CN109918758B - Method for solving parameters in Duncan-Zhang hyperbola model based on Excel - Google Patents
Method for solving parameters in Duncan-Zhang hyperbola model based on Excel Download PDFInfo
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Abstract
The application belongs to the field of geotechnical engineering, and discloses a method for solving parameters in a Duncan-Zhang hyperbolic model based on Excel, which is used for importing triaxial compression test original data into an Excel worksheet; processing the triaxial compression test original data by using an Excel function calculation function to obtain triaxial compression test most basic data, initial data, auxiliary parameters of a Duncan-Zhang hyperbola model and model parameters of the Duncan-Zhang hyperbola model; calculating shear strength indexes of the triaxial compression test by utilizing an Excel software programming solving function; and finally, drawing a plurality of Moire stress circles and intensity envelope lines by utilizing an Excel software automatic drawing function. The application realizes that the operation is carried out on the visual interface, and has the advantages of simple operation, accurate calculation result, automatic drawing and attractive graph. Meanwhile, the worksheet can be stored for repeated use, so that the working efficiency is improved. The method related by the application can be widely applied to experimental teaching and scientific research.
Description
Technical Field
The application relates to a method for solving parameters in a Duncan-Zhang hyperbola model based on Excel, and belongs to the technical field of geotechnical engineering.
Background
Triaxial compression test is a method for measuring shear strength of soil body, usually 3-4 soil samples are used, axial pressure is applied under different confining pressures respectively, and shearing is carried out until the soil body is destroyed. In 1963, kangna proposed that the stress-strain relationship of the earth is hyperbolic, i.e., based on the results of a large number of triaxial compression tests
Wherein: sigma (sigma) 1 -axial principal stress
σ 3 -confining pressure
σ 1 -σ 3 -primary stress difference;
ε 1 -axial strain;
a. d-sample constant.
Duncan et al propose an incremental elastic model, commonly referred to as Duncan-Zhang hyperbolic model, which is currently widely used based on this hyperbolic stress-strain relationship.
The theoretical solving process of eight model parameters in the Duncan-Zhang hyperbolic model is described below for a single sample:
(1) Solving process of parameters in tangential deformation modulus
In the triaxial compression test, formula (1) can be expressed as
It can be found thatAnd epsilon 1 Approximately in a linear relationship, where a is the intercept of a straight line and d is the slope of the straight line, see fig. 1.
In the triaxial compression test, since the confining pressure is constant, the tangential deformation modulus is
At the start of the test ε 1 ＝0，E t ＝E i Then
Indicating that a is the initial deformation modulus E i Is the inverse of (c). In the formula (1), if ε 1 To → infinity
I.e. d represents the limit principal stress difference (sigma 1 -σ 3 ) ult Is the inverse of (c).
And obtaining the asymptotic value of the initial deformation modulus and the main stress difference from the a and d. The destruction ratio is calculated as follows:
plotting the initial deformation modulus vs. atmospheric pressure as a logarithmic value lg (E i /p a ) The log value lg (sigma) is taken as the ratio of ambient pressure to atmospheric pressure 3 /p a ) The relationship diagram shows that the two are approximately in a straight line relationship, see fig. 2. The initial deformation modulus obtained has the following relation with the consolidation pressure:
k, n are respectively lg (E i /p a ) And lg (sigma) 3 /p a ) Intercept and slope of the line. According to the moire-coulomb intensity criterion:
where c and f are the intercept and tilt, respectively, of the single specimen Mo Erpo bad envelope.
The tangential deformation modulus can be obtained by combining and transforming the above formulas:
from the above solving process, 5 model parameters in the tangential deformation modulus formula can be obtained: K. n, c, f and R f 。
(2) Solving process of parameters in tangent Poisson ratio
Duncan et al, based on experimental data, assume axial strain ε in a conventional triaxial compression test 1 And lateral strain-epsilon 3 There is also a hyperbolic relationship between, see FIG. 3 (b), i.e
As can be seen from the formula (10),and-e 3 The relationship is approximated as a straight line relationship so that the intercept f and the slope D can be determined, see fig. 3 (a), f=v i ，v i I.e. the initial poisson's ratio.
Experiments show that the initial Poisson's ratio v of the soil i And confining pressure sigma 3 In connection with drawing them in logarithmic coordinates, it can be assumed that a straight line is present, see FIG. 3 (c), i.e
v i ＝f＝G-Flg(σ 3 /p a )(11)
G and F are each v i -lg(σ 3 /p a ) Intercept and v in a relationship line i Is extremely bad.
Differentiating (10)
From the formulas (4), (11), (12) and their transformation formulas, it is possible to obtain:
thus far, the Duncan-Zhang hyperbolic model has been found8 parameters of (2): model parameter K, model parameter n, cohesion (c), internal friction angle (f), destruction ratio R f Model parameters G, F and D.
