CN106096202A - A kind of modeling method of the shear strength parameters time effect model of nanometer water earth - Google Patents

Abstract

The present invention relates to the modeling method of the shear strength time effect model of a kind of nanometer water earth, respectively by mechanical test, X x ray diffractometer x and specific surface area and the test of lacunarity analysis instrument, the test result of thermogravimetric analyzer test, set up the core function of model, microstructure mapping function, moisture existence form Tuning function, combining closely of macromechanics behavior and microstructure change is achieved in modeling process, compared with conventional model, error of the present invention is little, provides reliable reference frame for nano material in the utilization of strand Geotechnical Engineering.

Description

A kind of modeling method of the shear strength parameters time effect model of nanometer water earth

Technical field

The invention belongs to civil engineering material test and numerical value analysis technical field, be specifically related to a kind of nanometer water earth The modeling method of shear strength time effect model.

Background technology

Traditional soft-soil foundation treatment method mainly uses cement material to reinforce, and forms cement earth pile by the aquation of cement Or cement soil wall, this both can improve the intensity of soft soil foundation, it is also possible to blocks the percolation path of soil water to a certain extent, Architectural engineering, road engineering, the hydraulic engineerings such as structure foundation reinforcing, roadbed treatment, dyke seepage control obtain extensively should With, there is the advantages such as easy construction, cost are low, remarkably productive, but still have that low bearing capacity, afterwards its sedimentation are big etc. a series of to be lacked Fall into.On the other hand, nano material has the characteristics such as granule is little, specific surface area is big, light water earth is had effective hole and fills out Fill and cementation and activity secondary excitation effect, and then improve the macro-mechanical characters of conventional soil cement so that it is on weak soil ground Having broad application prospects in matter engineering.Nanometer water earth (three-phase mixture of nano material, cement, weak soil composition) The determination of cutting performance is the premise of engineering design, generally has direct shear test, unconfined compression test, triaxial compression test etc. 3 Plant method of testing.Laboratory test and the engineering practice of above 3 kinds of method of testings all show, soil cement and nanometer water earth are respectively provided with The time effect of the engineering properties gradually hardened along with the increase of age, i.e. shear strength.

In recent years, people have had more deep discussion to the time effect in engineering, such as document " static pressed pile ultimate bearing capacity Ageing " (Zhang Mingyi, Shi Wei, Wang Chongge, etc. ageing [J] of static pressed pile ultimate bearing capacity. rock mechanics and engineering Report, 2002,2l (increasing 2): 260l-2604.) propose the hyperbolic model of weak soil pile foundation bearing capacity time effect；Document is " full With bury pile bearing capacity time effect model test " (Guilin. saturated soft clay pile bearing capacity time effect model test [J]. Geotechnique basis, 2008,22 (5): 67-69.) propose the logarithmic model of weak soil pile foundation bearing capacity time effect；Document " cement Soil mixing pile time effect and quality testing methods of marking are inquired into " (fourth great waves, Yang Baoquan. cement mixing method time effect with Quality testing methods of marking inquires into [J]. Advances In Science And Technology of Water Resources, and 2005,25 (1): 48-50.) and document " deep-mixed pile The field test research of composite foundation " (Sun Jun, Ying Houqiang, Zou Jian. the field test research [J] of compound foundation with deep mixing pile. Advances In Science And Technology of Water Resources, 2002,22 (6): 52-54.) propose simple power function model based on 28 days age strengths.Literary composition (Ruan Jinlou, Ruan Bo, sun army is raw, etc. silty clay soil cement to offer " silty clay soil cement Study on unconfined compression strength " Study on unconfined compression strength [J]. railway science and engineering journal, 2009,6 (3): 56-61.) then propose soil cement The hyperbolic model of the time effect of unconfined compressive strength.

Above time effect model is only to set up from the angle of data matching, only considers macromechanics rule, Object of study is the concrete-pile in weak soil or cement earth pile or soil cement, for the shear strength of nanometer water earth uncomfortable Close.Owing to nano material is complicated with cement and the coefficient microcosmic mechanism of weak soil, these models are to nanometer water earth the most less Being suitable for, error of fitting is bigger.Therefore, in the urgent need to being combined with microcosmic test by mechanical test, new modeling method is proposed also Setting up new time effect model, the time effect of accurate description nano cement shear strength of soil, for nano material in shore The utilization of sea Geotechnical Engineering provides reliable reference frame.

Summary of the invention

In order to overcome, correlation time in existing Geotechnical Engineering, effect model was not suitable for the shearing of nanometer water earth by force to the present invention The defect of degree, it is provided that the modeling method of the shear strength time effect model of a kind of nanometer water earth, it is possible to describe accurately and receive The process that rice soil cement shear strength develops in time.

