out theory according to the character of theory of mechanics and the soil body and solves, but in computation process, has made certain hypothesis, and its hypothesis is often inconsistent with Practical Project, therefore theoretical parsing cannot correctly show the mechanics parameter of foundation soil.Test method is generally chosen or determined by on-the-spot in-situ test by indoor geotechnological experimental result, because soil sample is disturbed, the imperfection of test method and in-situ test place be subject to the impact of artificial subjective factor, makes test findings cannot reflect all sidedly the character of foundation soil body.Parametric inversion analytical approach is to use inversion theory to calculate, analyze the mechanics parameter of foundation soil body according to the data of Foundation Pit Construction field measurement (as displacement, stress, pore pressure), make mechanics parameter more approach the actual mechanical property of the soil body, using as engineering design according to and carry out positive analysis Deformation Prediction, this method becomes the focus of current research gradually.But the correlative study that parametric inversion is analyzed shows, its optimization aim function is the non-linear multi-peak function of a high complexity, at present, the method of optimizing is mainly the method for the Optimized Back-analysis such as the back analysis of BP neural network, simplicial method back analysis, but these methods or objective function are easily absorbed in local minimum, algorithm is when complicated, and Optimal Parameters too much and robustness is not strong.

[summary of the invention]

The present invention is in order to address the above problem, having designed a kind of shift value of monitoring that utilizes comes inverting to obtain the basic parameter eigenwert of soil mass of foundation pit, between finite element numerical result of calculation and actual monitoring value, the least square function of difference is multiplied by a specific weighting coefficient as objective function, the gauss-newton method of application enhancements carries out optimization to objective function, by iterating, calculate and make the finite element numerical result of calculation monitor value of approaching to reality gradually, thereby determine the optimum solution of undetermined parameter, set up relation between monitor value and soil mass of foundation pit parameter essential characteristic value for analyzing the Back Analysis Method of Deep Thick Soft Ground subway foundation pit Soil Parameters.

To achieve these goals, provide a kind of method for Deep Thick Soft Ground subway foundation pit Soil Parameters back analysis, the method comprises the following steps:

(1). adopt ABAQUS large-scale general finite element analysis software to set up rational computation model, according to the geological characteristics of Deep Thick Soft Ground, the constitutive model of the soil body adopts modified Cam-clay Modified Cam-Clay and input model to calculate required known parameters and the initial value for the treatment of inverted parameters;

(2). the core calculations program of establishment Soil Parameters back analysis new method is also embedded in ABAQUS finite element software, and the core algorithm of this back analysis new method is as follows:

A. determine least square weighting objective function: S (b)=[y-y'(b)] ^tω [y-y'(b)]=e ^tω e, wherein, b is a vector treating inverted parameters, the parameter that this vector comprises needed inverting, y is the vector of actual monitoring value, is y'(b) the FEM (finite element) calculation value corresponding with monitor value, and ω is weight coefficient matrix, and e is residual vector;

B. calculating least square weighting objective function is a non-linear regression iterative process, adopts correction Gauss-Newton method to calculate, and the mathematical description of this process is: $(C^T{X}_r^T\mathrm{\ω}{X}_{r}C+I{m}_r)C^{-1}{d}_r=C^T{X}_r^T\mathrm{\ω}(y-y^{\′}\left(b_r\right))$ With b _r+1=ρ _rd _r+ b _r, wherein, d _rbe a vector optimizing b vector by upgrading initial inverting input parameter value, subscript r is the number of times of estimating iteration, X _ra matrix of coefficients that is used for assessing br susceptibility, X _rin each value basis calculate, C is a diagonal angle scaled matrix, each element in this matrix i is unit matrix, m _ran adjustment parameter that is used for improving non-linear regression, ρ _ran iteration attenuation parameter, especially, the large and very high problem of nonlinear degree for residual error, after iterative computation surpasses 3 times, least square weighting objective function changing value is appointed general while being so less than 0.01 replace with carry out iterative computation again:

C. sensitivity coefficient matrix Xr adopts method of finite difference to calculate, and the difference according to Difference Calculation mode, has: forward difference form and central difference schemes two kinds of forms, wherein, y ' _iit is the result of finite element of the i time; b _jto treat j parameter in inverted parameters vector; Δ b _jb _ja disturbance quantity; Δ ₂be used for representing difference scheme centered by this difference scheme;

