CN102914633A - Method for determining optimum water content for soil compaction - Google Patents
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- CN102914633A CN102914633A CN2012103925772A CN201210392577A CN102914633A CN 102914633 A CN102914633 A CN 102914633A CN 2012103925772 A CN2012103925772 A CN 2012103925772A CN 201210392577 A CN201210392577 A CN 201210392577A CN 102914633 A CN102914633 A CN 102914633A
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Abstract
The invention discloses a method for determining optimum water content for soil compaction. The method includes: firstly, mixing five kinds of soil samples with different water content according to current specification requirements, acquiring five groups of different water content data and dry density data through compaction tests; secondly, building a Lagrange interpolating polynomial formula taking the water content as variable and the dry density as function value, dissolving Lagrange interpolating polynomial functions of test data, primarily derivating through functions, determining extreme value within current water content range, namely the optimum theoretical water content; thirdly, determining a practical optimum water content range, replenishing and mixing soil samples with three kinds of the most possible optimum water content; and finally, compacting the three kinds of the optimum water content soil samples, and determining the optimum water content. The method for determining the optimum water content for soil compaction well reduces value error of the optimum water content, and is compact in theory, simple to operate, high in practicality and applicable to acquiring parameters of the optimum water content of engineerings including soil filling, compacting or the like, and a current specification method is well improved.
Description
Technical field
The present invention relates to Geotechnical Engineering field embankment soil stabilization Moisture Content Control Technology field, particularly a kind of method of definite soil tamp optimum moisture content.
Background technology
China is the country of mountain region area maximum in the world, and the large embankment formula of digging is greatly had to adopt in the more place of mountainous city and transport development.The water cut of banketing and dry density are that the important parameter of real Design of Reinforcement and effect assessment is rammed or hit to filling body.China's existing geotechnique's experiment rules regulation: will judge in advance the optimum moisture content scope when determining soil body optimum moisture content based on compaction test, mix the soil sample of making 5 kinds of different moisture contents, obtain 5 groups of different moisture contents and dry density data through compaction test, 5 groups of data are depicted as smooth curve, from figure, draw optimum moisture content and the maximum dry density of this soil sample.Present stage, engineering and academia were all by computing machine or manually by sweep the compaction test data point is linked to be smooth curve, and the connection of curve does not have strict unified mathematical law as foundation under the requirement of satisfying rules.Computing machine often is defaulted as the greatest measure point of reality input the maximum extreme point of this curve, causes the distortion of optimum moisture content and maximum dry density; Artificial line is drawn and is often depended on grid dividing precision and illustrator's experience for the judgement of the maximum extreme point of curve, has stronger randomness and subjectivity.In a word, determine that based on compaction test the method for soil body optimum moisture content exists larger error and obvious subjectivity, does not also have tight theoretical foundation so far at present.
All there is certain inherent law in the most phenomenon of nature, and therefore many practical problemss all can be described its inherent law with certain function, and the many function rules of ground and Geological Engineering circle are to carry out empirical fit with observation by experiment.Lagrange (Lagrange) method of interpolation is a kind of polynomial interpolation approximating method with France's 18th century mathematician Joseph Louis Lagrange (Joseph Louis Lagrange) name, it provides a polynomial function that just passes several known points on the two dimensional surface, and the certain existence of this function and unique.
Summary of the invention
In view of this, technical matters to be solved by this invention provides a kind of method of comprehensively determining the soil tamp optimum moisture content based on interpolation fitting and additional 3 groups of compaction tests.The method is a kind of mathematics and test coupling optimization method that can reduce well the soil tamp optimum moisture content value error of current specifications employing.
The object of the present invention is achieved like this:
A kind of method based on determining the soil tamp optimum moisture content provided by the invention may further comprise the steps:
S1: the soil sample of mixing in advance different moisture content processed;
S2: soil sample is hit reality, cutting ring cutting and drying and processing, obtain soil sample water content and dried density data;
S3: determine take water cut x as variate-value that according to following formula dry density F (x) is the Lagrange interpolation polynomial of functional value:
In the formula,
The n experimental group number, x
iAnd x
jBe the water cut of test soil sample, y
jBe test water cut x
jCorresponding dry density;
S4: solving equation F ' (x)=0 determines theoretical optimum moisture content x
0
S5: according to the theoretical water cut x of the best
0The optimum moisture content ω definite with the current specifications method
0Replenish the soil sample of mixing the multiple actual most probable optimum moisture content of system;
S6: the most probable optimum moisture content soil sample of replenishing is carried out compaction test and hit real soil body dry density test, determine the actual optimum moisture content of soil tamp.
