10th Asian Regional Conference of IAEG (2015)

A positive reinforcement method for rock slope(Extended Abstract)
Faquan Wu(1), Jie Wu(2), Han Bao(1)(1) Chinese Academy of Sciences, Beijing, 100029, China(2) Zhongkeji’ao (Beijing) Geo-Engineering Consulting Co. Ltd, Beijing, 100029, China

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Introduction

From the viewpoint of mechanism, theapproaches of slope reinforcement can beclassified into two categories, the passive andthe positive reinforcement. Essentially, thepositive reinforcement is a protection system
which relies on the synergistic action of rockmass and engineering structures to fully develop
the self-bearing capacity.
Take the slope reinforcement as example, thecurrent concept is to control the behavior ofdisaster using artificial structure, which can becalled passive reinforcement theory. It
concentrates more on the negative effect ofgeological disasters caused by deformation anddestruction of slope, but ignored the positive
function of the self-bearing capacity of slope
rock. Therefore, the passive reinforcement isusually relatively conservative, and thus the costis larger.
The current procedure of slope reinforcement
design is: predict the shape and position of thepotential sliding surface through field
investigation, and then calculate the sliding force
along the assumed surface; decide thecontrolling points according to the distributionof sliding force along the surface, and then, thesupport or anchoring system can be designed.
Obviously, such design doesn’t fully consider
and make use of the self-bearing capacity ofslope rock. In order to minimize the risk, asmany anchor bolts or piles as possible will be set
to control the break of slope.
Generally speaking, positive reinforcementof rock engineering is a subject in exploration.
The paper is to initiate the terms of potentialityof slope self-stability and positive reinforcement,propose the method for locating of anchor
bolts/cables and determination of force anddepth of anchorage. The calculation in themethod is done with the software Flac3D byItasca Co. Ltd and developed modules.

Potential self-stability of slope andpositive reinforcement

 Potential slope self-stability
The potential slope self-stability (PSS) means
the capacity of a slope to maintain stable undernatural states. This potentiality can be fully
developed while the slope reaches the criticalstate of instable and failure.
The PSS in rock slope has the characteristicof self-organization. By modifying the existing
circumstances of rock with engineering
measures, the potential capability can beactivated towards different level favorable to theslope stability.
The PSS depends mainly on the slope
geological structure, i.e. the combination ofgeo-material, dominant low-strength structural
surfaces and the free surface of slope, slope
stress field and the interaction of these twofactors.
Definitely, slope stress field is the driving
force of slope deformation and failure. However,on the other hand, the stress influences thestrength property of the slope rock mass.
According to Mohr-Coulomb theory, thecompressive strength,  1＝of any rock element
is positive-linearly correlated with the lateralcompression stress,  3 , i.e.,  1＝ 3 tan 2＋ c ，（ ＝ ＋ ） （1）42where  is the internal friction angle ofrock mass.
The formula (1) indicates that the strength ofslope rock mass is influenced not only by theinternal friction angle  and uniaxial
compression stress  c of rock material, butalsobythelateralstress  3 .
2
Since tan   1 ,the contribution of  3 is remarkable.

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 Positive reinforcement of slope
In essence, slope protection project depends
on the cooperation between slope rock mass andengineering structure. It aims at maximizing theutilization of the strength capacity of rock mass
with its self-adjustment. This is called “positivereinforcement (PR)”.
From the contribution to PSS analysed above,
we can modify the stress condition and improve
PSS of slope by pre-stressed artificial structure.
This measure provides assistant condition for thestress self-adjustment in rock mass.

Fig. 1 Cloud chart of   3 value
Since the shear stress and shear strength at any
point in rock slope are respectively,

3. Positive reinforcement method of slope
based on self-adjustment of PSS

＝ 3 through the calculation of slope stress field.
Meanwhile, using Morh-Coulumb model, wecan also calculate the critical value of lateralthen the stability factor, K, at the point can bewritten as

stress,  3c , with which the rock mass could
keep from being broken, that is 3c 

1  ctan 2 

1  3sin 2 ，2   3c
 c＝ 1
sin 2 ，2

 Requirement for reinforcement
We can obtain the cloud charts of  1 and

K＝ c （2） 1   3c
1  3 .

（4）

We define the difference between actuallyexisted  3 and the critical lateral stress  3 c
at the corresponding point in slope rock mass as  3   3   3c   3 1  ctan 2

(3)

Obviously, the lower the value of   3 is,the higher the requirement for reinforcement.
The negative value of   3 indicates thedemanded reinforcement force at the point.
Fig.1 shows the   3 value distribution inFig. 2 Distribution of stability factor in slope
Using the equation above, we can estimate
the local stability of rock mass and obtain its
distribution in the slope.
Figure 2 shows the cloud chart of stability
factor in a slope calculated by equation (4).
Compared with figure 2, we can see that in bothof the two, the stability factor and PSS are wellfitted to each other.

a typical slope. It is usually affirmative that theposition with lowest PSS often appears at thesurface, and more specifically, located at lower
1/3 to 2/3 of the slope surface. This means thatreinforcement can be normally applied byadding force on slope surface, particularly at themiddle and lower part of slope surface. In
experience, anchorage is a more efficient choicefor the measure.

 Anchorage force
According to the requirement of thedesigning safety factor, the pre-stress foranchorage, σ3K, can be calculated based onequation (4), i.e., Stability Factor
We can also define the Stability Factor in the
traditional way of limit equilibrium method.

 3 K＝ 1 (1 1)  3c .
KK（5）The lateral compression stress at this time is2

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3  3 3K  3 1  (1 3c).（6）KReferences

If the area covered by each anchor cable (bolt) is
A, the anchoring force of single anchor should beZhong Li (2008), Calculation method for active
slope reinforcement based on stress control
in critical slip surface, Chinese Journal ofRock Mechanics and Engineering. Vol. 27,
No.5, pp, 979-989

1F  3A  A[3  3K  3  1  (1  3c )].
K（7） Anchoring direction and depth
Based on the distribution of stability factor inrock slope, the length of anchor cable (bolt) canbe figured out.
For instance, if the safety factor is required tobe K=1.2 according to the technical standards,
then the anchorage cable can be extended to thearea where the stability factor is larger than 1.2(Fig. 3).
The anchorage direction can be designed
referring to the contour trend of stability factor,
i.e. approximately perpendicular to the extending
direction of the contour of K.

Fig 3 The depth and direction of anchorage cable
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Conclusion Remarks

Different from passive reinforcement, thepositive reinforcement advocate making full useof the bearing capacity of rock mass withappropriate reinforcement approaches in order toguarantee rock mass maintaining in stable. From
the opinion of the potentiality of self-stability,
the idea of positive reinforcement is proposed
which is to maximize the utilization ofself-bearing capacity of rock mass, with its
self-adjustment and the interaction of rock mass
and artificial structures. Based on this idea, thesoftware Flac3D and Mohr-Coulomb model areapplied to analyze the stress field and safety
factor in rock engineering like slopes and tunnels,
then determine the reinforcing area and thereinforcement demand degree Δσ3.
The procedure of the proposed method isdesigned after analyzing the influence ofgeological structure slope. For slopes withgeneral shape, the suitable position forreinforcement is located at the 1/3 to 1/2 ofheight from the slope toe.

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