D. in order to ensure rationality and the correctness of back analysis algorithm, also need optimized algorithm to carry out matching statistical study, from three aspects, start with, consider models fitting statistics: i) adopt error variance assess overall Weighted Residual Value, wherein, S (b) is least square weighting objective function, and ND is the quantity of monitor value, and NP is the quantity for the treatment of inverted parameters; Ii) each iteration complete after efficiency of inverse process adopt FI=[S (b) _initially-S (b) _optimize]/S (b) _initiallyevaluate, wherein, S (b) _initiallyfor initial least square weighting target function value, S (b) _optimizefor optimizing rear least square weighting target function value; Iii) adopt related coefficient $R_N^2={\left[{(e_0-m)}^T\mathrm{\τ}\right]}^2/\left[{(e_0-m)}^T(e_0-m)\left({\mathrm{\τ}}^T\mathrm{\τ}\right)\right]$ Assess univers parameter back analysis algorithm;

E. actual monitoring value weight coefficient ω matrix of coefficients is a diagonal matrix, each element of this matrix wherein, σ _ifor b _istandard deviation value, b _ibe i the parameter value for the treatment of inverting;

(3). combined parameters inversion algorithm program and ABAQUS finite element program carry out iterative computation, if reaching, least square weighting objective function calculates convergence precision requirement, stop calculating, now inverting parameters obtained is required Soil Parameters value, and will in inverting parameters obtained again substitution finite element model, calculate to predict the soil deformation in Deep Thick Soft Ground excavation of subway foundation pit process.

Iteration attenuation coefficient ρ _rspan between 0～1.0.

Standard deviation value adopts σ _i=2E _i/ 1.96 estimate, wherein Ei is that instrument arranges self error.

Within the parameter value for the treatment of inverting is limited at certain interval in optimizing process, this interval adopts mathematic(al) representation to be described as:

wherein, y ₀implication is y _i-b _iin space, b _ivalue change curve and y _ithe intersection value of axle.

The present invention compared with prior art, can be merged modified Cam-clay well, analyzes and the distortion of prediction Deep Thick Soft Ground subway foundation pit; Adopt improved least square weighting function as the objective function of optimizing simultaneously, make to optimize analysis more accurate; Increase sensitivity to parameter setting, make inverting parameters obtained more reasonable; In conjunction with actual observation numerical value, constantly go inverting and revise Soil Parameters and then constantly predict next stage soil deformation, and it is more accurate along with the quantity increase of monitor value to predict the outcome, can provide extraordinary monitoring and method for early warning for the construction of Deep Thick Soft Ground subway foundation pit engineering, in deep soft subway foundation pit engineering, in the definite process of Soil Parameters, there is higher using value.

[accompanying drawing explanation]

Fig. 1 is the process flow diagram that parametric inversion of the present invention is analyzed;

Exchanges data schematic diagram between majorized function and ABAQUS program when Fig. 2 is parametric inversion calculating;

Fig. 3 is that in embodiment 1, drainage consolidation test initial parameter is calculated acquired results and experimental result comparison diagram;

Fig. 4 be in embodiment 1 not drainage consolidation test initial parameter calculate acquired results and experimental result comparison diagram;

Fig. 5 is calculation of parameter acquired results and comparison of test results figure after drainage consolidation test inverting in embodiment 1;

Fig. 6 is not calculation of parameter acquired results and comparison of test results figure after drainage consolidation test inverting in embodiment 1;

Fig. 7 is sedimentation value and the actual monitoring shift value comparison diagram that initial parameter in embodiment 2, inverting parameters obtained calculate;

[embodiment]

Below in conjunction with accompanying drawing, the invention will be further described, and the structure of this device and principle are very clearly concerning this professional people.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.