Further, the described soil sample of step S1 is the soil sample of making at least 5 kinds of different moisture contents according to the current specifications requirement.
Further, described step S2 and step S6 soil sample dry density are to require soil sample is hit reality, cutting and drying and processing and the dry density data that obtain according to the compaction test flow process.
Further, it is the soil sample of 3 kinds of actual most probable optimum moisture contents that described step S5 replenishes soil sample, and its water cut is respectively x
0, x
0± α (x
0-ω
0), α is the difference coefficient, ω
0The optimum moisture content that the current specifications method is determined.
Further, described theoretical optimum moisture content is the extreme value of a function point x by interpolation letter F (x) being carried out differentiate and making F ' (x)=0 determine
0
Further, described difference factor alpha span is 0.3～0.7.
Further, described difference factor alpha can be come value according to the water sensitivity power of the soil body, and the stronger then value of water sensitivity is less, and more weak then value can be relatively large, and the weak soil body reference value of water sensitivity is 0.5.
Further, at definite theoretical optimum moisture content x
0Determine optimum moisture content ω with the standard method
0The basis on, again mix 3 groups of most probables of system and be the actual soil sample of optimum moisture content and carry out compaction test, hit in 3 groups and do solid work the corresponding soil body water cut of density maximal value and be optimum moisture content.
The invention has the advantages that: the present invention adopt based on interpolation fitting and replenish the method that 3 groups of compaction tests are comprehensively determined the soil tamp optimum moisture content.The method can reduce mathematics and the test coupling process of the soil tamp optimum moisture content value error of current specifications employing well.This inventive method not only has tight mathematical theory, and implementation step is clear, and processing ease is practical.Although carried out 3 groups of soil tamp experiments than the current specifications method, because one group of compaction test expense is very low, how many expenses do not increase, and determines that the precision of water cut is the key that directly affects the engineering soil strength more.By can determine the theoretical optimum moisture content of soil tamp to the Lagrange interpolation polynomial differentiate of soil tamp test figure, on the optimum moisture content basis that theoretical optimum moisture content and standard method are determined, again prepare again the soil body sample of 3 groups of different moisture contents, determine optimum moisture content by compaction test more at last, the value precision has had preferably raising, is fit to apply.And existing research has shown that water content and dried density data point line is single-peaked level and smooth convex curves (epirelief shows the theoretical optimum moisture content that must exist to obtain theoretical maximum dry density) in the compaction test of most soil bodys, so namely do not have interpolation fundamental polynomials problem complicated and changeable, the numerical value non-steady state can not occur yet.
Description of drawings
In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention is described in further detail below in conjunction with accompanying drawing, wherein:
Fig. 1 is the inventive method process flow diagram;
Fig. 2 is water content and dried density matched curve of the present invention and standard method line comparison example figure;
Fig. 3 is the comparison example figure that the inventive method and current specifications method are determined the soil tamp optimum moisture content.
Embodiment
Below with reference to accompanying drawing, the preferred embodiments of the present invention are described in detail; Should be appreciated that preferred embodiment only for the present invention is described, rather than in order to limit protection scope of the present invention.
General introduction embodiment 1
The method of a kind of definite soil tamp optimum moisture content provided by the invention may further comprise the steps:
S1: the soil sample of mixing in advance different moisture content processed; Described soil sample is the soil sample of making at least 5 kinds of different moisture contents according to current specifications (earthwork test rule (SL237-1999)) requirement.
S2: soil sample is hit experiment by current specifications, and test the dry density y of each soil sample
iWith water cut x
i(%).Use core cutter method to measure the density p of each soil sample
i, the remaining soil when keeping each sample equating.Each soil sample must be carried out 2 replicate determinations, and its parallel difference must not be greater than 0.03g/cm
3, get its arithmetic mean value.Use oven drying method to measure the water cut x of the remaining soil of above-mentioned each sample
i(%), each soil sample need be carried out 2 replicate determinations, and it allows Parallel errors must satisfy earthwork test rule regulation (x
i＜10 is 0.5%, 10≤x
i≤ 40 is 1.0%, x
i＞40 is 2.0%), get its arithmetic mean value.Based on formula
Calculate the dry density y of each soil sample
i
S3: determine take water cut x as variate-value that according to following formula dry density F (x) is the Lagrange interpolation polynomial of functional value:
In the formula,
The n experimental group number, x
iAnd x
jBe the water cut of test soil sample, y
jBe test water cut x
jCorresponding dry density.
