CN109583105A - A kind of calculation method of semi-rigid type base drying shrinkage stress - Google Patents
A kind of calculation method of semi-rigid type base drying shrinkage stress Download PDFInfo
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Abstract
The present invention proposes a kind of calculation method of semi-rigid type base drying shrinkage stress, comprising the following steps: compaction test, the basic assumption in calculating, calculates semi-rigid type base temperature contraction stress, calculates semi-rigid type base drying shrinkage stress and calculates shrinkage stress total in semi-rigid type base mechanical property test；Calculation method through the invention can clearly calculate the drying shrinkage stress of semi-rigid type base, be conducive to the clearly optimal construction method of road construction, so as to increase the coefficient of friction resistance of semi-rigid structure interlayer, the frictional resistance restraining force of generation can restrict the shrinkage stress of semirigid structure material, it can be efficiently against contraction fissure, calculation method of the present invention is in the design and construction of high-grade highway simultaneously, the pavement structure different for the weather conditions in different areas, calculation method of the present invention also can be applied to solve the problems, such as contraction fissure, the calculated result accuracy that calculation method of the present invention obtains is high, error range is small, practical application accuracy rate with higher.
Description
Technical field
The present invention relates to highway construction field more particularly to a kind of calculation methods of semi-rigid type base drying shrinkage stress.
Background technique
The superiority that semi-rigid asphalt pavement has other pavement structures irreplaceable, however, with semi-rigid drip
A large amount of uses on green road surface gradually find it there is also some serious problems, and here it is in semi-rigid type base, especially water
The early stage of mud Stabilized Base Asphalt Pavement occurs more than Asphalt Pavement with Flexible Base and frequent crack, and this problem is in state
It is outer also commonplace.
Currently, semi-rigid asphalt pavement is generallyd use in the design of China Higher grade highway pavement, semi-rigid type base drip
Green road base will include lime-flyash stabilized soil stabilized granular base course and cement stabilized granular base course, and representative is that two ashes are broken
Stone and cement stabilized macadam, the temperature that these two types of semi-rigid materials all has contracts and Dry Shrinkage Performance, and semi-rigid type base is easily made to generate collection
Crack, and lead to the generation of asphalt surface course reflection crack or reflection crack, with the immersion of rain (snow) water, traffic load repeatedly
Under effect, generation, which is washed away, starches phenomenon with purt, so that road surface is generated structural destruction quickly, since the generation of contraction fissure makes road
Declined with property and durability, the increase of construction investment and maintenance cost becomes great difficulty urgently to be solved in current engineering construction
Topic, the frictional resistance stress that can restrict semi-rigid type base shrinkage stress is found out in research and calculating to semi-rigid type base shrinkage stress
Size is particularly important.Therefore, the present invention proposes a kind of calculation method of semi-rigid type base drying shrinkage stress, to solve existing skill
Shortcoming in art.
Summary of the invention
In view of the above-mentioned problems, calculation method through the invention can clearly calculate the drying shrinkage stress of semi-rigid type base,
Be conducive to the clearly optimal construction method of road construction, so as to increase the coefficient of friction resistance of semi-rigid structure interlayer, produce
Raw frictional resistance restraining force can restrict the shrinkage stress of semirigid structure material, can be efficiently against contraction fissure.
