THE 12TH CONFERENCE ON CURRENT RESEARCHES Aug.

29-31 2007
IN GEOTECHNICAL ENGINEERING IN TAIWAN Chi-Tou

台北盆地沖鑽式地錨破壞機率研究

廖洪鈞 1 卿建業 2 蘇嘉瑋 3

1
國立台灣科技大學營建工程系教授
2
國立台灣科技大學營建工程系助理教授
3
國立台灣科技大學營建工程系研究助理

摘 要
在台北盆地，幾乎所有地錨的施工都是先以旋轉套管鑽孔，再以水將殘餘土以高
壓沖出。這樣的施工過程常使實際的鑽孔直徑比套管直徑大，且鑽孔壁常呈現不規則
的形狀。這兩項因素都有利於提升地錨拉拔力，然而提升程度有多少常常是不確定
的。為了求保守，一般計算設計拉拔力時都不考慮這兩項因素。讓人不解的，在這樣
保守的計算下，大部分規範（如 FIP 1982）仍採用相當高的安全係數（安全係數 = 3） ，
驗證此安全係數是否過於保守，是本研究的主要議題。本研究根據台北盆地的 46 根
地錨現地實驗資料，經過嚴謹的全機率分析，得到以下的結論：安全係數=3 所對應的
設計破壞機率小於 10-4；若設計的地錨為暫時性結構，這樣的設計破壞機率過於保守。
若採用設計破壞機率 10-2，所需要的安全係數約在 0.9 到 1.8 之間；若採用設計破壞機
率 10-3，所需要的安全係數約在 1 到 2.4 之間。這比規範所採用的安全係數小了許多。

關鍵詞：地錨、拉拔力、可靠度、安全係數。

■ Calibration of Reliability-based Resistance Factors for Soil Anchors in

Taipei Basin
■ ABSTRACT

The goal of this research is to calibrate the reliability-based resistance factor of flush
drilled soil anchors for their ultimate pullout capacities based on in-situ anchor pullout test
data in the alluvial soil underlying the Taipei basin. Efforts are taken to quantify the
uncertainties with a full probabilistic analysis approach. The resistance factor is calibrated
based on the in-situ test results of 46 anchors with a rigorous theoretical approach which
constructs the relationship between the resistance factor and failure probability. With this
relationship, the reliability corresponding to the code regulation can be verified. From the
results of the analysis, it is found that the borehole enlargement due to the flush drilling is
quite significant: the actual diameter of the fixed anchor end may be much larger than the
nominal diameter of the drilling casing. Consequently, the safety factor of three
recommended by most anchor codes is found to be too conservative.

Key Words: anchor, pullout resistance, reliability, safety factor

1 INTRODUCTION However, safety factor is not a consistent measure

of uncertainties: it does not tell us how reliable the
Traditionally, soil anchor designs are usually designed anchor system is. Mathematically, safety factor
achieved by the safety-factor approach, which accounts is not a consistent indicator of reliability: the safety
for the uncertainties in soil anchors (e.g.: uncertain soil factor of the same limit state may change depending on
parameters, uncertain mechanisms, uncertainties in the the mathematical expression of the limit state function
laboratory and in-situ tests, etc.) with an empirical basis. [1]. As a consequence, geotechnical engineers tend to be
The safety-factor approach has been working reasonably conservative in choosing safety factors, and sometimes
well: as long as a large safety factor is adopted, the they can be overly conservative in order to ensure
anchor system can usually be made quite reliable. reliable anchor designs. This over design does not fit in

