Prestressed tensioning method and its application to ...

Journal of Chongqing University English Edition [ISSN 1671-8224]

Vol. 16 No. 1

March 2017

38

doi:10.11835/j.issn.1671-8224.2017.01.04

To cite this article: ZHANG Peng, LONG Yan-cheng, LUO Bing. Prestressed tensioning method and its application to testing anchor stress of anchor cables for side-slope

stabilization [J]. J Chongqing Univ Eng Ed [ISSN 1671-8224], 2017, 16(1): 38-50.

Prestressed tensioning method and its application to testing anchor stress of anchor cables for side-slope stabilization

ZHANG Peng 1,2,†, LONG Yan-cheng 3, LUO Bing 1, 2 1 China Merchants Chongqing Communications Technology Research & Design Institute Co.,Ltd. Chongqing 400067, P. R. China

2 China Highway Engineering Technology & Research Center, Chongqing 400067, P. R. China

3 Guizhou Expressway Group Co.,Ltd., Guiyang, Guizhou 550004, P. R. China

Received 19 May 2016; received in revised form 1 July 2016

Abstract: The anchor stress extent of a prestress anchor cable project has a direct relation with the project safety and

performance. Prestressed tensioning method is a kind of nondestructive testing method, by which a reverse stretching load is

applied on the external exposure section of anchor cable under construction or in service, and then the elongation variation of

stress bars is measured to determine the anchor stress. We elaborated the theory and testing mechanism of prestressed tensioning

method, and systematically studied key issues during the prestressed tensioning process of anchor cable by using physical model

test, including the composition of tension stress-elongation curve, the variation of anchor stress, the compensation of locked

anchor stress, and the judgment of anchor stress, and verified the theory feasibility of prestressed tensioning method. A case study

on slope anchor cable of one highway project was conducted to further discuss on the test method, operation procedures and

judgment of prestressed tensioning method on obtaining anchor stress, and then the test data of three situations were analyzed.

The result provides a theoretical basis and technical base for the application of prestressed tensioning method to the evaluation of

construction quality and operation conditions of anchor cable project.

Keywords: anchor cable; anchor stress; prestressed tensioning method; model test

CLC number: U417.1 Document code: A

1 Introduction a

Since the initial application abroad in 1958, the

prestress anchor cable has been widely used in

engineering fields like water conservancy, hydro-power,

† ZHANG Peng (张朋): [email protected].

Funded by the Science and Technolog Program of Ministry of

Transport of P. R. China (No. 2012318352100).

mining, metallurgy, railways, roads, buildings and

military projects, especially slope strengthening,

foundation pit supporting, hydraulic structure

strengthening, etc. The superiority and socioeconomic

benefits of active shoring are irreplaceable comparing

with other conventional methods [1]. As a key parameter

in anchoring technology, the anchor stress (also known as

anchor prestress, work load, work stress, anchorage force,

etc.) of a prestress anchor cable is influenced by

P. Zhang, et al.

Side slope anchor cable

J. Chongqing Univ. Eng. Ed. [ISSN 1671-8224], 2017, 16(1): 38-50 39

subjective and objective factors, such as the hydro-

geological condition, climatic environment, and

uncertainties of design and construction. The changes of

stress value and work conditions have direct impact on

the safety of the structure [2-6]. Hence, how to detect the

anchor stress of prestress anchor cable under construction

or in service is a key issue for engineering construction

and operation management department. Currently, the

main method contains presetting force-meter on the outer

anchor head [7-8], nondestructive testing method based on

acoustic theory [9-15], and the prestressed tensioning

method (also known as pulling method, re-drawing

method, etc.) based on the prestressed tensioning stress-

elongation curve. Among these methods, the prestressed

tensioning method has been applied worldwide due to its

reliability, high precision and operational convenience [16-

20]. However, until now, its theory and test mechanism

has not been clearly explained and verified, and the

detection error, scope of application, accuracy and

judgment standard still need further illustration.