The present invention proposes a kind of calculation method of semi-rigid type base drying shrinkage stress, comprising the following steps:
Step 1: compaction test
The maximum water holding capacity and maximum dry density of cement stabilized macadam in semi-rigid type base are surveyed using compaction test, and will be measured
Data record, provide control parameter for the mechanical property test of semi-rigid type base；
Step 2: mechanical property test
S1. the sample block of above-mentioned completion compaction test is placed on the lifting platform of pavement material intensity tester, allows test specimen
Deformation is increased with the uniform speed of 1mm/min carries out compressive strength test, wherein pressing Compressive Strength RCCalculation formula such as formula (1) institute
Show:
RC=P/A (1)
In formula (1), P is maximum pressure when sample block destroys；A is the cross-sectional area of sample block, A=π d40/ 4, d are sample block
Diameter；
S2. sample block was placed on pavement material intensity tester after 24 hours by by sample block health to stipulated time and completely full water
Lifting platform on, allow the deformation of test specimen to increase with the uniform speed of 1mm/min and carry out diametral compression test, wherein cleavage strength RjCalculating
Shown in formula such as formula (2):
Rj=2P/ π dH (2)
In formula (2), P be P be sample block destroy when maximum pressure；H is sample block height；D is the diameter of sample block；
S3. sample block is subjected to compression rebound modulu test, calculates compression rebound modulu E；
Step 3: the basic assumption in calculating
A1. setting below the semi-rigid type base on road surface is underlayment, it is then assumed that the underlayment and base that mutually constrain are equal
For deformable elastic construction, constraint of the bottom underlayment to semi-rigid type base is solved；
A2. when underlayment and semi-rigid type base generate relative displacement in the horizontal direction, the friction stree of contact surface point can
It is obtained according to formula (3):
τx=-Cx·ux (3)
In formula (3), the friction stree of contact surface point is directly proportional to the horizontal displacement of the point；CxFor frictional resistance system
Number；uxFor horizontal displacement at x in base；Negative sign indicates that friction stree is forever opposite with displacement；
A3. semi-rigid type base is assumed in the range of thickness change, and the temperature change and change of moisture content being subjected to are equal
Even, the temperature shrinkage and dry contraction and shrinkage stress generated is also uniform；
A4. the longitudinal restraint for assuming the road semi-rigid type base Zhi Shouyan length direction, without by lateral confinement；
Step 4: semi-rigid type base temperature contraction stress is calculated
B1. the cross section for assuming semi-rigid type base is rectangle, at the arbitrary point x of base, intercepts the microbody of one section of long dx,
Microbody width is B, and with a thickness of H, section mean temperature shrinkage stress is σt(x), shear stress τx, i.e. base and base interlayer
Friction stree, taking semi-rigid type base length is L, and the equilibrium equation of microbody horizontal direction can be obtained according to formula (4):
[σt(x)+dσt(x)]BH-σt(x)BH+τxBdx=0 (4)
Formula (5) are can be obtained into formula (4) abbreviation:
B2. when semi-rigid type base when the temperature drops, displacement components u in base at the section xxAccording to formula (6) it follows that
ux=uσ+αttx (6)
In formula, uxFor the displacement in base at the section x, synthesized by constrained displacement with free displacement；uσPosition is constrained for section
It moves；αtFor temperature shrinkage coefficient；T is the temperature drop-out value of base；
Formula (6) both sides obtaining formula (7) x differential again, then by formula (7)) both sides obtain formula to x differential again
(8):
B3. the temperature contraction stress in base at the section x is solved according to formula (9), then formula (9) both sides obtained x differential public
Formula (10):
B4. formula in B3 (9) substitution formula (10) is obtained formula (11), then brings formula (11) into formula that B1 is obtained
(5) in, new formula (12) are obtained:
B5. the formula (3) in step 3 A1 is substituted into formula (12), and enabledObtain new formula
(13), formula (14) then by formula (13) progress general solution are obtained:
The general solution of this differential equation are as follows:
ux=C1chβx+C2shβx (14)
B6. hypothetical boundary condition are as follows: 1. as x=0, ux=0；2. as x=L/2, σt(x)=0 it, is then solved
Formula (14)；
Step 5: semi-rigid type base drying shrinkage stress is calculated