S4: determine theoretical optimum moisture content x
0Described theoretical optimum moisture content is the extreme value of a function point x by Lagrange's interpolation letter F (x) being carried out differentiate and making F ' (x)=0 determine
0
S5: replenish and mix water cut x processed
BiBe respectively x
B1=x
0, x
B2=x
0+ α (x
0-ω
0) and x
B3=x
0+ α (x
0-ω
0) 3 kinds of soil samples, α is difference coefficient (span is 0.3～0.7), ω
0The optimum moisture content that the current specifications method is determined.Replenish x when mixing each water cut of system
BiAmount of water m
XbiBe m
Xbi=0.01x
Bi* m
Di, m
DiThe dry ground quality.
S6: the dry density behind the soil tamp that the additional 3 kinds of most probables mixing system of repeating step S2 test determining step S5 are actual optimum moisture content, the corresponding water cut of its dry density maximal value is the soil tamp optimum moisture content.
The present invention will be further described below in conjunction with specific embodiment and accompanying drawing.
Obtain the water cut x of 5 groups of Chongqing building lot gravelly soils by modified compaction test
j(%) with dry density y
j(g/cm
3) data group (x
j, y
j) (j=1,2,3,4,5): (x
1, y
1)=(3.6,1.9); (x
2, y
2)=(5.8,2.02); (x
3, y
3)=(8.8,2.06); (x
4, y
4)=(11.1,2.01); (x
5, y
5)=(13.0,1.91), according to current specifications specified moisture content x
1%, x
2% and x
3% is all less than plastic limit.
The first step: with these 5 groups of data difference substitution Lagrange's interpolation fundamental polynomials
Try to achieve:
Second step: with the Lagrange's interpolation fundamental polynomials f that tries to achieve
j(x) (j=1,2,3,4,5) substitution Lagrange interpolation polynomial
Obtain its corresponding Lagrange interpolation polynomial F (x):
F(x)=-0.000029461x
4+0.00103744x
3-0.02010156x
2+0.18639641x+1.44603379
The 3rd step: function F (x) is asked first order derivative to x:
F′(x)=-0.00011782x
3+0.00311232x
2-0.04020312x+0.18639641
Function F (x) is asked the secondary differentiate to x:
F″(x)=-0.00035346x
2+0.00622464x-0.4020312
Being F in [3.6,13.0] scope in the variable x interval of test water cut " (x)＜0, shows in the interval existence of this water cut and obtains theoretical maximum dry density y
0Optimum moisture content x
0
The 4th step: solving equation F ' (x)=0 gets x
0=8.281, with x
0=8.281 generation people interpolating function F (x) get F (x
0)=y
0=2.0617.Be that theoretical optimum moisture content is 8.281%, corresponding theoretical maximum dry density is 2.0617g/cm
3
The 5th step: trying to achieve standard method optimum moisture content by the current specifications method is 8.8%.Replenish and mix water cut x processed
Bi% is respectively x
B1=8.28, x
B2=8.02 and x
B33 kinds of soil samples (α gets 0.5) of=8.54.
The 6th step: 3 kinds of soil samples of replenishing are hit respectively experiment, and its corresponding dry density y is determined in test
BiBe respectively y
Bi=2.063, y
B2=2.061 and y
B3=2.062.Determine that the soil tamp optimum moisture content is 8.28%, corresponding maximum dry density is 2.063g/cm
3
Fig. 2 is Lagrange interpolation polynomial matched curve and the standard method line of this example soil tamp water cut and dry density, and there is theoretical optimum moisture content x in the interpolation fitting curve all by test figure point and be downward opening convex
0Corresponding maximum dry density y
0, see as shown in Figure 21 expression interpolation fitting curve, 2 expression standard method curves, 3 expression test figure points, curve theory optimum moisture content A(x among the figure
0, y
0)=A (2.281,2.0617).The optimum moisture content that existing geotechnique experiment code method is determined and maximum dry density are seen among Fig. 2 in the standard line curve standard method optimum moisture content B(x ' among the figure
0, y
0')=B(8.8,2.06), in fact be test figure group (x
3, y
3).