2 Prestressed tensioning method

The prestress anchor cable bears tensile force, and it

includes an inner anchoring section, a free section, an

outer anchoring section and an outer exposure section

(Fig. 1). Prestressed tensioning is a kind of testing

method, by which a reverse stretching load is applied on

the external exposure section of the anchor cable under

construction or in service, and then the elongation

variation of stress bars is measured to determine the

anchor stress. In an ideal state, there is no slippage

between the inner anchoring section and slurry, which

provides the anchoring force. The working stress of the free section is the anchor stress 0 , and the rock block or

concrete structure provides an outer anchoring section with supporting force 0N . The anchor bearing plate

supports the anchor, 0 0N A , where A is the area of

the anchor cable. During the prestressed tensioning

process, the loading equipment (lifting jack) clamps the

outer exposure section and applies prestressed tensioning

2N . The stress of outer exposure section 2 increases

gradually from 0, 2 2N A , and meanwhile the stress of

working anchor supported by bearing plate 1 decreases

gradually. 1 1 1N A , and 2 1 0N N N , where 1A is

the sectional area of working anchor. When 1 is equal

to 0 , 1N reduces to 0, and at this time,

2 0 0 2N N A A . If the tension process continues,

the free section and outer exposure section will be joint

load carrying to extend, which leads to an inflection point

because of the decreasing slope of tension stress-

elongation curve. The tension load at this inflection point

is equal to anchor stress or working stress of the free

section.

N2

σ0

N0 N1

Tool anchor

Loading equipment

Stop block

Outer

anchoring

Outer

exposed

section

Free section Inner anchoring

Fig. 1 Schematic diagram of prestressed tensioning method

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The general anchor cable stress bar adopts steel

strand, of which the designed working load is less than

75 of the ultimate load of steel strands. Therefore, the

anchor stress of anchor cable under construction or in

active service is in the elastic deformation phase of

steel strands. Under the prestressed tensioning process

(the maximum tension is equal to 75 of the ultimate

load), when 2 1 0N N N and 1 0N , the

computational formula of tension stress and elongation

is

fl

nSE . (1)

When 2 0N N and 1 0N , the computational

formula of tension and elongation is

0 00f f L l f L l f Lf l

nSE nSE nSE

, (2)

where f is the tension stress, 0f is the anchor stress, δ

is the elongation, L is the length of free section, l is the

length of prestressed tensioning section, n is the

number of steel strands, S is the sectional area of a

single steel strand, and E is the elasticity modulus. Eqs.

(1) and (2) show that the tension stress-elongation

curve consists of 2 crossing straight lines with different

slopes, and the mutational site of slope or crossing

point of straight lines is the value of anchor stress.

With the same anchor cable, the smaller the length ratio

of prestressed tensioning section and free section is, the

more obvious the reflection point is. The theoretical

tension stress-elongation curve is shown in Fig. 2. When max 195.3 kN,f 0 156 kN,f 1 m,l 1,n

2140 mm ,S and 190.4 GPa,E the length ratios of

prestressed tensioning section and free section are 1/40,

1/30, 1/20, 1/10, and 1/5, respectively.

When the prestressed tensioning load is applied on

the prestress anchor cable (the outer steel strand has

been cut, and the connector can be used if the length of

outer exposure section is not enough [10]), the curve of

tension stress-elongation can be used to judge the

anchor stress. Indoor physical analog experimental

studies are conducted to study the key issues, including

the test mechanism, composition of tension stress-

elongation curve, the variation of anchor stress, the

compensation of anchor stress, and the judgment of

anchor stress.