C1. dry to take length for the semi-rigid type base of L, semi-rigid type base is dry produced by by underlayment constraint in drying shrinkage process
Stress under compression is denoted as σd(x), the microbody of one section of dx long is still intercepted at the x of arbitrary point, width B rubs suffered by the bottom with a thickness of H
It wipes stress and is still denoted as τx；
Then shown in the equilibrium equation of microbody horizontal direction such as formula (15), then formula (15) is solved to obtain formula
(16):
[σd(x)+dσd(x)]BH-σd(x)BH+τxBdx=0 (15)
C2. when water content reduces in semi-rigid type base, the displacement in base at the section x can be solved according to formula (17)
ux
ux=uσ+αdωx
(17)
In formula, uxFor the displacement in base at the section x, uxIt is synthesized by constrained displacement with free displacement；uσPosition is constrained for section
It moves；αdFor dry constriction coefficient；ω is the water content decreasing value of base；
Formula (17) both sides are obtained into formula (18) to two subdifferential of x:
Drying shrinkage stress at section can indicate again such as formula (19):
Then by formula (19) both sides to x differential, further according to the available new formula (20) of formula (18):
Formula (16) are substituted into formula (20), further according to the formula (3) in step 3 A1, and are enabledIt can
To obtain new formula (21):
C3. the side identical and two equations with the form of formula (13) in step 4 B5 according to differential equation formula (21)
Boundary's condition also this identical rule, therefore formula (22) can be derived from according to temperature contraction stress:
By formula (22) it is found that as x=0, drying shrinkage stress also obtains maximum value, i.e., as shown in formula (23)；
Step 6: shrinkage stress total in semi-rigid type base is calculated
Temperature contraction stress and drying shrinkage stress are overlapped, shrinkage stress total in semi-rigid type base is obtained.
Further improvement lies in that: the compaction test detailed process in the step 1 are as follows: the test specimen of compaction test will be used for
According to the resulting optimum moisture content mix of heavy compaction, maximum dry density control is prepared using Static compaction method, is placed in health-preserving chamber
Health, control health temperature are 2 degrees Celsius of 20 scholar, should be controlled in southern area in 2 degrees Celsius of 25 scholar, and health humidity is 90%,
Conditioned time is 2-3 days.
Further improvement lies in that: sample block is subjected to compression rebound modulu test in the step 2 S3, passes through Inversion Calculation
Module is based on the effective compression rebound modulu E of road surface gain of parameter semi-rigid type base, and wherein the calculation formula of compression rebound modulu E is such as
Shown in formula (24):
E=PH/L (24)
In formula (24), P is unit pressure；H is sample block height；L is sample block resilience amount.
Further improvement lies in that: being set below the semi-rigid type base on road surface in the step 3 A1 is underlayment, with base
It compares, the thickness very little of underlayment it is then assumed that the underlayment and base that mutually constrain are deformable elastic construction, then is led to
The shear stress crossed between underlayment and base and the relationship of restrained shrinkage deformation are come the constraint that shows underlayment to semi-rigid type base.
Further improvement lies in that: the coefficient of frictional resistance value of underlayment is C in the step 3 A2x=0.6N/mm3。
Further improvement lies in that: in the step 4 B6, it is assumed that boundary condition are as follows: 1. as x=0, ux=0, formula
(14) solution procedure are as follows: be 1. easy to acquire C by boundary condition1=0, it is further according to formula (9) and formula (7) it can be concluded that new
Formula (25):
According to asking to obtain C1=0 and formula (14) available formula (26).
Further improvement lies in that: in the step 4 B6, it is assumed that boundary condition are as follows: 2. as x=L/2, σt(x)=0, public
The solution procedure of formula (14) are as follows: 2. boundary condition is substituted into formula (25) and formula (26) can acquireAgain
According toAnd formula (27) finds out ux；
Formula (27) are substituted into formula (25), formula (28) is obtained, section temperature contraction stress can be solved:
By formula (28) it is found that as x=0, temperature contraction stress is maximum, shown in maximum value such as formula (29).
Further improvement lies in that: the specific formula for calculation of shrinkage stress total in semi-rigid type base in the step 6 are as follows:
Formula (29) is added with formula (23), formula (30) is obtained, maximum collapse stress total in semi-rigid type base can be calculated.