As can be seen from the above solving process, when triaxial compression test data is processed, the manual calculation and drawing workload is large, a great deal of repetitive work is required, and the drawing method also introduces some human errors. There is also an Excel electronic form processed by triaxial compression test data, but the intensity envelope of a plurality of moire stress circles is drawn into a straight line, two end points of the straight line are adjusted by a mouse to be tangent to each moire stress circle in the graph as much as possible, and the method has the advantages of large artificial influence factor, lower accuracy and low efficiency.
Disclosure of Invention
The application aims to provide a method for solving parameters in a Duncan-Zhang hyperbola model based on Excel, which utilizes the function calculation function of Excel to automatically solve each parameter in the Duncan-Zhang hyperbola model, utilizes the planning and solving function of Excel to simply and accurately calculate the shear strength index of a triaxial compression test, and utilizes the drawing function to automatically draw a plurality of Moire stress circles and intensity envelopes, thereby realizing that the operation is carried out on a visual interface, and having simple operation, accurate calculation result, automatic drawing and attractive graph.
In order to achieve the above object, the present application provides a method for solving parameters in a Duncan-Zhang hyperbola model based on Excel, comprising the following steps:
(1) Importing the original data of the triaxial compression test into an Excel worksheet;
(2) Processing the original data of the triaxial compression test under four confining pressures by using Excel,
obtaining four kinds of triaxial compression test basic indexes under confining pressure;
(3) Three-axis compression test most basic index under four confining pressures by using Excel calculation formula
Calculating to obtain four triaxial compression test initial indexes under confining pressure;
(4) Three-axis compression test most basic index under four confining pressures by using Excel calculation formula
And the primary stress difference is destroyed under four confining pressures to calculate, so that model parameters of a part of Duncan-Zhang hyperbola model and first part of auxiliary parameters are obtained;
(5) Three-axis compression test most basic index under four confining pressures by using Excel calculation formula
Calculating to obtain four moire stress circle parameters under confining pressure;
(6) Editing an objective function expression by using moire stress round parameters under four confining pressures, solving two variables k and b in the objective function by using an Excel software programming solving function, and solving a shear strength index of a triaxial compression test by using the two variables k and b;
(7) Using Excel calculation formula to perform partial Duncan-Zhang hyperbola model in step 4)
Calculating the first part of auxiliary parameters to obtain second part of auxiliary parameters of the Duncan-Zhang hyperbola model;
(8) Auxiliary parameters of the second part of the Duncan-Zhang hyperbola model by using an Excel calculation formula
Calculating the number, and adding the shear strength index of the triaxial compression test calculated in the step 6) to obtain model parameters of all Duncan-Zhang hyperbola models;
(9) Using Excel calculation formula to calculate moire stress circle parameters under four confining pressures in step 5)
Processing to obtain four confining pressure series moire stress circle coordinate points, selecting the four confining pressure series moire stress circle coordinate points, and automatically drawing four confining pressure moire stress circles on the same graph by utilizing an Excel drawing function;
(10) Combining the moire stress round parameters under the four confining pressures in the step (5) and the shear strength index of the triaxial compression test in the step (6), processing by using an Excel calculation formula to obtain a series of intensity envelope coordinate points, selecting a series of intensity envelope coordinate points, and automatically drawing an intensity envelope on the graph in the step (9) by using an Excel drawing function.
Further, the three-axis compression test under four confining pressures described in the step (2) includes: primary stress difference, axial strain, and lateral strain.
Further, the initial indexes of the triaxial compression test under the four confining pressures in the step (3) include: the ratio of axial strain to primary stress difference and the ratio of lateral strain to axial strain.
Further, the model parameters and the first part of auxiliary parameters of the part of the duncan-tensor hyperbola model in the step (4) include: model parameter D, ratio of axial strain to primary stress difference-intercept of axial strain line (a), ratio of axial strain to primary stress difference-slope of axial strain line (D), initial poisson ratio, auxiliary parameter a, auxiliary parameter B, and destructive primary stress difference.
Further, the moire stress circle parameters under four confining pressures in the step (5) include: axial principal stress, moire stress circle center coordinates, and moire stress circle radius.
Further, the shear strength index of the triaxial compression test in step (6) includes: internal friction angle and cohesion.
Further, the second partial auxiliary parameters of the full Duncan-Zhang hyperbola model in the step (7) comprise: initial deformation modulus, ultimate principal stress difference, initial deformation modulus vs. atmospheric pressure log and confining pressure vs. atmospheric pressure log.
Further, the model parameters of the all-duncan-tensor hyperbola model in the step (8) include: model parameter D, internal friction angle, cohesion, failure ratio, model parameter K, model parameter n, model parameter G, and model parameter F.
Further, the calculation formulas of the initial indexes of the triaxial compression test under the four confining pressures in the step (3) are as follows:
ratio of axial strain to primary stress difference = axial strain/primary stress difference;
ratio of lateral strain to axial strain = lateral strain/axial strain.