Fig. 2 Tension stress-elongation curve under ideal conditions

3 Model experiment and test

3.1 Experiment model and test equipment

A concrete pier base is adopted to simulate an

anchor cable structure with the pier strength of C50, a

length of 15 m, a width of 0.7 m, a height of 1.2 m and

a round hole casing diameter of 19 cm in the buried

zone. Fig. 3 shows the experiment model and test

equipment. The prestressed tensioning section of the

anchor cable model (exposed section) is equipped with

a limit device, a loading device (DS-10 tensioning

system), a tool anchor, and so on. The fixed end of

outer anchor is composed of a tool anchor, a

dynamometer and a pier base, the free end is in the

inner casing pipe of the pier base, and the inner anchor

end is fixed by a loading device (DS-10 tensioning

system) and a working anchor. The experimental

anchor cable structure consists of four steel strands

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with a diameter of 15.2 mm, a length of 17 m, an

effective cross section area of 140 mm2, a prestressed

tensioning fb of about 269.7 kN, a non-proportional

extension force of 247.4 kN, an elongation of 5.5 and

an elastic modulus of 190.37 GPa. The working anchor,

the tool anchor and the clip are OVM15-4. HRC

measurement results show that the anchor hardness is

equal to or greater than 20, and the clip is equal to or

greater than 57. The limit device is custom-made. The

DS-10 tension system can collect and record the tensile

load and elongation with a load range of 0 kN to

1 300 kN and its resolution ratio is 0.01 kN, the

displacement meter ranges from 0 mm to 200 mm and

its resolution ratio is 0.01 mm, and the dynamometer

ranges from 0 kN to 1 300 kN and its resolution ratio is

0.01 kN.

3.2 Experimental process

The DS-10 tension system and the dynamometer will

be calibrated before experiments, and the deviation is

less than or equal to 1‰. The model exerts f0 through

DS-10 type tension system. Since the concrete

resilience can be ignored and stress of the anchor free

end is not changed basically, the stress of outer anchor

fixed section and inner anchor fixed section is basically

equal and the deviation is less than 0.5. When the

anchor cable structure stress is stabilized at the range of

set value f0, the DS-10 tension system is loaded on the

exposed section of anchor and the prestressed

tensioning load is exerted with the maximum tension

fmax, which is 72 of the steel strand tension resistance

(4 strands 195.3 kN/strand). At the same time, the

tension load and elongation are recorded every 10 kN.

After the prestressed tensioning is over, the prestressed

tensioning side will load the equipment and remove the

loads, while the dynamometer will still keep recording

the changes of outer fixed section stress of the anchor

cable structure. When the anchor cable structure

working stress (the dynamometer test value) becomes

stable, the anchor stress will be removed by the DS-10

tension system of the inner fixed section of anchor

cable structure. The above is a circle of the experiment

test. After one experiment is completed, the next

prestressed tensioning test experiment will start. There

are nine groups of experiments, and the set values of

the stress of the anchor cable structure are shown in

Table1.