Further improvement lies in that: in the formula (30), since temperature is to reduce, t is negative value, also, with drying shrinkage
Progress, water content is gradually reduced, and thus, the variable quantity ω of water content is also negative value.
The invention has the benefit that calculation method through the invention can clearly calculate the drying shrinkage of semi-rigid type base
Stress is conducive to the clearly optimal construction method of road construction, so as to increase the frictional resistance system of semi-rigid structure interlayer
Number, the frictional resistance restraining force of generation can restrict the shrinkage stress of semirigid structure material, can be efficiently against contraction fissure, together
When calculation method of the present invention in the design and construction of high-grade highway, the road surface different for the weather conditions in different areas is tied
Structure, calculation method of the present invention also can be applied to solve the problems, such as contraction fissure, and the calculated result that calculation method of the present invention obtains is quasi-
True property is high, and error range is small, practical application accuracy rate with higher.
Specific embodiment
In order to realize invention technological means, reach purpose and effect is easy to understand, below with reference to specific implementation
Mode, the present invention is further explained.
The present embodiment proposes a kind of calculation method of semi-rigid type base drying shrinkage stress, comprising the following steps:
Step 1: compaction test
The test specimen of compaction test will be used for according to the resulting optimum moisture content mix of heavy compaction, maximum dry density control,
It is prepared using Static compaction method, is placed in health-preserving chamber health, control health temperature is 20 degrees Celsius, should be controlled in southern area 25
Degree Celsius, health humidity is 90%, and conditioned time is 2 days, hits real try out in the maximum of cement stabilized macadam in test semi-rigid type base
Water content and maximum dry density, and the data record that will be measured provide control ginseng for the mechanical property test of semi-rigid type base
Number；
Step 2: mechanical property test
S1. the sample block of above-mentioned completion compaction test is placed on the lifting platform of pavement material intensity tester, allows test specimen
Deformation is increased with the uniform speed of 1mm/min carries out compressive strength test, wherein pressing Compressive Strength RCCalculation formula such as formula (1) institute
Show:
RC=P/A (1)
In formula (1), P is maximum pressure when sample block destroys；A is the cross-sectional area of sample block, A=π d40/ 4, d are sample block
Diameter；
S2. sample block was placed on pavement material intensity tester after 24 hours by by sample block health to stipulated time and completely full water
Lifting platform on, allow the deformation of test specimen to increase with the uniform speed of 1mm/min and carry out diametral compression test, wherein cleavage strength RjCalculating
Shown in formula such as formula (2):
Rj=2P/ π dH (2)
In formula (2), P be P be sample block destroy when maximum pressure；H is sample block height；D is the diameter of sample block；
S3. sample block is subjected to compression rebound modulu test, it is semi-rigid to be based on road surface gain of parameter by Inversion Calculation module
The effective compression rebound modulu E of base, wherein shown in the calculation formula of compression rebound modulu E such as formula (24):
E=PH/L (24)
In formula (24), P is unit pressure；H is sample block height；L is sample block resilience amount；
Step 3: the basic assumption in calculating
A1. setting below the semi-rigid type base on road surface is underlayment, compared with base, the thickness very little of underlayment, then
It is assumed that the underlayment and base that mutually constrain are deformable elastic construction, then pass through the shear stress between underlayment and base
Constraint of the underlayment to semi-rigid type base is showed with the relationship of restrained shrinkage deformation；
A2. when underlayment and semi-rigid type base generate relative displacement in the horizontal direction, the friction stree of contact surface point can
It is obtained according to formula (3):
τx=-Cx·ux (3)
In formula (3), the friction stree of contact surface point is directly proportional to the horizontal displacement of the point；CxFor frictional resistance system