Fig. 3 finds the solution optimum moisture content and dry density C point (8.28, the 2.063) comparison diagram that best theoretical water cut and dry density A point, standard method optimum moisture content and dry density B point and the inventive method are determined for the Lagrange interpolation polynomial match of this example.
This method is first by numerical interpolation approach true value, on the optimum moisture content basis of being determined by fitting theory optimum moisture content and current specifications method, the optimum moisture content difference of replenishing 3 kinds of preparations centered by the theoretical water cut of the best and determining with standard is the different moisture content soil sample in amplitude interval, and hit reality and dry density test, and then determine actual optimum moisture content.If the array C (8.28,2.063) that this method is determined is true value, C represents optimum moisture content, 4 expressions replenish experimental data point, the array B(8.8 that finds the solution of current specifications method then, 2.06) optimum moisture content error is 6.28%, and the dry density error is 0.15%.
The method of the invention is by mathematical theory the standard method to be determined the optimization of soil tamp optimum moisture content, and implementation step is clear, and processing ease is practical.Compare the current specifications method, although increased by 3 kinds of water cut soil body tests, improved widely the value precision of optimum moisture content, control has important application value to the engineering reinforcement effect for this.
The above is the preferred embodiments of the present invention only, is not limited to the present invention, and obviously, those skilled in the art can carry out various changes and modification and not break away from the spirit and scope of the present invention the present invention.Like this, if of the present invention these are revised and modification belongs within the scope of claim of the present invention and equivalent technologies thereof, then the present invention also is intended to comprise these changes and modification interior.
Claims (8)
1. the method for a definite soil tamp optimum moisture content is characterized in that: may further comprise the steps:
S1: the soil sample of mixing in advance different moisture content processed;
S2: soil sample is hit reality, cutting ring cutting and drying and processing, obtain soil sample water content and dried density data;
S3: determine take water cut x as variate-value that according to following formula dry density F (x) is the Lagrange interpolation polynomial of functional value:
In the formula,
The n experimental group number, x
iAnd x
jBe the water cut of test soil sample, y
jBe test water cut x
jCorresponding dry density;
S4: solving equation F ' (x)=0 determines best theoretical water cut x
0
S5: according to the theoretical water cut x of the best
0The optimum moisture content ω definite with the current specifications method
0, replenish the soil sample of mixing the multiple actual most probable optimum moisture content of system;
S6: carry out compaction test and hit real soil body dry density test replenishing soil sample, determine the soil tamp optimum moisture content.
2. the method for definite soil tamp optimum moisture content according to claim 1, it is characterized in that: the described soil sample of step S1 is the soil sample of making at least 5 kinds of different moisture contents according to the current specifications requirement.
3. the method for definite soil tamp optimum moisture content according to claim 1 is characterized in that: described step S2 and step S6 soil sample dry density are to require soil sample is hit reality, cutting and drying and processing and the dry density data that obtain according to the compaction test flow process.
4. the method for definite soil tamp optimum moisture content according to claim 1, it is characterized in that: the additional soil sample of described step S5 is the soil sample of 3 kinds of actual most probable optimum moisture contents, and its water cut is respectively x
0, x
0± α (x
0-ω
0), α is the difference coefficient, ω
0Be the definite optimum moisture content of current specifications method.
5. the method for definite soil tamp optimum moisture content according to claim 1 is characterized in that: the theoretical water cut of described the best is the extreme value of a function point x by interpolation letter F (x) being carried out differentiate and making F ' (x)=0 determine
0
6. the method for definite soil tamp optimum moisture content according to claim 4, it is characterized in that: described difference factor alpha span is 0.3～0.7.
7. the method for definite soil tamp optimum moisture content according to claim 6, it is characterized in that: described difference factor alpha can be come value according to the water sensitivity power of the soil body, the stronger then value of water sensitivity is less, and more weak then value can be relatively large, and the weak soil body reference value of water sensitivity is 0.5.
8. the method for definite soil tamp optimum moisture content according to claim 1 is characterized in that: at definite best theoretical water cut x
0Determine optimum moisture content ω with the standard method
0The basis on, the soil sample that again to mix 3 groups of actual most probables of system be optimum moisture content is also carried out compaction test, hits in 3 groups to do solid work the corresponding soil body water cut of density maximal value and be optimum moisture content.
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| CN109060479A (en) * | 2018-08-29 | 2018-12-21 | 长安大学 | A kind of configuration method of the dynamic model test soil body |
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Application publication date: 20130206 |