D3-12-1
THE 12TH CONFERENCE ON CURRENT RESEARCHES Aug. 29-31 2007
IN GEOTECHNICAL ENGINEERING IN TAIWAN Chi-Tou
the nowadays needs in terms of economic and surface. So the exact borehole diameter could not be
ecological considerations. In contrast, since safety factor determined and the diameter of the drilling casing was
does not directly provide information about reliability, it usually assumed as the nominal anchor diameter in the
is possible that designers may choose a safety factor practice. After drilling was completed, the assembled
corresponding to unsatisfactory reliability. tendons were installed into the casing and cement grout
Therefore, it is essential to verify if the safety with a water/cement ratio 0.45-0.5 was injected into the
factor adopted in the design code is appropriate: What is borehole under a pressure of 200kPa. During grouting,
the corresponding reliability for the safety factor the drilling casing was withdrawn gradually. After the
adopted in codes? Does the corresponding reliability casing for the fixed anchor end has been removed, a
meet the design requirements? Is the adopted safety pressure of about 1000kPa was used to pressure-grout
factor too conservative? One way of answering those the anchor. In general, the grout takes for anchors were
questions is through a probabilistic analysis that about double the volume calculated from the nominal
constructs the relationship between the factor of safety dimension of anchors. Due to the high fines content,
and reliability (one minus failure probability). In this cement grout cannot permeate into the voids of the
pa per,thet erm“ resis
ta n
cef actor”,s impl yt her ec i
proc a
l alluvial soils. The main purpose of pressure-grouting is
of safety factor, will be employed instead of factor of to recompact the soils loosened during borehole drilling.
safety. The further details of anchor installation can be referred
More specifically, the afore-mentioned verification to [10].
will be only conducted for soil anchor designs in the
Taipei basin in Taiwan through a reliability-based 3 MODELS FOR PULLOUT CAPACITY
theoretic design approach. Reliability-based analysis
and design methods have been proposed for deep For the probabilistic analysis, a non-probabilistic
foundations [2,3,4], for shallow foundations [5], for predictive model for the anchor capacity must be
retaining walls [6], and for slope stability [7,8] to name provided. The following model is often adopted to
a few. For soil anchors, a systematic study of the compute the nominal pullout capacity of an anchor:
possible implementation of a reliability-based design
method is still lacking.
Nc (i ) (i ) Ns (i ) (i ) 
su lc K  tan  (i ) ls(i ) 
A database containing the in-situ test results of 46
soil anchors in the Taipei basin is compiled and C d
n
 (1)
analyzed to construct the relationship between the i1 i
1 
resistance factor and target reliability. This relationship
will be used to verify the anchor design code in Taiwan.
where d is the nominal diameter of the anchor fixed end,
Since only local database of Taipei is used for the
often taken as the diameter of the drilling casing; Nc and
analysis, the conclusion may be only applicable to
anchor designs in Taipei. Ns is the total number of clayey and sandy soil layers
(i) (i)
within the fixed end; lc (or ls ) is the fixed length
(i)
2 DATABASE within the i-th clayey (or sandy) layer, while Su (or
(i) ) is the undrained shear strength (or effective friction
(i)
The database contains the in-situ pullout test angle) of the i-th clayey (or sandy) layer; σ is the
results of 46 soil anchors in the Taipei basin. For each average vertical effective stress in the i-th sandy layer;
anchor, the following information is available: (a) the K(i) is the earth pressure coefficient in the i-th sandy
pullout force v.s. anchor head movement of the test layer, i.e. the effective normal stress on the anchor shaft
(i)
anchors; (b) the soil profile nearby the anchor location, divided by σ . It is assumed here that the soil around
(i)
including soil classification, soil layer thickness, SPT-N the fixed end is in at-rest state, so K is roughly
value, unit weights, location of water table, and, in some 1-sin((i)) if the anchor is vertical and is 1 if the anchor
cases, the undrained shear strength of the clayey layers; is horizontal. In the case that the anchor is inclined with
(c) the configuration of the anchor, including the free an angle equal to ( = 90o is vertical), a simple
length and fixed length, the diameter of the drilling Mohr-Coulomb analysis is used to find K .
(i)