For reaching above-mentioned purpose, the present invention is achieved by the following technical solutions:

The modeling method of the shear strength parameters time effect model of a kind of nanometer water earth, comprises the following steps:

(1) nanometer water earth is carried out the shearing test of multiple age, it is thus achieved that nano cement shear strength of soil becomes in time The measured data changed；

(2) mathematical feature of measured data, Selection Model core function are summed up；

(3) x-ray diffractometer, specific surface area and lacunarity analysis instrument and thermogravimetric analyzer is used to carry out corresponding age Microcosmic is tested, and respectively obtains nanometer water earth internal tightness, mean porosities, moisture and existence form microstructure Change；

(4) selection is corresponding with above-mentioned each microstructure change microstructure mapping function, moisture existence form adjust letter Number, combination model core function, set up the time effect model of the shear strength of nanometer water earth；

(5) verify the mathematical feature of new model, determine model parameter.

In described step (2), the mathematical feature of measured data includes the theoretical interval [t of age t₁, t₂], shear strength Theoretical interval [the y of increasing value y₁, y₂] and the initial value of measured data, incremental, concavity and convexity and maximum of intensity.

The interval of the model core argument of function age in described step (2) is [T₁, T₂], and this interval can The interval corresponding with measured data by microstructure mapping function realizes one_to_one corresponding；Dependent variable interval is all [y₁, y₂]。

Model core function in described step (2) is trigonometric sine function.

Microstructure mapping function in described step (4) is according to x-ray diffractometer, specific surface area and lacunarity analysis The regularity summarization that nanometer water earth internal tightness that instrument records, mean porosities changed with age builds.

Microstructure mapping function in described step (4) is bounded hyperbolic function.

Inside the nanometer water earth that moisture existence form Tuning function in described step (4) records according to thermogravimetric analyzer The rule that moisture existence form changed with age comprehensively builds, and embodies a concentrated reflection of the nano material bundle water interactions after normalization and cuts The contrast of shearing stress.

Moisture existence form Tuning function in described step (4) is power function.

The operation principle of the present invention and having the beneficial effect that:

1, the present invention is that the time effect model of shear strength parameters accurately building nanometer water earth provides a kind of new Method, this model, based on shear strength test, has higher accuracy and the suitability, can be that nano material is at strand ground The utilization of engineering provides reliable reference frame；

2, tested with specific surface area and lacunarity analysis instrument (SAP) by mechanical test, x-ray diffractometer (XRD) respectively, The test result that thermogravimetric analyzer (TGA) is tested, sets up the core function of model, microstructure mapping function, moisture exist shape Formula Tuning function, achieves combining closely of macromechanics behavior and microstructure change in modeling process.

3, control, by microstructure mapping function, the mapping rates that independent variable is interval, overcome in tradition modeling method Modeling initial stage necessary mutually the same deficiency.

The modeling method of the shear strength time effect model of nanometer water earth of the present invention, is penetrated by mechanical test, X-respectively Line diffractometer and specific surface area and the test of lacunarity analysis instrument, the test result of thermogravimetric analyzer test, set up the core of model Function, microstructure mapping function, moisture existence form Tuning function, achieve macromechanics behavior and micro-in modeling process Seeing combining closely of structure change, compared with conventional model, error of the present invention is little, for nano material in the fortune of strand Geotechnical Engineering With providing reliable reference frame.

Accompanying drawing explanation

Fig. 1 is the modeling procedure figure of the present invention；

Fig. 2 is the compactness curve synoptic diagram of the different larval instar nanometer water earth of the embodiment of the present invention；

Fig. 3 is the bundle water interactions normalization relativity with mechanical strength development of the embodiment of the present invention；

Fig. 4 is the core function schematic diagram of the embodiment of the present invention；

The mathematical feature schematic diagram of the time effect model of Fig. 5 embodiment of the present invention.

Detailed description of the invention

Below in conjunction with specific embodiment, the present invention is further illustrated, but protection scope of the present invention is not limited to This.

As it is shown in figure 1, the modeling method of the shear strength time effect model of nanometer water earth of the present invention, including following step Rapid:

(1) nanometer water earth is carried out the shearing test of multiple age, it is thus achieved that measured data.Carry out under 4 to 8 ages Shearing test, preferably 8 ages such as 1d, 4d, 7d, 14d, 28d, 60d, 90d, 120d.

In the present embodiment, according to requirement of engineering, the additive ratio of design nano cement soil water mud is 10%, nano magnesia Incorporation be 2%, the density of sample is 1.9g/cm³, moisture content is 10%.Use unconfined compression strength test, respectively test The shear strength of age and correspondence thereof is shown in Table 1.