Table 1 Set values and test results of the stress for the anchor

experiment

f0/fb/ f0/fmax Stress/kN Test

result/kN Deviation

14 0.2 156.24 158.23 1.27

22 0.3 234.65 235.23 0.25

29 0.4 312.43 313.97 0.54

36 0.5 389.39 390.97 0.41

44 0.6 469.36 471.49 0.45

51 0.7 546.70 547.74 0.19

58 0.8 625.47 634.03 1.37

65 0.9 703.30 693.66 1.37

72 1.0 781.19 751.81 3.76

3.3 Results and analysis

The similarities and differences between curve of

measured tensioning force-elongation and the theory

curve are analyzed. Fig. 4 shows the curve of measured

tensioning force (f)-elongation (δ) for anchor cable

model under different f0. Because the stress under the

anchor and the tensile force are in the elastic

deformation stage of the steel strands, according to

Eqs.(1) and (2), the corresponding theoretical extension

values of prestressed tensioning at various levels will

be calculated so as to compare and verify them. As a

result, the actual test curves are two approximately

P. Zhang, et al.



straight lines which are similar to the theoretical curves,

and thus it can test and verify the feasibility of the

prestressed tensioning theory. When f f0, the actual f-

δ curve slope is smaller than the theoretical one; when

f f0, the measured f-δ curve slope is basically equal to

or slightly less than the theoretical slope; the

theoretical f-δ curve inflection point is very clear and

distinct while the actual f-δ curve inflection point is

smoother and it can be an interval section. Under the

same prestressed tensioning f, the actual δ is bigger

than the theoretical δthv. It is implied that for actually

tested elongation in the prestressed tensioning test

process, the anchor cable is not only influenced by the

steel strands elongation caused by the prestressed

tensioning loads, but also influenced by the anchor tool,

clips, anchor padding plates, concrete and interactive

force variation between different anchor fixed sections.

The appearance of resilience, retraction and slippage

are the inevitable phenomena and it will also influence

the anchor cable [21-25].

The actually measured inflecting point in the f-δ

curve is a smooth inflecting section rather than a single

point, which is the BC section in Fig. 4 and the actual

anchor stress lies in this section. The straight line

fitting is conducted on AB and CD sections separately,

and the cross point of the 2 lines O is the value of

anchor stress. It can be seen from Table 1 that under

the condition that f0 is below 72 of the ultimate load,

when f0 0.7 fmax, the deviation of test results gradually

reduces with increasing f0, the maximum deviation with

σ0/fmax 0.2 is 1.27, and the minimum deviation with

σ0/fmax 0.7 is 0.19; when f0 0.7 fmax, the deviation

increases gradually, f0 781.19 kN, the free section

suffers small and short-time prestressed tensioning

loading effect from the outer exposure section, and the

deviation is 3.76. It is indicated that the prestressed

tensioning has an optimum effect when fmax is 1.5 times

of f0.

Reverse

tension

Outer

fixed end Free end

Inner fixed end

Anchor cable

Load equipment Working anchor

Tool anchor

Limit

device

Dynamometer

Concrete pier base Load equipment

Tool anchor

Load equipment Dynamometer Steel reinforce concrete Loading device

Fig. 3 Experiment model and test equipment

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Fig. 4 Theoretical and test curves of tension stress versus elongation

P. Zhang, et al.



Fig. 5 shows the correlation curve of f and f0. When

f 0.9f0, f0 basically remains the same with the increase

of f, and the curve is similar to a horizontal line. When

f 0.95f0, f0 increases slowly with the increase of f. The

f-f0 curve is on a nonlinear rising trend if f0 f 0.95 f0.

When f f0, the f-f0 curve has a linear correlation,

indicating that the anchor cable has been extended, and

the free section and outer exposure section are joint

load carrying to extend. As shown in Fig. 5, the anchor

stress is 546.7 kN, the nonlinear correlation section of f

and f0 is in the range of 515 kN to 550 kN. When they

exceed 550 kN, f0 will have a linear increase with the

increase of f (see the section after point M in Fig. 5).

Fig. 5 Relationship between tension stress and anchor stress

Fig. 6 shows the curve of locked anchor stress flk

after prestressed tensioning under different f0. When

f0 703 kN, flk is in the range of 720 kN to 730 kN.

When f0 781.19 kN and fmax 781 kN, flk basically

remains the same. It is indicated that when f is applied,

fmax should be larger than f0 with stress compensation

action if f0 is insufficient. When the conditions of steel

strand, anchor clamp and rock-soil body are defined,

the compensation value is influenced by f0 and f. When

f 0.9 f0, the value of flk is mainly influenced by the

steel strands and the anchor clamp. Generally, flk is in

the range of 90 to 93 of fmax.