Further, the calculation formulas of the model parameters of the partial Duncan-Zhang hyperbola model and the first partial auxiliary parameters in the step (4) are as follows:
model parameter d=slope (ratio of N lateral strains to axial strain, N lateral strains);
ratio of axial strain to primary stress difference-INTERCEPT of axial strain line (a) =intersept (ratio of N axial strains to primary stress difference, N axial strains);
ratio of axial strain to primary stress difference-SLOPE of axial strain line (d) =slope (ratio of N axial strains to primary stress difference, N axial strains);
initial poisson ratio = nteercept (ratio of N lateral strains to axial strain, N lateral strains);
auxiliary parameter a=lookup (15, N axial strains, N primary stress differences);
auxiliary parameter b=max (N primary stress differences);
primary stress difference=if (auxiliary parameter a < = auxiliary parameter B, auxiliary parameter B).
Further, the calculation formulas of the moire stress circle parameters under the four confining pressures in the step (5) are as follows:
axial principal stress = primary stress difference damaged + confining pressure;
moire stress circle center coordinates= (axial principal stress+confining pressure)/2;
further, the calculation process of the k and b variables in the objective function of the planning solution in the step (6) is as follows:
input at objective function cell:
= ((k x) mohr stress circle center coordinates at confining pressure 1+b)/SQRT (k x 2+1) -mohr stress circle radius at confining pressure 1)/((k x mohr stress circle center coordinates at confining pressure 2+b)/SQRT (k x 2+1) -mohr stress circle radius at confining pressure 2)/((k x mohr stress circle center coordinates at confining pressure 3+b)/SQRT (k x 2+1) -mohr stress circle radius at confining pressure 3)/((k x 4) mohr stress circle center coordinates at confining pressure +b)/SQRT (k x 2+1) -mohr stress circle radius at confining pressure 4)/(2);
finding a planning solution in a pull-down menu of a tool bar of Excel software, or loading a macro to load the planning solution; clicking the plan solving, and displaying a dialog box of the plan solving parameter; setting a target cell, selecting a minimum value from the options of 'equal', inputting a variable cell, clicking 'adding' in 'constraint', inputting constraint condition formulas with k and b larger than zero one by one, and finally determining according to 'determination';
after clicking the "solving", a "planning solving result" dialog box appears, the solving result is prompted, clicking the "determining" box, and the closest planning solving result information is filled into the target cells and the variable cells in the worksheet to finish the storage of the planning solving result; the k, b values are output in the variable cells.
Further, the shear strength index of the triaxial compression test in the step (6) is calculated as follows:
internal friction angle=atan (k) ×180/PI ();
cohesive force = b.
Further, the calculation formula of the second auxiliary parameter of the duncan-tensor hyperbola model in the step (7) is as follows:
initial deformation modulus=1/a;
limit principal stress difference = 1/d;
initial deformation modulus vs. atmospheric pressure logarithmic value=log 10 (initial deformation modulus/101);
the ambient pressure takes a logarithmic value=log 10 (ambient pressure/101) than the atmospheric pressure.
Further, the calculation formula of the model parameters of the all-Duncan-Zhang hyperbola model in the step (8) is as follows:
ratio of failure = failure principal stress difference/limit principal stress difference;
model parameter k=10 (interval (4 initial deformation modulus vs. atmospheric pressure logarithmic value, 4 confining pressure vs. atmospheric pressure logarithmic value));
model parameter n=slope (4 initial deformation modulus vs. atmospheric pressure logarithmic values, 4 confining pressure vs. atmospheric pressure logarithmic values);
model parameter g=intersept (4 initial poisson ratios, 4 ambient pressure to atmospheric pressure take a logarithmic value); model parameter f= -SLOPE (4 initial poisson ratios, 4 ambient pressures vs. atmospheric pressure take a logarithmic value).
Further, in the step (9), the process of drawing four moire stress circles under confining pressure on the same graph is as follows:
firstly, respectively inputting angle values of 0 and 5 into two cells in a first row under confining pressure, then selecting 0 and 5 numbers to apply a dragging copy function until the numbers in the blackened cells are 180; input at the first row of the other two columns of cells aligned with the first column respectively:
= (confining pressure one+0.5 x (axial principal stress-confining pressure one))+0.5 x (axial principal stress-confining pressure one) COS (0 x pi ()/180);
=0.5 x (axial principal stress-confining pressure one) xsin (0 x pi ()/180);
then selecting the upper two columns of cells, applying a mouse to drag a copying function until the tail end of column data, selecting an XY scatter diagram from an icon type of an Excel software inserted option bar, selecting a non-point smooth line scatter diagram from a sub-diagram type, and drawing a smooth round moire stress circle;
and drawing the moire stress circles under the residual confining pressures in the same graph according to the method for drawing the moire stress circles under the confining pressures, thereby drawing the moire stress circles under the four confining pressures.
Further, the process of drawing the intensity envelope on the graph of step (9) in step (10) is as follows:
a "0" is entered in the first cell, and below the first cell: radius under confining pressure 4/center coordinates under 4+confining pressure 4 =3;
input in the second row first cell:
＝k*0+b；
and (3) selecting a second row of first cells, pulling down one column by using a mouse to drag a copying function, selecting the four cell data areas, selecting an XY scatter diagram from an icon type of an Excel software 'insert' option bar, and selecting a non-data point broken line scatter diagram from a sub-diagram type, namely drawing an intensity envelope on the diagram in the step (9).