Nano cement shear strength of soil surveyed by table 1

Age/d	1	4	7	14	28	60	90	120
									Intensity/MPa	0.23	0.71	1.01	1.70	2.53	3.40	3.61	3.69

(2) carry out the Microstructure characterization of correspondence nanometer water earth of above age simultaneously.Use x-ray diffractometer (XRD), specific surface area and lacunarity analysis instrument (SAP), the microcosmic micro structure of thermogravimetric analyzer (TGA) test nanometer water earth, Obtain the time effect of the microstructures such as nanometer water earth internal tightness, mean porosities, moisture existence form.

In the present embodiment, test data are processed that to obtain the microstructure of different larval instar nanometer water earth as follows.X- Typical grain size that x ray diffractometer x (XRD) records, compactness curve, Fig. 2 is shown in by the schematic diagram after normalized.Specific surface Long-pending and lacunarity analysis instrument (SAP) test result shows, owing to nano magnesia compensate for cement to the filling effect of soil cement The contraction of self, mean porosities change is little, but intergranular cementation is gradually strengthened, the reinforcement rule of cementation Restrain similar with Fig. 1.Thermogravimetric analyzer (TGA) test result shows, the moisture in nanometer water earth has certain stability, but State is different, along with the increase of age, the nano-particle inner-bundle water yield in early days gradate as hydrated cementitious needed for freedom Water, the later stage performance for nanometer water earth intensity provides guarantee；Bundle water interactions after normalization and mechanical test obtain Intensity contrast relation, is shown in Fig. 3.

(3) mathematical feature of measured data is excavated.Theoretical interval [t including age t₁, t₂], shear strength increase Theoretical interval [the y of value y₁, y₂], shear strength increasing value change with age initial value, incremental, concavity and convexity, theory Big value.

According to table 1, in the present embodiment, the theoretical interval of age t is [0, ∞], the theory of shear strength increasing value y Interval is [0, A], represents that theoretical increasing value when age is zero is zero.Wherein, A is one and positive treats rational method； Initial value is (0,0), represents that theoretical increasing value when age is zero is zero；Shear strength increasing value y is dull with the increase of age t It is incremented by, and away from axis of abscissas direction evagination, has asymptotic value and its numerical value corresponding to constant A.

(4) Selection Model core function.According to mathematical feature, choose suitable model core function f (t), and determine it The interval of independent variable is [T₁, T₂], the phase of adjustment of simultaneously, the interval of dependent variable is all [y₁, y₂]。

In the present embodiment, employing trigonometric sine function:

F (t)=a sin (t) (1)

Interval [the X of its independent variable₁, X₂] it is [0, pi/2], the interval [Y of dependent variable₁, Y₂] it is [0, a], see figure 4。

(5) microstructure mapping function is built.According to x-ray diffractometer (XRD), specific surface area and lacunarity analysis instrument (SAP) rule that the nanometer water earth internal tightness that records, mean porosities changed with age, comprehensive builds this microstructure Mapping function g (t).This mapping parameters can keep the interval of shear strength increasing value constant, and by the value district of age Between [T₁, T₂] it is mapped as [t one by one₁, t₂]。

According to the compactness curve of different larval instar nanometer water earth in the analysis in step (2) and Fig. 2, take microstructure and reflect Penetrating function is following bounded hyperbolic function:

$g\left(t\right)=\frac{\mathrm{\π}t}{b+2t}---\left(2\right)$

Now, the interval [0, a] keeping shear strength increasing value is constant, the interval [0, pi/2] of independent variable One is mapped as [0, ∞].Wherein, b is one and positive treats rational method.

(6) moisture existence form Tuning function is built.The nanometer water earth internal water recorded according to thermogravimetric analyzer (TGA) Divide the rule that existence form changes, comprehensive structure moisture existence form Tuning function h (t) with age.

According to the bundle water interactions after normalization in Fig. 3 and the contrast of shear strength increasing value, find that they approximate in power Functional relationship.Owing to aforesaid model core function having represented parameter a of shear strength increasing value maximum, so by water Point existence form Tuning function is configured to:

H (t)=t^k (3)

(7) the time effect model of shear strength is set up.Comprehensive moisture existence form Tuning function h (t), microstructure are reflected Penetrate function g (t), model core function f (t), set up the model formation y=h (f (g of the shear strength increasing value containing undetermined parameter (t)))。

$y=c+a{\sin }^k\left(\frac{\mathrm{\π}t}{b+2t}\right)---\left(4\right)$

When being zero in view of age, shear strength has certain initial value, is designated as c, then the shear strength of t should be Initial value and increasing value sum, therefore the time effect model of shear strength is:

$Y=c+a{\sin }^k\left(\frac{\mathrm{\π}t}{b+2t}\right)---\left(5\right)$

(8) verify the mathematical feature of model formation, check it the most identical with the mathematical feature of measured data.