Number；uxFor horizontal displacement at x in base；Negative sign indicates friction stree forever with displacement on the contrary, the coefficient of frictional resistance of underlayment
Value is Cx=0.6N/mm3；
A3. semi-rigid type base is assumed in the range of thickness change, and the temperature change and change of moisture content being subjected to are equal
Even, the temperature shrinkage and dry contraction and shrinkage stress generated is also uniform；
A4. the longitudinal restraint for assuming the road semi-rigid type base Zhi Shouyan length direction, without by lateral confinement；
Step 4: semi-rigid type base temperature contraction stress is calculated
B1. the cross section for assuming semi-rigid type base is rectangle, at the arbitrary point x of base, intercepts the microbody of one section of long dx,
Microbody width is B, and with a thickness of H, section mean temperature shrinkage stress is σt(x), shear stress τx, i.e. base and base interlayer
Friction stree, taking semi-rigid type base length is L, and the equilibrium equation of microbody horizontal direction can be obtained according to formula (4):
[σt(x)+dσt(x)]BH-σt(x)BH+τxBdx=0 (4)
Formula (5) are can be obtained into formula (4) abbreviation:
B2. when semi-rigid type base when the temperature drops, displacement components u in base at the section xxAccording to formula (6) it follows that
ux=uσ+αttx (6)
In formula, uxFor the displacement in base at the section x, synthesized by constrained displacement with free displacement；uσPosition is constrained for section
It moves；αtFor temperature shrinkage coefficient；T is the temperature drop-out value of base；
Formula (6) both sides obtaining formula (7) x differential again, then by formula (7)) both sides obtain formula to x differential again
(8):
B3. the temperature contraction stress in base at the section x is solved according to formula (9), then formula (9) both sides obtained x differential public
Formula (10):
B4. formula in B3 (9) substitution formula (10) is obtained formula (11), then brings formula (11) into formula that B1 is obtained
(5) in, new formula (12) are obtained:
B5. the formula (3) in step 3 A1 is substituted into formula (12), and enabledObtain new formula
(13), formula (14) then by formula (13) progress general solution are obtained:
The general solution of this differential equation are as follows:
ux=C1chβx+C2shβx (14)
B6. hypothetical boundary condition are as follows: 1. as x=0, ux=0；2. as x=L/2, σt(x)=0 it, is then solved
Formula (14):
Hypothetical boundary condition are as follows: 1. as x=0, ux=0, the solution procedure of formula (14) are as follows: 1. held very much by boundary condition
Easily acquire C1=0, further according to formula (9) and formula (7) it can be concluded that new formula (25) obtains:
According to asking to obtain C1=0 and formula (14) available formula (26).
Hypothetical boundary condition are as follows: 2. as x=L/2, σt(x)=0, the solution procedure of formula (14) are as follows: by boundary condition
2. substituting into formula (25) and formula (26) can acquireFurther according toAnd formula (27)
Find out ux；
Formula (27) are substituted into formula (25), formula (28) is obtained, section temperature contraction stress can be solved:
By formula (28) it is found that as x=0, temperature contraction stress is maximum, shown in maximum value such as formula (29):
Step 5: semi-rigid type base drying shrinkage stress is calculated
C1. dry to take length for the semi-rigid type base of L, semi-rigid type base is dry produced by by underlayment constraint in drying shrinkage process
Stress under compression is denoted as σd(x), the microbody of one section of dx long is still intercepted at the x of arbitrary point, width B rubs suffered by the bottom with a thickness of H
It wipes stress and is still denoted as τx；
Then shown in the equilibrium equation of microbody horizontal direction such as formula (15), then formula (15) is solved to obtain formula
(16):
[σd(x)+dσd(x)]BH-σd(x)BH+τxBdx=0 (15)
C2. when water content reduces in semi-rigid type base, the displacement in base at the section x can be solved according to formula (17)
ux
ux=uσ+αdωx
(17)
In formula, uxFor the displacement in base at the section x, uxIt is synthesized by constrained displacement with free displacement；uσPosition is constrained for section
It moves；αdFor dry constriction coefficient；ω is the water content decreasing value of base；
Formula (17) both sides are obtained into formula (18) to two subdifferential of x:
Drying shrinkage stress at section can indicate again such as formula (19):
Then by formula (19) both sides to x differential, further according to the available new formula (20) of formula (18):
Formula (16) are substituted into formula (20), further according to the formula (3) in step 3 A1, and are enabledIt can