casing, the number of steel tendons, etc. The actual Equation (1) assumes that the developed shear
pullout capacity of each anchor is determined from the resistance along the fixed end is uniform within the
curve of in-situ pullout force v.s. anchor head movement same soil layer. However, it is reported by [11] that the
using the method recommended by FIP [9]. distribution of developed shear resistance along the
The boreholes of all test anchors were drilled with fixed anchor length is not uniform even in a
rotary casing and the debris was flushed out with water homogeneous soil layer: the developed shear resistance
from outside of the casing. Since the amount of alluvial is fully developed at the top of the fixed end but is only
soils being flushed out is difficult to control, the process partially mobilized away from the top. This
might result in a borehole with a larger diameter than non-uniformity is more pronounced when the
that of the drilling casing and an irregular borehole
D3-12-2
THE 12TH CONFERENCE ON CURRENT RESEARCHES Aug. 29-31 2007
IN GEOTECHNICAL ENGINEERING IN TAIWAN Chi-Tou
s (1:Njs)
surrounding soils are stiff. Hawkes and Evans [11] 1:46(1:Nj ) and unit weights  1:46 of all sandy
proposed the following equation to account for such layers (Njs is the number of sandy layers in the fixed
decay: end of the j-th anchor) and ratios between undrained
shear strengths and effective vertical stresses
x c
1:46(1:Nj ) and unit weights  (1:Njc)
e x / d (2) 1:46 of all clayey
0 layers (Njc is the number of clayey layers in the fixed
end of the j-th anchor). If the soil is above water
(i) (i)
table, γ and γ mean the unsaturated unit
where τ 0 is the shear resistance developed at the top of
s,j c,j
weights of the i-th sandy and clayey soil layers,
the fixed end; τ x is the shear resistance developed at a
respectively; otherwise, they are the saturated ones.
distance of x from the top of the fixed end; αis called (b) Uncertain model parameters, including the effective
the decay parameter, whose value usually depends on diameter D1:46 and decay parameter α1:46.
the stiffness of the surrounding soils. When specifying the joint prior PDF of the basic
In reality, the αparameters of different soil layers uncertainties, the following assumptions are
should be different, but in this paper, the αparameters of taken:
different soil layers are assumed to be identical since the (a) The αparameters of all anchors are assumed to be
soil stiffnesses within the fixed end do not drastically uncertain but identical, i.e. α1=…= α46= α. This
change. Under such a simplifying assumption, a more assumption should be mild because all anchors are in
sophisticated model can be derived as follows: the Taipei basin, so the decay behavior along the
fixed end of all anchors may be similar. An obvious
Nc Uc( i )   limitation is that α must be positive. Moreover,


1
  s(i )
u 
x e x / d
dx 




according to [11], α≒0.1 for rock anchors, which
i
c
L(i )
 implies αfor soil anchors should be less than 0.1.
C d  (3)
Other than these, there is not much prior information
Ns  (i) Us( i ) 

 K tan  (i)  xex/ d dx 
 about the decay parameter. Therefore, the prior PDF
1 
  of αis taken to be uniform over [0, 0.1].