Concrete steps of the present invention are as shown in Figure 1:

(1) adopt ABAQUS large-scale general finite element analysis software to set up rational computation model, according to the geological characteristics of Deep Thick Soft Ground, the constitutive model of the soil body adopts modified Cam-clay Modified Cam-Clay and input model to calculate required known parameters and the initial value for the treatment of inverted parameters; The parameter for the treatment of inverting has four, is defined as respectively b ₁=κ, b ₂=λ, b ₃=M and b ₄=G.κ, λ are respectively rebound curve and the slope of normal compression curve in e-lnp plane of equal stress ratio, can adopt κ=C _c/ 2.303 and λ=C _s/ 2.303 calculate, C _cwith C _sbe respectively compression index and exponent of expansion; M is the slope of critical conditions line in p-q plane, M=6sin φ/(3-sin φ), the angle of internal friction that φ is soil body material; G is the modulus of shearing of soil body material;

(2) adopt the core calculations program of formula translation establishment Soil Parameters back analysis new method and be embedded in ABAQUS finite element software, calculate the shift value of the point of the finite element model corresponding with actual monitoring value position, then substitution least square weighting objective function S (b)=[y-y'(b)] ^tω [y-y'(b)]=e ^tin ω e, be optimized calculating, as shown in Figure 2.Actual monitoring value weight coefficient ω matrix of coefficients is a diagonal matrix, each element of this matrix wherein, σ _ifor b _istandard deviation value, adopt σ _i=2E _i/ 1.96 estimate, wherein E _ifor instrument arranges self error, b _ibe i the parameter value for the treatment of inverting;

(3) calculating least square weighting objective function is a non-linear regression iterative process, adopts correction Gauss-Newton method to calculate, and the mathematical description of this process is: $(C^T{X}_r^T\mathrm{\ω}{X}_{r}C+I{m}_r)C^{-1}{d}_r=C^T{X}_r^T\mathrm{\ω}(y-y^{\′}\left(b_r\right))$ With b _r+1=ρ _rd _r+ b _r, wherein, d _rit is a vector optimizing b vector by upgrading initial inverting input parameter value; Subscript r is the number of times of estimating iteration; X _rbe one and be used for assessing b _rthe matrix of coefficients of susceptibility, the difference according to Difference Calculation mode, has: $\frac{\mathrm{\Δ}{y}_i^{\′}}{\mathrm{\Δ}{b}_j}=\frac{y_i^{\′}(b_j+\mathrm{\Δ}{b}_j)-y_i^{\′}\left(b_j\right)}{\mathrm{\Δ}{b}_j}$ (forward difference form) and $\frac{{\mathrm{\Δ}}_2{y}_i^{\′}}{{\mathrm{\Δ}}_2{b}_j}=\frac{y_i^{\′}(b_j+\mathrm{\Δ}{b}_j)-y_i^{\′}(b_j-\mathrm{\Δ}{b}_j)}{2\mathrm{\Δ}{b}_j}$ (central difference schemes) two kinds, wherein, y ' _iit is the result of finite element of the i time; b _jto treat j parameter in inverted parameters vector; Δ b _jb _ja disturbance quantity, this disturbance quantity recommended value is Δ b _j=0.005; Δ ₂be used for representing difference scheme centered by this difference scheme, C is a diagonal angle scaled matrix, each element in this matrix i is unit matrix; m _rit is an adjustment parameter that is used for improving non-linear regression; ρ _rbe an iteration attenuation parameter, span is 0～1.0, and recommended value is 0.5, and especially, the large and very high problem of nonlinear degree for residual error, will when after iterative computation surpasses 3 times, least square weighting objective function changing value is still less than 0.01 replace with carry out iterative computation again;

(4) in order to ensure rationality and the correctness of back analysis algorithm, also need optimized algorithm to carry out matching statistical study, from three aspects, start with, consider models fitting statistics: i) adopt error variance s ²=S (b)/(ND-NP) assess overall Weighted Residual Value, wherein, S (b) is least square weighting objective function, and ND is the quantity of monitor value, and NP is the quantity for the treatment of inverted parameters; Ii) each iteration complete after efficiency of inverse process adopt FI=[S (b) _initially-S (b) _optimize]/S (b) _initiallyevaluate, wherein, S (b) _initiallyfor initial least square weighting target function value, S (b) _optimizefor optimizing rear least square weighting target function value; Iii) adopt related coefficient $R_N^2={\left[{(e_0-m)}^T\mathrm{\τ}\right]}^2/\left[{(e_0-m)}^T(e_0-m)\left({\mathrm{\τ}}^T\mathrm{\τ}\right)\right]$ Assess univers parameter back analysis algorithm;

(5) in order to guarantee that iterative loop is calculated, can carry out smoothly, an iteration error allowable value need to be set, will meet the recommended value of TOL is 0.1%;

(6) combined parameters inversion algorithm program and ABAQUS finite element program carry out iterative computation, if reaching, least square weighting objective function calculates convergence precision requirement, stop calculating, now inverting parameters obtained is required Soil Parameters value, and will in inverting parameters obtained again substitution finite element model, calculate to predict the soil deformation in Deep Thick Soft Ground excavation of subway foundation pit process.