To obtain new formula (21):
C3. the side identical and two equations with the form of formula (13) in step 4 B5 according to differential equation formula (21)
Boundary's condition also this identical rule, therefore formula (22) can be derived from according to temperature contraction stress:
By formula (22) it is found that as x=0, drying shrinkage stress also obtains maximum value, i.e., as shown in formula (23)；
Step 6: shrinkage stress total in semi-rigid type base is calculated
Temperature contraction stress and drying shrinkage stress are overlapped, shrinkage stress total in semi-rigid type base, semi-rigid type base are obtained
The specific formula for calculation of interior total shrinkage stress are as follows: formula (29) is added with formula (23), formula (30) is obtained, can calculate
Maximum collapse stress total in semi-rigid type base out；
In formula (30), since temperature is to reduce, t is negative value, also, with the progress of drying shrinkage, water content is gradually
Reduce, thus, the variable quantity ω of water content is also negative value.
Calculation method through the invention can clearly calculate the drying shrinkage stress of semi-rigid type base, be conducive to road construction
Optimal construction method is specified, so as to increase the coefficient of friction resistance of semi-rigid structure interlayer, the frictional resistance restraining force of generation
The shrinkage stress of semirigid structure material can be restricted, can be efficiently against contraction fissure, while calculation method of the present invention exists
In the design and construction of high-grade highway, the pavement structure different for the weather conditions in different areas, calculation method of the present invention
Also it can be applied to solve the problems, such as contraction fissure, the calculated result accuracy that calculation method of the present invention obtains is high, and error range is small,
Practical application accuracy rate with higher.
The basic principles, main features and advantages of the invention have been shown and described above.The technical staff of the industry should
Understand, the present invention is not limited to the above embodiments, and the above embodiments and description only describe originals of the invention
Reason, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes and improvements
It all fall within the protetion scope of the claimed invention.The claimed scope of the invention is by appended claims and its equivalent circle
It is fixed.
Claims (9)
1. a kind of calculation method of semi-rigid type base drying shrinkage stress, it is characterised in that: the following steps are included:
Step 1: compaction test
The maximum water holding capacity and maximum dry density of cement stabilized macadam in semi-rigid type base, and the number that will be measured are surveyed using compaction test
According to record, control parameter is provided for the mechanical property test of semi-rigid type base；
Step 2: mechanical property test
S1. the sample block of above-mentioned completion compaction test is placed on the lifting platform of pavement material intensity tester, allows the deformation of test specimen
Increased with the uniform speed of 1mm/min and carry out compressive strength test, wherein pressing Compressive Strength RCShown in calculation formula such as formula (1):
RC=P/A (1)
In formula (1), P is maximum pressure when sample block destroys；A is the cross-sectional area of sample block, A=π d40/ 4, d are the straight of sample block
Diameter；
S2. sample block is placed on the liter of pavement material intensity tester by by sample block health to stipulated time and completely full water after 24 hours
It drops on platform, allows the deformation of test specimen to increase with the uniform speed of 1mm/min and carry out diametral compression test, wherein cleavage strength RjCalculation formula
As shown in formula (2):
Rj=2P/ π dH (2)
In formula (2), P be P be sample block destroy when maximum pressure；H is sample block height；D is the diameter of sample block；
S3. sample block is subjected to compression rebound modulu test, calculates compression rebound modulu E；
Step 3: the basic assumption in calculating
A1. setting below the semi-rigid type base on road surface is underlayment, it is then assumed that the underlayment and base that mutually constrain are can
The elastic construction of deformation solves constraint of the bottom underlayment to semi-rigid type base；
A2. when underlayment and semi-rigid type base generate relative displacement in the horizontal direction, the friction stree of contact surface point can basis