According to the application, the function calculation function of Excel is utilized to automatically solve each parameter in the Duncan-Zhang hyperbola model, especially the 'planning and solving' function of Excel is utilized to simply and accurately calculate the shear strength index of the triaxial compression test, and the drawing function is utilized to automatically draw a plurality of Moire stress circles and intensity envelopes, so that the operation on a visual interface is realized, the operation is simple, the calculation result is accurate, and the automatic drawing and the figure are attractive. Meanwhile, the application can be stored as an application program, can be repeatedly used, avoids complicated calculation and drawing processing, saves a great deal of time, improves the working efficiency, has strong practicability, and can be widely applied to experimental teaching and scientific research. According to the application, functions of function calculation, planning solving and drawing of Excel software are utilized, model parameters and shear strength indexes of a triaxial compression test in a Duncan-Zhang hyperbolic model are solved, automatic drawing is realized, moire stress circles and intensity envelope lines under four confining pressures are drawn in the same drawing, and the method is simple and convenient to operate, accurate in calculation result and high in practicability.
Drawings
The accompanying drawings are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain, without limitation, the embodiments of the application.
FIG. 1 is a schematic diagram of a stress-strain relationship of soil in a Duncan-Zhang hyperbolic model;
FIG. 2 shows lg (E i /p a ) And lg (sigma) 3 /p a ) A relationship diagram;
FIG. 3 is a schematic representation of model parameters related to tangential Poisson's ratio in a Duncan-Zhang hyperbolic model;
FIG. 4 is a schematic diagram of a method for solving shear strength index of triaxial compression test using Excel program;
FIG. 5 is a schematic calculation of the most basic and initial indicators, the model parameters of a partial Duncan-Zhang hyperbolic model and the first partial auxiliary parameters in a triaxial compression test under confining pressure;
FIG. 6 is a schematic calculation diagram of the most basic and initial indicators, model parameters of a partial Duncan-Zhang hyperbolic model and first partial auxiliary parameters of a triaxial compression test under a second confining pressure;
FIG. 7 is a schematic calculation of the most basic and initial indicators, the model parameters of the partial Duncan-Zhang hyperbolic model and the first partial auxiliary parameters of the triaxial compression test under the third confining pressure;
FIG. 8 is a schematic calculation of the most basic and initial indicators, model parameters of a partial Duncan-Zhang hyperbolic model and first partial auxiliary parameters of a triaxial compression test under the confining pressure of four;
FIG. 9 is a schematic calculation of moire stress circle parameters under four confining pressures;
FIG. 10 is a schematic calculation of shear strength index for triaxial compression test using Excel software programming;
FIG. 11 is a schematic calculation of shear strength index for triaxial compression test using Excel software programming;
FIG. 12 is a schematic calculation of shear strength index for triaxial compression test using Excel software programming;
fig. 13 is a schematic diagram showing calculation of the second partial auxiliary parameters of the danin-Zhang hyperbola model and the model parameters of the whole danin-Zhang hyperbola model;
fig. 14 is a schematic diagram of a method for drawing moire stress circles and intensity envelopes thereof under four confining pressures in the same drawing using an automatic drawing function of Excel software.
Detailed Description
The following describes the detailed implementation of the embodiments of the present application with reference to the drawings. It should be understood that the detailed description and specific examples, while indicating and illustrating the application, are not intended to limit the application.
The principle of the method for solving the shear strength index of the triaxial compression test by using Excel programming is described as follows, referring to fig. 4:
when intensity envelope lines of all moire stress circles are drawn, the intensity envelope lines cannot be tangent to all the moire stress circles due to the reasons of non-uniformity, personal errors, equipment errors and the like of soil samples, and some deviation exists always. According to a planning solving theory in operation theory, a minimum value of a square sum of deviation is solved, and an intensity envelope line of a Moire stress circle can be determined, so that a shear strength index of a triaxial compression test is solved. And establishing an objective function, determining constraint conditions, expressing decision variables by using a mathematical formula, and quantifying an objective to be optimized into a function of the group of variables.
First, any one Moire stress circle center O i (x i 0) to the straight line y=kx+b is:
wherein: slope of k-line
Intercept of b-line
Drawing 4 Moire stress circles with 4 different confining pressures, wherein the center coordinates of the Moire stress circles are O respectively 1 (x 1 ，0)、O 2 (x 2 ，0)、O 3 (x 3 ，0)、O 4 (x 4 0), radius R respectively 1 、R 2 、R 3 、R 4 The distances from the 4 circle centers to the straight line are d respectively 1 、d 2 、d 3 、d 4 Can obtain 4 deviations d 1 －R 1 、d 2 －R 2 、d 3 －R 3 、d 4 －R 4 Their sum of squares expressions are:
the above variables are k and b, the actual nonlinear programming problem is solved, the minimum value of the objective function is solved, and the mathematical model can be written as:
minf(X)(17)
in the triaxial compression test, since the shear strength parameter c of the soil is non-negative in value, the constraint conditions are: k is greater than or equal to 0, and b is greater than or equal to 0.