Fig. 6 Set values of the anchor stress and the locked anchor

stress after prestressed tensioning

4 Engineering application

The case is a side slope of a highway (on the border

of Guizhou province and Yunan province) between

Bijie and Duge in Guizhou province. The field region

is located in the plateau mountain area of western

China with complex topographic conditions and a

relative altitude difference of 226 m. The overlying

strata is the residual slope layer of Quaternary system

containing macadam silty clay and gravelly soil, and

the underlying bedrock is sandstone, mudstone, split

coal and limestone of Dyas. The stress bar of anchor

cable adopts high strength and low-relaxed steel

strands, with its nominal diameter Φ 15.24 mm, the

nominal area A 140 mm2, the elasticity modulus

E 195 GPa, and the standard value of tensile strength

fptk 1 860 MPa, and the stretching resistance

fb 260.4 kN. The steel strand of the anchor cable is

designed to go through the split coal internally anchor

on the low weathered layer of limestone. The number

P. Zhang, et al.



and parameters of tested anchor cables are shown in

Table 2.

The test data is collected and recorded by using AP-

10 prestress detecting system, and the installation of

detecting device is shown in Fig. 7. The range of the

ergometer is from 0 kN to 1 300 kN and its resolution

is 0.01 kN. The range of displacement meter is from

0 mm to 200 mm and its resolution is 0.01 mm. The

initial value of prestressed tensioning stress is 80 kN,

and the tension stress and elongation is recorded with

an interval stress of 20 kN. The theoretical maximum

tension stress is 1 200 kN. The test results are as

follows.

Table 2 Parameters of test anchor cables

Anchor cable Steel strand number Anchor section

Length/m Designed work

load/kN Free section Outer exposed section

An-1 7 10 30 1.5 800

An-2 7 10 30 1.5 800

An-3 7 10(8) 30(19) 1.5 800

a b

Fig. 7 Schematic diagram of detecting system

P. Zhang, et al.



4.1 An-1 anchor cable

The curve of An-1 anchor cable f-δ is shown in Fig.

8. Based on the elasticity modulus and the section area,

the theoretical maximum elongation Δδmax of different

tension stress increment is calculated. When f f0 and

Δδmax is with the tension increment of Δf 20 kN (at

this time, the stress-loading strand length is equal to the

sum of the length of inner anchoring section, the free

section, the outer anchoring section and the prestressed

tensioning section), Δδmax Δf (L l)/(nAE)

20 kN (30 000 mm 10 000 mm 760 mm)/(7

140 mm2195 GPa) 4.27 mm. When measured Δδ

Δδmax, the total shear force on the inner anchoring

section increases with increasing tension stress,

slippage among slurry, rock-soil body and stress bars

may happen, and partial wire break of steel strand or

the rock-soil body of the outer anchoring section may

be damaged by compression [26-27]. The loading process

will be stopped to avoid damaging the anchoring

structure.

Fig. 8 Tension stress-elongation curve of An-1 anchor cable

In Fig. 8, when the prestressed tensioning force f

raises from 982.62 kN to 1 004.4 kN, the steel strand

and counter-force structure have no abnormality. When

Δδ 6.46 mm and exceeds Δδmax, a slippage happens

between stress bars of internal anchoring structure.

Then the loading is stopped, and the stress at this time

is 1.25 times of the design load. The single tension

stress is 143.48 kN, which is less than 0.75 times of the

stretching resistance fb, and the steel strand is under the

elastic deformation phase. The f-δ curve consists of two

curves similar to straight lines, which is similar to the

theory. Combined with the judgment method of anchor

stress, the straight line fittings, y 68.65 x 20.616

and y 5.424 1 x 741.45 are adopted, repectively, on

the two curves, and the cross point of the two lines is

the value of the anchor stress f0 803.29 kN, which is

in line with the record result of the prestressed

tensioning process.