Formula (3) obtains:
τx=-Cx·ux (3)
In formula (3), the friction stree of contact surface point is directly proportional to the horizontal displacement of the point；CxFor coefficient of frictional resistance；uxFor
Horizontal displacement at x in base；Negative sign indicates that friction stree is forever opposite with displacement；
A3. assume semi-rigid type base in the range of thickness change, the temperature change and change of moisture content being subjected to be it is uniform,
Its temperature shrinkage generated and dry contraction and shrinkage stress are also uniform；
A4. the longitudinal restraint for assuming the road semi-rigid type base Zhi Shouyan length direction, without by lateral confinement；
Step 4: semi-rigid type base temperature contraction stress is calculated
B1. the cross section for assuming semi-rigid type base is rectangle, at the arbitrary point x of base, intercepts the microbody of one section of long dx, microbody
Width is B, and with a thickness of H, section mean temperature shrinkage stress is σt(x), shear stress τx, i.e. the friction of base and base interlayer
Stress, taking semi-rigid type base length is L, and the equilibrium equation of microbody horizontal direction can be obtained according to formula (4):
[σt(x)+dσt(x)]BH-σt(x)BH+τxBdx=0 (4)
Formula (5) are can be obtained into formula (4) abbreviation:
B2. when semi-rigid type base when the temperature drops, displacement components u in base at the section xxAccording to formula (6) it follows that
ux=uσ+αttx (6)
In formula, uxFor the displacement in base at the section x, synthesized by constrained displacement with free displacement；uσFor section constrained displacement；αt
For temperature shrinkage coefficient；T is the temperature drop-out value of base；
Formula (6) both sides obtaining formula (7) x differential again, then by formula (7)) both sides obtain formula (8) to x differential again:
B3. the temperature contraction stress in base at the section x is solved according to formula (9), then formula (9) both sides is obtained into formula to x differential
(10):
B4. formula in B3 (9) substitution formula (10) is obtained formula (11), then brings formula (11) into formula (5) that B1 is obtained
In, obtain new formula (12):
B5. the formula (3) in step 3 A1 is substituted into formula (12), and enabledIt obtains new formula (13), then
Formula (13) progress general solution is obtained into formula (14):
The general solution of this differential equation are as follows:
ux=C1chβx+C2shβx (14)
B6. hypothetical boundary condition are as follows: 1. as x=0, ux=0；2. as x=L/2, σt(x)=0 solution formula, is then carried out
(14)；
Step 5: semi-rigid type base drying shrinkage stress is calculated
C1. dry to take length for the semi-rigid type base of L, drying shrinkage produced by semi-rigid type base is constrained in drying shrinkage process by underlayment is answered
Power is denoted as σd(x), the microbody of one section of dx long is still intercepted at the x of arbitrary point, width B rubs suffered by bottom and answers with a thickness of H
Power is still denoted as τx；
Then shown in the equilibrium equation of microbody horizontal direction such as formula (15), then formula (15) is solved to obtain formula
(16):
[σd(x)+dσd(x)]BH-σd(x)BH+τxBdx=0 (15)
C2. when water content reduces in semi-rigid type base, the displacement components u in base at the section x can be solved according to formula (17)x
ux=uσ+αdωx
(17)
In formula, uxFor the displacement in base at the section x, uxIt is synthesized by constrained displacement with free displacement；uσFor section constrained displacement；αd
For dry constriction coefficient；ω is the water content decreasing value of base；
Formula (17) both sides are obtained into formula (18) to two subdifferential of x:
Drying shrinkage stress at section can indicate again such as formula (19):
Then by formula (19) both sides to x differential, further according to the available new formula (20) of formula (18):
Formula (16) are substituted into formula (20), further according to the formula (3) in step 3 A1, and are enabledIt is available
New formula (21):
C3. the perimeter strip identical and two equations with the form of formula (13) in step 4 B5 according to differential equation formula (21)
Part also this identical rule, therefore formula (22) can be derived from according to temperature contraction stress:
By formula (22) it is found that as x=0, drying shrinkage stress also obtains maximum value, i.e., as shown in formula (23)；
Step 6: shrinkage stress total in semi-rigid type base is calculated
Temperature contraction stress and drying shrinkage stress are overlapped, shrinkage stress total in semi-rigid type base is obtained.