The calculation method for solving model parameters and shear strength indexes of triaxial compression test in Duncan-Zhang hyperbola model based on Excel software comprises the following steps:
in connection with FIG. 5, the following steps are performed in the "confining pressure one" worksheet:
first, an Excel file is newly built, and initial data is imported. Specifically, four original data of axial displacement, steel ring deformation, pore pressure and volume change are respectively introduced in columns A to D, and each data is sequentially introduced from row 6 to row 61. And processing the original data of the triaxial compression test under four confining pressures by using Excel software to obtain main stress difference, axial strain and lateral strain which are the most basic indexes of the triaxial compression test under confining pressures, wherein the main stress difference, the axial strain and the lateral strain are respectively positioned in G, E and H columns and are positioned in lines 6 to 61.
Step two, inputting 0 into an I6 cell, inserting a function=E7/G7 into the I7 cell, then selecting the I7 cell to apply a mouse dragging copying function until reaching I61, and obtaining the ratio of all axial strains to main stress differences under confining pressure;
thirdly, inputting 0 into a J6 cell, inserting a function=H27/E7 into the J7 cell, then selecting the J7 cell to apply a mouse dragging copying function until reaching J61, and obtaining the ratio of all lateral strain and axial strain under confining pressure;
fourth, at L9 cell insertion function=slope (i6:i61, e6:e61), the ratio of confining pressure to primary stress difference-SLOPE of axial strain line (d) is obtained;
fifthly, obtaining the ratio of the axial strain to the main stress difference of the confining pressure at the L10 unit cell insertion function=INTERCEPT (I6: I61, E6: E61)/100 and the INTERCEPT (a) of the axial strain line;
sixthly, obtaining a confining pressure one-step model parameter D at the L11 cell insertion function=SLOPE (J6: J61, H6: H61);
seventh, at the L12 cell insertion function=INTERCEPT (J6: J61, H6: H61), obtaining the initial Poisson's ratio under confining pressure;
eighth step, in the L13 cell insertion function=LOOKUP (15, E6: E61, G6: G61), the confining pressure one-step auxiliary parameter A is obtained;
ninth, obtaining a confining pressure lower auxiliary parameter B at L14 cell insertion function=LOOKUP (15, E6: E61, G6: G61);
tenth, obtaining the confining pressure primary stress breaking difference at a moment in the L15 cell insertion function=IF (L13 < =L14, L14);
in connection with fig. 6 to 8, the following steps are performed:
eleventh, repeating the operations of the first step to the tenth step in the work tables of the confining pressure II, the confining pressure III and the confining pressure IV respectively, and obtaining indexes and parameters in the first step to the tenth step under each confining pressure;
referring to fig. 9, the following steps are performed in the "triaxial compression test shear strength index" worksheet:
and twelfth, inputting four confining pressures in the worksheet, wherein the confining pressures are sequentially positioned in A3 to A6. And four destructive main stress differences corresponding to the confining pressures are input and are sequentially positioned in B3 to B6.
Thirteenth, inserting a function=B3+A3 into the C3 unit cell, then selecting the C3 unit cell, applying a mouse to drag the copy function until the C6 unit cell is reached, and obtaining the axial main stress under four confining pressure shafts;
fourteenth step, inserting a function= (A3+C3)/2 into the D3 unit lattice, then selecting the D3 unit lattice, applying a mouse to drag the copying function until D6, and obtaining the round center coordinates of Moire stress under four confining pressure shafts;
fifteenth step, inserting a function= (C3-A3)/2 into the E3 unit lattice, then selecting the E3 unit lattice, applying a mouse to drag a copying function until E6, and obtaining the Moire stress circle radius under four confining pressure shafts;
referring to fig. 10, the following steps are performed in the "triaxial compression test shear strength index" worksheet:
in a sixteenth step, the first step, in E3 cell insertion function= ($F3D3+ $G3)/SQRT ($F32+1) -E3)/(($F3D4+ $G3)/SQRT ($F32+1) -E4)/(($F3D5+ $G 3)/SQRT ($F32+1) -E5)/($F3+ $D6+ $G3)/SQRT ($F32+1) -E6)/(SQRT;
seventeenth, find "planning solution" in Excel software "tool" column drop down menu, or "load macro" load "planning solution" into. Clicking on "planning solution" brings up a "planning solution parameters" dialog box. Setting a target cell: selecting "minimum" in the "equal" option, entering $F$3 in "variable cell": when "add" is clicked in "constraint", a constraint equation of $f3 > =0, $g3 > =0 is input, and finally "solution" is performed.
Referring to fig. 11 to 12, the following steps are performed in the "triaxial compression test shear strength index" worksheet:
eighteenth, after clicking "solving" in the previous step, a "planning solving result" dialog box appears, and prompts the solving result, clicking "determining" can fill the closest planning objective function solving result into $H$3 cells in the worksheet, and complete the saving of the planning solving result, and output k and b values in $F$3 and $G$3 cells.