i L(i )
s 
 (b) The effective diameters of the j-th anchor Dj in the
database is assumed to be equal to the diameter of
where Uc(i) and Lc(i) are the distances (along the fixed the drilling casing, denoted by dj, multiplied by an
anchor length) to the top of the fixed end from the upper enlargement factor ρ j, and it is assumed that the ρ 1:46
and lower interface of the i-th clayey layer, and similar factors of all anchors are independent but identically
for Us(i) and Ls(i) ; σ( x) is the effective vertical stress distributed. It is reasonable to assume the ρ 1:46
at a distance of x from the top of the fixed end, Su(i) (x) is factors to be independent because the enlargement
proportional to σ( x), and d is the diameter of the effect of one anchor does not seem to provide
drilling casing. information about the effect of another anchor. They
are assumed to be identically distributed because the
4 MODELING OF UNCERTAINTIES drilling and grouting procedure for all the anchors is
roughly the same. The ρ 1:46 factors are assumed to be
The basic uncertainties include the unit weight, lognormal with mean value μp and coefficient of
friction angle, ratio of undrained shear strength to variation δ p (c.o.v.: standard deviation divided by
vertical effective stress of each soil layer as well as the mean) where μp and δ p are two uncertain parameters.
effective diameter D and the decay parameter α. The prior PDF of μp is taken to be uniform
Uncertainties like σ( x), K(i) , and Su(i)(x) are not basic constrained by μp≧1, while that δ p is taken to be
since they are functions of the basic ones. uniform constrained by δ p≧0 Note that this
To quantify the uncertainties, it is desirable to first arrangement makes D1:46 out of the list of the basic
specify the joint prior probability density function (PDF) uncertainties, but now the basic uncertainties include
[12] ofa l
lba si
cun c erta
in tie s
.Th et e rm“ pri
or”PDF μp and δ p.
denotes the PDF before new data, i.e. the actual (c) In our database, borehole data of the unit weight is
capacities of the 46 anchors, is available. Later we will available for each soil layer. Despite the availability
mention t he“ pos t
erior” PDF [12] of the basic of the borehole data, the unit weight is, in principle,
uncertainties, which denotes the PDF after the new data still uncertain. The reported value of unit weight in
is available. We will constantly use the following the borehole data is taken to be its mean value,
notation for uncertain variables: Xj(i) is the X variable of denoted by μγs,j(i) for sandy soils and μγc,j(i) for
(i)
the i-th soil layer in the fixed end of the j-th anchor, and clayey soils , while their c.o.v., denoted by δ γ
s ,
j
(i)
X1:j(1:i) denotes {X1(1),
…X1(i),…,Xj(1), …,Xj(i)}. Let us first and δ γ
c,j , are taken to be 10% based on the c.o.v.
divide the basic uncertainties into two categories: of the unit weight suggested by [1]. All unit weights
(a) Uncertain soil parameters, including friction angles are assumed to be independent and lognormal since

D3-12-3
THE 12TH CONFERENCE ON CURRENT RESEARCHES Aug. 29-31 2007
IN GEOTECHNICAL ENGINEERING IN TAIWAN Chi-Tou
the knowledge of one unit weight does not seem to
provide information on another. N cj U cj ( i )  
 (i) j
i 1 Lc
   
x / d j
 (i )
x   x e dx
(d) Based on the report published by Moh and j
 
Associates [13] , the mean value of β (i)
j , denoted by   j   (4)
(i)
μβ,j , is taken to be 0.21 and c.o.v., denoted by δ β
(i)
j,
,
j d j 
s 
is taken to be 30% if the i-th clayey layer of the j-th Nj  U cj ( i ) 
 
anchor is below 12m; otherwise, its mean value and  K j tan 
(i )
j 
(i )
j 
x  e
x / d j
dx 

i 1  

c.o.v. are taken to be 0.36 and 20%, respectively.   Lcj ( i ) 

(i)
The β j values of different layers and for different
anchors are assumed to be independent and
lognormally distributed.
(e) The mean value of ,j(i) is estimated based on the
where  (1: N s ) (1: N c )
Y j  S , j j , C , j j , j
(1: N sj ) (1: N cj )
, j  denotes

SPT-N value of the i-th sandy layer of the j-th anchor. the collection of the uncertain soil parameters for the
Using the results reported in [13] , the mean value j-th anchor in the database.
and c.o.v. of ,j(i) ,denoted by μj(i) and δ j
(i)
, can
be identified from the SPT-N value. The ,j values (i) 4.1 Joint prior PDF of all uncertainties
of different layers and for different anchors are Once the prior PDF of each individual basic
assumed to be independent and lognormally uncertainty is specified, it is possible to combine all
distributed. prior PDFs into a single joint prior PDF of all
Perhaps, the most important uncertainty in the uncertainties. For the ease of future discussion, let us
problem is the uncertain pullout capacity of an anchor. denote the model parameters {μp ,δ p ,α} by M and denote
In most literature, the uncertain (actual) capacity of the the collection of all uncertainties {M ,Y1:46 ,C1:46 } by Z,
j-th anchor C,j is usually taken to be the product of the then the joint prior PDF of Z is
pr edict e dc a pacity wi tha“ mode lf a c t
or”, whi c h
characterizes the model uncertainty. However, for our f Z f M,Y1:46, C1:46 
model, the ρ j parameter plays a similar role to the model 46 
factor. It seems reasonable not to use an extra factor but  f Cj | M,Yj f 
Yj f M 
treat ρ j1 
j as a combined parameter characterizing both the
borehole enlargement effect and the model uncertainty.  46  Nsj Ncj Nsj Ncj 
If this approach is taken, it is clear that the uncertain 
 f Cj | M,Yj f 
S, j 
(i)
 f
C, j 
(i)
 f
j 
(i)
 f j(i) 