2. a kind of calculation method of semi-rigid type base drying shrinkage stress according to claim 1, it is characterised in that: the step
Compaction test detailed process in one are as follows: mix the test specimen for being used for compaction test according to the resulting optimum moisture content of heavy compaction
It closes, maximum dry density control is prepared using Static compaction method, is placed in health-preserving chamber health, and control health temperature is that 20 scholars 2 are Celsius
Degree should be controlled in southern area in 2 degrees Celsius of 25 scholar, and health humidity is 90%, and conditioned time is 2-3 days.
3. a kind of calculation method of semi-rigid type base drying shrinkage stress according to claim 1, it is characterised in that: the step
Sample block is subjected to compression rebound modulu test in two S3, being based on road surface gain of parameter semi-rigid type base by Inversion Calculation module has
Compression rebound modulu E is imitated, wherein shown in the calculation formula of compression rebound modulu E such as formula (24):
E=PH/L (24)
In formula (24), P is unit pressure；H is sample block height；L is sample block resilience amount.
4. a kind of calculation method of semi-rigid type base drying shrinkage stress according to claim 1, it is characterised in that: the step
Being set below the semi-rigid type base on road surface in three A1 is underlayment, compared with base, the thickness very little of underlayment, it is then assumed that phase
The underlayment and base mutually constrained is deformable elastic construction, then passes through the shear stress between underlayment and base and constraint
The relationship of contraction distortion shows constraint of the underlayment to semi-rigid type base.
5. a kind of calculation method of semi-rigid type base drying shrinkage stress according to claim 1, it is characterised in that: the step
The coefficient of frictional resistance value of underlayment is C in three A2x=0.6N/mm3。
6. a kind of calculation method of semi-rigid type base drying shrinkage stress according to claim 1, it is characterised in that: the step
In four B6, it is assumed that boundary condition are as follows: 1. as x=0, ux=0, the solution procedure of formula (14) are as follows: 1. held very much by boundary condition
Easily acquire C1=0, further according to formula (9) and formula (7) it can be concluded that new formula (25) obtains:
According to asking to obtain C1=0 and formula (14) available formula (26).
7. a kind of calculation method of semi-rigid type base drying shrinkage stress according to claim 6, it is characterised in that: the step
In four B6, it is assumed that boundary condition are as follows: 2. as x=L/2, σt(x)=0, the solution procedure of formula (14) are as follows: 2. by boundary condition
Substituting into formula (25) and formula (26) can acquireFurther according toAnd formula (27)
Find out ux；
Formula (27) are substituted into formula (25), formula (28) is obtained, section temperature contraction stress can be solved:
By formula (28) it is found that as x=0, temperature contraction stress is maximum, shown in maximum value such as formula (29).
8. a kind of calculation method of semi-rigid type base drying shrinkage stress according to claim 7, it is characterised in that: the step
The specific formula for calculation of shrinkage stress total in semi-rigid type base in six are as follows: formula (29) is added with formula (23), obtains public affairs
Formula (30), can calculate maximum collapse stress total in semi-rigid type base.
9. a kind of calculation method of semi-rigid type base drying shrinkage stress according to claim 8, it is characterised in that: the formula
(30) in, since temperature is to reduce, t is negative value, also, with the progress of drying shrinkage, water content is gradually reduced, thus,
The variable quantity ω of water content is also negative value.
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Application publication date: 20190405 |