Nineteenth, inserting a function=atan (F3) ×180/PI (), at the C8 cell, to obtain an internal friction angle;
twentieth, obtaining a cohesive force at C9 cell insertion function=g3;
in connection with fig. 13, the following steps are performed in the "model parameters in Duncan-Zhang hyperbolic model" worksheet:
step twenty-first, inserting a function=1/B2 into the F2 cell, then selecting the F2 cell, applying a mouse to drag the copy function until reaching F5, and obtaining initial deformation moduli under four confining pressure shafts;
twenty-second, inserting a function=1/C2 into the G2 cell, then selecting the G2 cell, dragging the copying function by a mouse until G5 is reached, and obtaining the lower limit principal stress difference of the four confining pressure shafts;
twenty-third, inserting a function=LOG10 (F2/101) into the J2 cell, then selecting the J2 cell, applying a mouse to drag the copy function until J5, and obtaining initial deformation modulus values under four confining pressure shafts compared with atmospheric pressure;
twenty-fourth step, at K2 cell insertion function=log 10 (A2/101), then selecting J2 unit grids, applying a mouse to drag a copying function until J5, and obtaining values of the lower confining pressure of the four confining pressure shafts compared with the atmospheric pressure;
twenty-fifth, obtaining a destruction ratio at A8 cell insertion function=average (I2: I5);
twenty-sixth, inserting a function=10 (INTERCEPT (J2: J5, K2: K5)) into the C8 cell to obtain a model parameter K;
twenty-seventh, obtaining a model parameter n at D8 cell insertion function=slope (J2: J5, K2: K5);
twenty-eighth step, inserting a function=INTERCEPT (D2: D5, K2: K5) into the E8 cell to obtain a model parameter G;
twenty-ninth step, in F8 unit cell insertion function= -SLOPE (D2: D5, K2: K5), obtaining model parameter F;
referring to fig. 14, the following steps are performed in the "triaxial compression test shear strength index" worksheet:
thirty-step, inputting angle values 0 and 5 in the A12 and A13 cells respectively, and then selecting numbers 0 and 5 in the A12 and A13 cells to apply a drag copy function until the A48 cells. At B12 cell insertion function = ($a3+0.5 ($c3- $a3)) +0.5 ($c3- $a3) × COS (a12× PI ()/180). At C12 cell insertion function = 0.5 ($c3- $a3) × SIN (a12×pi ()/180);
thirty-first, selecting B12 and C12 cells, applying a mouse dragging replication function until the B48 and C48 cells, and obtaining a surrounding pressure lower Moire stress circle coordinate;
thirty-second, selecting data areas of B12 to B48 and C12 to C48 cells, selecting an XY scatter diagram from an icon type of an Excel software insert option bar, and selecting a non-data point smooth line scatter diagram from a sub-diagram type, namely drawing Moire stress circles under the confining pressure of smooth circles.
Thirty-third, repeating the operations of thirty-second to thirty-second, drawing moire stress circles under the confining pressure second, confining pressure third and confining pressure fourth in the same figure.
Thirty-fourth step, "0" is input into the J11 cell, and the function=d6+3/4×e6 is inserted into the J12 cell. Selecting K11 cells from K11 cells by inserting function = $F$3 $J11+ $G$3 and pulling down the K12 cells by using a mouse to drag the copy function;
thirty-fifth, selecting J11 to J12, K11 to K12 cell data areas, selecting an XY scatter plot in an icon type, selecting a non-point broken line scatter plot in a sub-graph type, and drawing an intensity envelope in the plot.
Finally, the method of the present application is only a preferred embodiment and is not intended to limit the scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.
The foregoing details of the optional implementation of the embodiment of the present application have been described in detail with reference to the accompanying drawings, but the embodiment of the present application is not limited to the specific details of the foregoing implementation, and various simple modifications may be made to the technical solution of the embodiment of the present application within the scope of the technical concept of the embodiment of the present application, and these simple modifications all fall within the protection scope of the embodiment of the present application.
In addition, the specific features described in the above embodiments may be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, various possible combinations of embodiments of the present application are not described in detail.
In addition, any combination of various embodiments of the present application may be performed, so long as the concept of the embodiments of the present application is not violated, and the disclosure of the embodiments of the present application should also be considered.