 j1 
 i
1 i1 i
1 i1 

capacity of the j-th anchor C,j can be expressed as 
 if 0 0.1&  1&0
C j j C  
Yj 
 

0

 otherwise


  1   C Y j      



log S( i,)j  logC,j 
1 1
log
Cj 
  log
S , j    log C,j 

log 


  (i )
2log12 


 2 
1 



s 2log 
1 S , j 
2 





 c
1S , j  N
2 2log 
1 2
 ,j 



 1 2 



    N       

 
j j C C , j
e e e
     

 46  C j log  1  2
i1 S , j log 1 S , j
(i )
 2
 i 1
(i )

C , j log 1 C , j 
2


 
      
 j 1  1 log
(j i ) 
log
, j   1 log(j i ) 
log
, j   
  2log , j 
  2   2log ,j 
  2  

(5)
 1  1  1  1 
2 2
N sj 
  , j  Nj

c

  ,j  

e e
    
  i 1 j log 
(i )
1  , j 
2
i 1 j log 
(i )
1 , j  2 
  
 if 0 0.1&  1 &  0

0


 otherwise

This joint prior PDF of all uncertainties Z is the basis of 5 CALIBRATION OF RESISTANCE
the Bayesian analysis, which is employed in this study FACTOR
to calibrate the resistance factor.
Given the in-situ measured pullout capacities of
the 46 anchors, it is possible to calibrate the

D3-12-4
THE 12TH CONFERENCE ON CURRENT RESEARCHES Aug. 29-31 2007
IN GEOTECHNICAL ENGINEERING IN TAIWAN Chi-Tou
reliability-based resistance factor for anchor designs in
1G 
N
1
the Taipei basin. The reliability-based design can be PF*  k
(9)
achieved by restricting the failure probability of a future N k 1

design conditioning on the past data, i.e. consider the

following equation: where 1(.) is the indicator function: it is unity if the
inside statement is true and is zero otherwise.
Equivalently, ηcan be estimated as the 100．PF* largest
P
Cnew C * | C1:46 PF* (6) number in {G1, …, GN}. Once this relationship is
obtained, the calibration of the resistance factor is
achieved since one can determine the required resistance
where Cnew is the uncertain capacity of a new anchor, factor from the target failure probability. Note that the η
and C* is the design load of the anchor; the Cnew≦C* is v.s. PF* relationship depends on the configuration of the
the failure event; C1:46 is the capacity data in our new anchor, the soil profile at the new anchor site, and
database; P(Cnew≦C*|C1:46) is the failure probability the adopted capacity model for design CD.
conditioning on the capacity data, which, in principle,
can be computed with Bayesian analysis; PF* is the 6 ANALYSIS RESULTS AND
target failure probability. Equation (6) can be rewritten VERIFICATIONS
as
6.1 Samples of stochastic simulations