Embodiment 1

The triaxial compression test of two groups of modified Cam-clay was once done by external certain scientific research institution.One group is drainage consolidation test (referred to as D1), and one group is drainage consolidation test (be called for short U1) not.Two groups of samples all increase axial principal stress until soil sample produces shear failure.The new computing method of the parametric inversion that employing the present invention carries are carried out parametric inversion, and the triaxial compression test that inverting parameters obtained substitution finite element program is simulated to two groups of modified Cam-clay, acquired results is for as shown in Figures 3 to 6, wherein Fig. 3 is that drainage consolidation test initial parameter is calculated acquired results and experimental result comparison diagram, Fig. 4 calculates acquired results and experimental result comparison diagram for drainage consolidation test initial parameter not, Fig. 5 is calculation of parameter acquired results and comparison of test results figure after drainage consolidation test inverting, Fig. 6 is calculation of parameter acquired results and comparison of test results figure after drainage consolidation test inverting not.

Table 1 Soil Parameters inversion result

Initial parameter and inverting parameters obtained are as shown in table 1, and the new computing method that the Rock And Soil parametric inversion that visible the present invention carries is analyzed are that rationally, effectively the optimizer of establishment is correct.

Embodiment 2

Certain Deep Thick Soft Ground subway foundation pit is planned to build place and is positioned at Yangtze River floodplain geomorphic unit district, cover thickness large (thickness 59.2～61.3m), and each rock-soil layer is substantially even.Be subject to the effect of human activity, fill stratum thickness is larger, is 1.9～4.4m.Under fill stratum, the degree of depth 50.5～59.0m is soft clay, soft clay and silt, powder fine sand interbedded formation and the powder fine sand sedimentary deposit of Holocene epoch middle and advanced stage deposition above, and it is lower to early stage deposition of the Holocene epoch is containing ovum gravel silty clay (or containing ovum gravel powder fine sand).Place underlying bedrock buried depth is 59.2～61.3m, and lithology is Cretaceous System (K) silty, pelitic siltstone and pebbly sandstone, glutenite.This place rich groundwater, the weak soil degree of depth is thicker, to excavation of subway foundation pit, will produce very adverse influence, in order effectively to predict excavation of foundation pit distortion, controls excavation of foundation pit risk and is very important.In order to predict more accurately excavation of foundation pit distortion situation, at this, need to carry out back analysis to the parameter of this Deep Thick Soft Ground subway foundation pit soil body, obtain more rational parameter, adopt finite element model to predict foundation pit deformation.The parametric inversion analyzing novel methods that adopts the present invention to carry carries out back analysis, and acquired results as shown in Figure 7.

Certain Deep Thick Soft Ground subway foundation pit Soil Parameters inversion result of table 2

Initial parameter and inverting parameters obtained are as shown in table 2, shift value and measured displacements value that the new computing method that the Rock And Soil parametric inversion that visible the present invention carries is analyzed calculate are more approaching, error is also less, it is good that the new method that shows parametric inversion proposed by the invention is used for carrying out displacement back analysis result of calculation, the inverted parameters obtaining can be carried out evaluation and the prediction of correlation engineering, has good actual application value.