Claims (15)
1. A method for solving parameters in a dane-Zhang hyperbola model based on Excel, which is characterized by comprising the following steps:
(1) Importing triaxial compression test original data into an Excel worksheet, wherein the original data comprise axial displacement, steel ring deformation, pore pressure and volume change;
(2) Processing the original data of the triaxial compression test under the four confining pressures by using Excel to obtain the most basic indexes of the triaxial compression test under the four confining pressures, wherein the most basic indexes comprise main stress difference, axial strain and lateral strain;
(3) Calculating the most basic indexes of the triaxial compression test under the four confining pressures by using an Excel calculation formula to obtain initial indexes of the triaxial compression test under the four confining pressures;
(4) Calculating the most basic indexes of the triaxial compression test under four confining pressures and the damage main stress difference under four confining pressures by using an Excel calculation formula to obtain model parameters of a part of Duncan-Zhang hyperbola model and first part of auxiliary parameters;
(5) Calculating the most basic indexes of the triaxial compression test under the four confining pressures by using an Excel calculation formula to obtain moire stress circle parameters under the four confining pressures;
(6) Editing an objective function expression by using moire stress round parameters under four confining pressures, solving two variables k and b in the objective function by using an Excel software programming solving function, and solving a shear strength index of a triaxial compression test by using the two variables k and b;
(7) Calculating the first part of auxiliary parameters of the partial Duncan-Zhang hyperbola model in the step 4) by using an Excel calculation formula to obtain the second part of auxiliary parameters of the Duncan-Zhang hyperbola model;
(8) Calculating the second part auxiliary parameters of the Duncan-Zhang hyperbola model by using an Excel calculation formula, and adding the shear strength index of the triaxial compression test calculated in the step 6) to obtain model parameters of all Duncan-Zhang hyperbola models, wherein the model parameters of all Duncan-Zhang hyperbola models comprise: model parameter D, internal friction angle, cohesion, destruction ratio, model parameter K, model parameter n, model parameter G, and model parameter F;
(9) Processing the four kinds of ambient pressure moire stress circle parameters in the step 5) by using an Excel calculation formula to obtain four kinds of ambient pressure moire stress circle coordinate points, selecting the four kinds of ambient pressure moire stress circle coordinate points, and automatically drawing four kinds of ambient pressure moire stress circles on the same graph by using an Excel drawing function;
(10) Combining the moire stress round parameters under the four confining pressures in the step (5) and the shear strength index of the triaxial compression test in the step (6), processing by using an Excel calculation formula to obtain a series of intensity envelope coordinate points, selecting a series of intensity envelope coordinate points, and automatically drawing an intensity envelope on the graph in the step (9) by using an Excel drawing function.
2. The method for solving parameters in a Duncan-Zhang hyperbola model based on Excel according to claim 1, wherein the initial index of triaxial compression test under four confining pressures in step (3) comprises: the ratio of axial strain to primary stress difference and the ratio of lateral strain to axial strain.
3. The method for solving parameters in a dane-zhang hyperbola model based on Excel according to claim 1, wherein the model parameters of the partial dane-zhang hyperbola model and the first partial auxiliary parameters in step (4) comprise: model parameter D, ratio of axial strain to primary stress difference-intercept of axial strain line (a), ratio of axial strain to primary stress difference-slope of axial strain line (D), initial poisson ratio, auxiliary parameter a, auxiliary parameter B, and destructive primary stress difference.
4. The method for solving parameters in a danken-tensor hyperbola model based on Excel according to claim 1, wherein the four moire stress circle parameters under confining pressure in step (5) comprise: axial principal stress, moire stress circle center coordinates, and moire stress circle radius.
5. The method for solving parameters in a dane-zhang hyperbolic model based on Excel according to claim 1, wherein the triaxial compression test shear strength index of step (6) includes: internal friction angle and cohesion.
6. The method of solving parameters in a dane-Zhang hyperbolic model based on Excel according to claim 1, wherein the second part of the auxiliary parameters of the whole dane-Zhang hyperbolic model of step (7) comprises: initial deformation modulus, ultimate principal stress difference, initial deformation modulus vs. atmospheric pressure log and confining pressure vs. atmospheric pressure log.
7. The method for solving parameters in a Duncan-Zhang hyperbola model based on Excel according to claim 2, wherein the calculation formula of the initial index of the triaxial compression test under the four confining pressures in the step (3) is as follows:
ratio of axial strain to primary stress difference = axial strain/primary stress difference;
ratio of lateral strain to axial strain = lateral strain/axial strain.
8. The method for solving parameters in a dane-Zhang hyperbola model based on Excel according to claim 3, wherein the calculation formulas of the model parameters of the partial dane-Zhang hyperbola model and the first partial auxiliary parameters in step (4) are as follows:
model parameter d=slope (ratio of N lateral strains to axial strain, N lateral strains);
ratio of axial strain to primary stress difference-INTERCEPT of axial strain line (a) =intersept (ratio of N axial strains to primary stress difference, N axial strains);
ratio of axial strain to primary stress difference-SLOPE of axial strain line (d) =slope (ratio of N axial strains to primary stress difference, N axial strains);
initial poisson ratio = nteercept (ratio of N lateral strains to axial strain, N lateral strains);
auxiliary parameter a=lookup (15, N axial strains, N primary stress differences);
auxiliary parameter b=max (N primary stress differences);
primary stress difference=if (auxiliary parameter a < = auxiliary parameter B, auxiliary parameter B).
9. The method for solving parameters in a Duncan-Zhang hyperbola model based on Excel according to claim 4, wherein the calculation formula of the four kinds of moire stress circle parameters under confining pressure in step (5) is as follows:
axial principal stress = primary stress difference damaged + confining pressure;
moire stress circle center coordinates= (axial principal stress+confining pressure)/2;
moire stress circle radius= (axial principal stress-confining pressure)/2.