The mathematical characteristic of computation model formula (5) is as follows:

Initial value: y |_T=0=c

First derivative:

And

Second dervative:

$\frac{d^{2}Y}{{\mathrm{dt}}^2}=-\frac{\mathrm{\π}abk{\sin }^{k-2}\left(\frac{\mathrm{\π}t}{b+2t}\right)\{\mathrm{\π}b+2bsin\left(\frac{2\mathrm{\π}t}{b+2t}\right)+4tsin\left(\frac{2\mathrm{\π}t}{b+2t}\right)-\frac{\mathrm{\π}bk}{2}(1+cos(\frac{2\mathrm{\π}t}{b+2t}\left)\right)\}}{{(b+2t)}^4}$

Asymptotic value:

According to higher mathematics principle, all mathematics that the time effect model of this shear strength can meet measured data are special Levy, obtain this time effect model according to the different values of a, b, k, c

(5) two typical profiles and relevant parameter are shown in Fig. 5.

(9) model parameter is determined, contrast model error.With model formation, measured data is simulated matching, it is thus achieved that right The model parameter answered, and determine model error with actual measurement contrast.

It is respectively adopted model of the present invention, hyperbolic model, logarithmic model to this 1d to 120d totally 8 age test intensity Matching, the results are shown in Table 2, the expression of model is:

Model of the present invention:

Hyperbolic model:

To tree-model: y=0.82lnt-0.21

According to table 2, calculate the relative error of three models fittings, be shown in Table 3.

Table 2 and table 3 show, in 3 models: logarithmic model result is worst；Hyperbolic model is preferable；Model of the present invention is Good, when only an age is 4d, the matching relative error of data point is more slightly larger than hyperbolic model, the matching of remaining 7 eyeball Relative error is respectively less than hyperbolic model, and the absolute value aggregate-value of relative error is also much smaller than hyperbolic model, and result is the most smart Really.

The actual measurement of table 2 nano cement shear strength of soil and model contrast/MPa

Table 3 nano cement shear strength of soil matching relative error contrast/%

Above-described embodiment is only used for illustrating the inventive concept of the present invention, rather than the restriction to rights protection of the present invention, All changes utilizing this design that the present invention carries out unsubstantiality, all should fall into protection scope of the present invention.

Claims (8)

1. the modeling method of the shear strength parameters time effect model of a nanometer water earth, it is characterised in that include following step Rapid:

(1) nanometer water earth is carried out the shearing test of multiple age, it is thus achieved that nano cement shear strength of soil is time dependent Measured data；

(2) mathematical feature of measured data, Selection Model core function are summed up；

(3) x-ray diffractometer, specific surface area and lacunarity analysis instrument and thermogravimetric analyzer is used to carry out the microcosmic of corresponding age Test, respectively obtains nanometer water earth internal tightness, mean porosities, moisture and the change of existence form microstructure Change；

(4) select the microstructure mapping function corresponding with above-mentioned each microstructure change, moisture existence form Tuning function, tie Matched moulds type core function, sets up the time effect model of the shear strength of nanometer water earth；

(5) verify the mathematical feature of new model, determine model parameter.

2. the modeling method of the shear strength parameters time effect model of nanometer water earth as claimed in claim 1, its feature exists In: in described step (2), the mathematical feature of measured data includes the theoretical interval [t of age t₁, t₂], shear strength increase Theoretical interval [the y of value y₁, y₂] and the initial value of measured data, incremental, concavity and convexity and maximum of intensity.

3. the modeling method of the shear strength parameters time effect model of nanometer water earth as claimed in claim 1, its feature exists In: the interval of the model core argument of function age in described step (2) is [T₁, T₂], and this interval can be by micro- The interval seeing structure mapping function corresponding with measured data realizes one_to_one corresponding；Dependent variable interval is all [y₁, y₂]。

4. the modeling method of the shear strength parameters time effect model of nanometer water earth as claimed in claim 3, its feature exists In: the model core function in described step (2) is trigonometric sine function.

5. the modeling method of the shear strength parameters time effect model of nanometer water earth as claimed in claim 1, its feature exists In: the microstructure mapping function in described step (4) records according to x-ray diffractometer, specific surface area and lacunarity analysis instrument Nanometer water earth internal tightness, the regularity summarization that changes with age of mean porosities builds.

6. the modeling method of the shear strength parameters time effect model of nanometer water earth as claimed in claim 5, its feature exists In: the microstructure mapping function in described step (4) is bounded hyperbolic function.

7. the modeling method of the shear strength parameters time effect model of nanometer water earth as claimed in claim 1, its feature exists In: the nanometer water earth internal moisture that the moisture existence form Tuning function in described step (4) records according to thermogravimetric analyzer The rule that existence form changed with age comprehensively builds, and the nano material bundle water interactions after concentrated reflection normalization is strong with shearing The contrast of degree.

8. the modeling method of the shear strength parameters time effect model of nanometer water earth as claimed in claim 7, its feature exists In: the moisture existence form Tuning function in described step (4) is power function.