Claims (4)

1. for a method for Deep Thick Soft Ground subway foundation pit Soil Parameters back analysis, it is characterized in that the method comprises the following steps:

(1). adopt ABAQUS large-scale general finite element analysis software to set up rational computation model, according to the geological characteristics of Deep Thick Soft Ground, the constitutive model of the soil body adopts modified Cam-clay Modified Cam-Clay and input model to calculate required known parameters and the initial value for the treatment of inverted parameters;

(2). the core calculations program of establishment Soil Parameters back analysis new method is also embedded in ABAQUS finite element software, and the core algorithm of this back analysis new method is as follows:

A. determine least square weighting objective function: S (b)=[y-y'(b)] ^tω [y-y'(b)]=e ^tω e, wherein, b is a vector treating inverted parameters, the parameter that this vector comprises needed inverting, y is the vector of actual monitoring value, is y'(b) the FEM (finite element) calculation value corresponding with monitor value, and ω is weight coefficient matrix, and e is residual vector;

B. calculating least square weighting objective function is a non-linear regression iterative process, adopts correction Gauss-Newton method to calculate, and the mathematical description of this process is: $(C^T{X}_r^T\mathrm{\ω}{X}_{r}C+I{m}_r)C^{-1}{d}_r=C^T{X}_r^T\mathrm{\ω}(y-y^{\′}\left(b_r\right))$ With b _r+1=ρ _rd _r+ b _r, wherein, d _rbe a vector optimizing b vector by upgrading initial inverting input parameter value, subscript r is the number of times of estimating iteration, X _ra matrix of coefficients that is used for assessing br susceptibility, X _rin each value basis calculate, C is a diagonal angle scaled matrix, each element in this matrix i is unit matrix, m _ran adjustment parameter that is used for improving non-linear regression, ρ _ran iteration attenuation parameter, especially, the large and very high problem of nonlinear degree for residual error, after iterative computation surpasses 3 times, least square weighting objective function changing value is appointed general while being so less than 0.01 replace with carry out iterative computation again:

C. sensitivity coefficient matrix X _radopt method of finite difference to calculate, the difference according to Difference Calculation mode, has: forward difference form and central difference schemes two kinds of forms, wherein, y ' _iit is the result of finite element of the i time; b _jto treat j parameter in inverted parameters vector; Δ b _jb _ja disturbance quantity; Δ ₂be used for representing difference scheme centered by this difference scheme;

D. in order to ensure rationality and the correctness of back analysis algorithm, also need optimized algorithm to carry out matching statistical study, from three aspects, start with, consider models fitting statistics: i) adopt error variance assess overall Weighted Residual Value, wherein, S (b) is least square weighting objective function, and ND is the quantity of monitor value, and NP is the quantity for the treatment of inverted parameters; Ii) each iteration complete after efficiency of inverse process adopt FI=[S (b) _initially-S (b) _optimize]/S (b) _initiallyevaluate, wherein, S (b) _initiallyfor initial least square weighting target function value, S (b) _optimizefor optimizing rear least square weighting target function value; Iii) adopt related coefficient $R_N^2={\left[{(e_0-m)}^T\mathrm{\τ}\right]}^2/\left[{(e_0-m)}^T(e_0-m)\left({\mathrm{\τ}}^T\mathrm{\τ}\right)\right]$ Assess univers parameter back analysis algorithm;

E. actual monitoring value weight coefficient ω matrix of coefficients is a diagonal matrix, each element of this matrix wherein, σ _ifor b _istandard deviation value, b _ibe i the parameter value for the treatment of inverting;

(3). combined parameters inversion algorithm program and ABAQUS finite element program carry out iterative computation, if reaching, least square weighting objective function calculates convergence precision requirement, stop calculating, now inverting parameters obtained is required Soil Parameters value, and will in inverting parameters obtained again substitution finite element model, calculate to predict the soil deformation in Deep Thick Soft Ground excavation of subway foundation pit process.

2. a kind of method for Deep Thick Soft Ground subway foundation pit Soil Parameters back analysis as claimed in claim 1, is characterized in that the span of iteration attenuation coefficient ρ r is between 0～1.0.

3. a kind of method for Deep Thick Soft Ground subway foundation pit Soil Parameters back analysis as claimed in claim 1, is characterized in that standard deviation value adopts σ _i=2E _i/ 1.96 estimate, wherein E _ifor instrument arranges self error.

4. a kind of method for Deep Thick Soft Ground subway foundation pit Soil Parameters back analysis as claimed in claim 1, within the parameter value that it is characterized in that treating inverting is limited at certain interval in optimizing process, this interval adopts mathematic(al) representation to be described as:

wherein, y ₀implication is y _i-b _iin space, b _ivalue change curve and y _ithe intersection value of axle.