10. The method for solving parameters in a dane-Zhang hyperbola model based on Excel according to claim 1, wherein the calculation process of the two variables k and b in the planning solving objective function in the step (6) is as follows:
input at objective function cell:
= ((k x) mohr stress circle center coordinates at confining pressure 1+b)/SQRT (k x 2+1) -mohr stress circle radius at confining pressure 1)/((k x mohr stress circle center coordinates at confining pressure 2+b)/SQRT (k x 2+1) -mohr stress circle radius at confining pressure 2)/((k x mohr stress circle center coordinates at confining pressure 3+b)/SQRT (k x 2+1) -mohr stress circle radius at confining pressure 3)/((k x 4) mohr stress circle center coordinates at confining pressure +b)/SQRT (k x 2+1) -mohr stress circle radius at confining pressure 4)/(2);
finding a planning solution in a pull-down menu of a tool bar of Excel software, or loading a macro to load the planning solution; clicking the plan solving, and displaying a dialog box of the plan solving parameter; setting a target cell, selecting a minimum value from the options of 'equal', inputting a variable cell, clicking 'adding' in 'constraint', inputting constraint condition formulas with k and b larger than zero one by one, and finally determining according to 'determination';
after clicking the "solving", a "planning solving result" dialog box appears, the solving result is prompted, clicking the "determining" box, and the closest planning solving result information is filled into the target cells and the variable cells in the worksheet to finish the storage of the planning solving result; the k, b values are output in the variable cells.
11. The method for solving parameters in a Duncan-Zhang hyperbola model based on Excel according to claim 5, wherein the shear strength index of the triaxial compression test in step (6) is calculated as follows:
internal friction angle=atan (k) ×180/PI ();
cohesive force = b.
12. The method for solving parameters in a Duncan-Zhang hyperbola model based on Excel according to claim 1, wherein the calculation formula of the second partial auxiliary parameters of the Duncan-Zhang hyperbola model in step (7) is as follows:
initial deformation modulus=1/a;
limit principal stress difference = 1/d;
initial deformation modulus vs. atmospheric pressure logarithmic value=log 10 (initial deformation modulus/101);
the ambient pressure takes a logarithmic value=log 10 (ambient pressure/101) than the atmospheric pressure.
13. The method for solving parameters in a Duncan-Zhang hyperbola model based on Excel according to claim 1, wherein the calculation formula of the model parameters of the entire Duncan-Zhang hyperbola model in step (8) is as follows:
ratio of failure = failure principal stress difference/limit principal stress difference;
model parameter k=10 (interval (4 initial deformation modulus vs. atmospheric pressure logarithmic value, 4 confining pressure vs. atmospheric pressure logarithmic value));
model parameter n=slope (4 initial deformation modulus vs. atmospheric pressure logarithmic values, 4 confining pressure vs. atmospheric pressure logarithmic values);
model parameter g=intersept (4 initial poisson ratios, 4 ambient pressure to atmospheric pressure take a logarithmic value);
model parameter f= -SLOPE (4 initial poisson ratios, 4 ambient pressures vs. atmospheric pressure take a logarithmic value).
14. The method for solving parameters in a Duncan-Zhang hyperbolic model based on Excel according to claim 1, wherein in the step (9), four kinds of moire stress circles under confining pressure are drawn on the same graph as follows:
firstly, respectively inputting angle values of 0 and 5 into two cells in a first row under confining pressure, then selecting 0 and 5 numbers to apply a dragging copy function until the numbers in the blackened cells are 180; input at the first row of the other two columns of cells aligned with the first column respectively:
= (confining pressure one+0.5 x (axial principal stress-confining pressure one))+0.5 x (axial principal stress-confining pressure one) COS (0 x pi ()/180);
=0.5 x (axial principal stress-confining pressure one) xsin (0 x pi ()/180);
then selecting the upper two columns of cells, applying a mouse to drag a copying function until the tail end of column data, selecting an XY scatter diagram from an icon type of an Excel software inserted option bar, selecting a non-point smooth line scatter diagram from a sub-diagram type, and drawing a smooth round moire stress circle;
and drawing the moire stress circles under the residual confining pressures in the same graph according to the method for drawing the moire stress circles under the confining pressures, thereby drawing the moire stress circles under the four confining pressures.
15. The method for solving parameters in a Duncan-Zhang hyperbolic model based on Excel according to claim 1, wherein the procedure of plotting the intensity envelope on the graph of step (9) in step (10) is as follows:
a "0" is entered in the first cell, and below the first cell: radius under confining pressure 4/center coordinates under 4+confining pressure 4 =3;
input in the second row first cell:
＝k*0+b；
and (3) selecting a second row of first cells, pulling down one column by using a mouse to drag a copying function, selecting the four cell data areas, selecting an XY scatter diagram from an icon type of an Excel software 'insert' option bar, and selecting a non-data point broken line scatter diagram from a sub-diagram type, namely drawing an intensity envelope on the diagram in the step (9).
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