9. Based on the elasticity modulus and the section area,

the theoretical minimum elongation Δδmin of different

tension stress increment is calculated. When f f0 and

Δδmin is with the tension increment of Δf 20 kN (at

this time, the stress-loading strand length is equal to the

length of prestressed tensioning section), Δδmin Δf

l/nAE 20 kN (730 mm)/(7 140 mm2 195 GPa)

0.08 mm. When the tested Δδ 0.08 mm, the free

section and the prestressed tensioning section jointly

carry the load to extend, and the slope of the f-δ curve

decreases gradually and produces a inflecting point, at

which the prestressed tensioning stress is equal to the

anchor stress. In Fig. 9, when An-2 anchor cable

prestressed tensioning force f raises from 731.82 kN to

746.93 kN, the steel strands and counter-force structure

have no abnormality. When Δδ 3.51 mm and exceeds

Δδmin, the inflection point obviously occurs on the

curve. It is indicated that the free section gradually

suffers prestressed tensioning loading effect from outer

P. Zhang, et al.



exposed section, and these two sections are jointly

carrying the load to extend. Then the loading is stopped,

and the stress at this time is 93.4 of the design load.

The single tension stress is 106.70 kN, which is less

than 0.75 times of fb, and the steel strands are still in

the elastic deformation phase. Combined with the

judgment method of anchor stress, the straight line

fittings, y 67.678x 35.372 and y 5.883 9 x

643.64 are adopted, repectively, on the two curves, and

the cross point of the two lines is the value of the

anchor stress f0 697.70 kN.




10. It can be seen that when the tension force raises

from 300.03 kN to 324.69 kN (Δf 24.69 kN), Δδ

10.38 mm. Δδ 14.32 mm when the tension force

raises from 366.26 kN to 376.59 kN (Δf 10.3 kN),

which far exceeds Δδmax. An inflecting point occurs on

the curve, and the anchor cable steel strands and

counter-force structure have no abnormality, which

indicates that the anchor cable internal anchoring

structure has destructive mutation, and the length of

anchorage section, slurry intensity, wall-rock features

as well as the caking power of these three cannot

satisfy design requirements. Then the loading is

stopped, and the stress at this time is 47.1 of the

design load. The single tension stress is 53.80 kN,

which is less than 0.75 times of fb, and the steel strands

are in the elastic deformation phase. Combined with

the judgment method of anchor stress, the straight line

fittings, y 29.019 x 88.15 and y 1.055 9 x

301.06 are adopted, repectively, on the two curves, and

the cross point of the two lines is the value of the

anchor stress f0 309.10 kN. It is verified that the inner

anchoring section is 8 m, the free section is 19 m, and

the inner anchoring section lies in the low weathered

layer of mudstone split coal. The construction of the

anchor cable did not achieve the designed work load.


5 Conclusions

1) The prestressed tensioning method is a quasi-

nondestructive method to test the anchor stress of the

anchor cable. In an ideal state, the f-δ curve exhibits

two linear elasticity deformation stages, represented by

two intersecting straight lines of different slopes, and

P. Zhang, et al.



the intersection point acts as the anchor stress value.

2) Influenced by rock mass springback, anchor tongs

retraction, pore friction, slippage of inner anchorage

section and other factors, the actual measured f-δ curve

is two non-linear elastic deformation stages with a

sleek inflection point. The slopes of two fitting

straight-lines are lower than the ideal state with a slight

deviation of test results. The model testing study shows

that when the ratio of the anchor stress to maximum

tension force is less than 0.7, the test deviation will

gradually decrease with the increasing specific value,

and the minimum deviation is 0.19%.

3) The prestressed tensioning method plays a stress-

compensation role for the anchor cable which lacks

anchor stress. Locking anchor stress after prestressed

tensioning or stress-compensation is mainly affected by

the maximum tension force, anchor stress, anchor tongs

retraction and other factors.

4) In engineering application, the maximum

prestressed tensioning force is preferably 1.5 times of

the design load of anchor cable, and theoretically

calculated maximum and minimum elongation are

generated by the grading increment of prestressed

tensioning force. Considering the correlation between

the prestressed tensioning force, actually measured

elongation of anchor cable and theoretically maximum

and minimum elongation, increasing load suspensive

condition is established to determine whether the

anchor prestress extent and the caking power of inner

anchorage section meet design requirements and the

occurrence of sliding failure.

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