P
Cnew C* | C1:46 P Ynew C* | C1:46 PF*
Ten thousand samples are drawn from
newC 

(7) f(ρnew,α|C1:46). These samples contain interesting
information about the behaviors of the 46 anchors. For
instance, the samples of the αparameter, as shown in
where ρ new is the model factor of the new anchor, which Figure 1, are distributed as f(α|C1:46), so the histogram of
is lognormally distributed with mean value equal to μp the sample values, also shown in the figure, basically
and c.o.v. equal to δ p (recall that it is assumed that all gives the relative degree of plausibility of the αvalue
model factors are independent identically lognormally learned from the data. From Figure 1, it is clear that the
distributed with mean equal to μp and c.o.v. equal to δ p ); decay parameter is mostly in the range of [0.001, 0.004],
Ynew contains all uncertain soil parameters of the new and the mean value and c.o.v. of the samples of the
anchor site. Note that Cα(Ynew) is uncertain because Ynew decay parameter are 0.0025 and 0.253, respectively.
is uncertain. Moreover, the possibility of α= 0 is close to zero, i.e.
Let us assume that the PDF of the soil properties compared to the Cα model, the C n model is basically
Ynew is known from site investigation and appropriate rejected.
uncertainty characterization. Therefore, the relationship
between the resistance factor and target failure
probability can be derived as follows:

 Ynew C D 
P newC   n
Ynew C * C D Ynewn C1:46 
P 
 C new

Ynew C D
Y C 
n
new 1:46
(8)

P 
Gnew , , Ynew C1:46 PF*

where Ynewn is the nominal value of Ynew, e.g. mean value

of Ynew ; CD(Ynewn) can be any predictive model chosen
by the designer; η = C*/CD(Ynewn) is exactly the
resistance factor, which is the reciprocal of the safety
factor. One can see that the resistance factor can be
simply estimated as the 100 ． PF* percentile of
G(ρ new,α,Ynew) conditioning on the data C1:46 . If one can
obtain stochastic simulation samples of G(ρ new,α,
Ynew)
(see [14] for details), denoted by {G1, …, GN} , Figure 1 The Markov chain samples of α(upper plot)
conditioning on the data C1:46, the relationship between and ρnew (lower plot) and the histograms.
resistance factor and target failure probability can be
estimated as the following according to the Law of The samples from f(ρ new|C1:46) , as shown in Figure 1,
Large Number: gives us the possible range of the model factor ρlearned
from the data. From the histogram in the figure, it is

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IN GEOTECHNICAL ENGINEERING IN TAIWAN Chi-Tou
clear that the model factor is mostly between 1 and 3. rankings is roughly uniform. In fact, hypothesis testing
This means the actual capacity of an anchor in Taipei is based on Kolmogorov-Smirnov test concludes that the
roughly two times larger than the capacity predicted by uniform-distribution hypothesis is not rejected at a
Eqn. (3) because of the combined effect of the significance level of 0.05. These results indicate that the
enlargement and model bias. Moreover, the mean value analysis is consistent.
and c.o.v. of the samples of the model factor are 2.049
and 0.186, respectively. 6.3 Relationship between resistance factor and target
Figure 2 shows the comparison between the actual failure probability
capacities and the ones predicted by Eqn. (3) The procedure introduced in a previous section is
multiplied by 2.049, where the uncertain soil parameters employed to estimate the relationship between
are held at their nominal values and the decay parameter resistance factor and target failure probability. The
is held at 0.0025. It is clear that the predicted capacities estimated relationship is not unique: it depends on the
unbiasedly reflect the actual ones, indicating that the configuration of the anchor, the soil profiles, and the
analysis results are consistent. chosen capacity design model CD. This non-uniqueness
imposes a difficulty, but it can be solved by just
selecting a representative set of anchor design scenarios
in Taipei basin and estimating the η-PF* relationships for
all scenarios to obtain the possible range of the
relationship. For example, one can first determine the
target failure probability PF* for anchor designs within
Taipei basin, then the range of the required resistance
factor can be found.

Figure 2 The actual v.s. predicted pullout capacities for

the anchors in the database.

6.2 Verification of the analysis results

In order to further verify the analysis results in a
more rigorous manner, the following approach is taken.
Remove the j-th anchor data from the database, i.e. the
remaining data only contains {C1, …, Cj-1,Cj+1,…, C46},
denoted by C1:46\ j. Then draw samples from
k
α\jk): k Figure 3 Empirical cumulative distribution of the 46
f(ρnew,α |C1:46\j), and denote the samples by {ρ new\j ,
=1, …, N}. Also draw Yj samples from their prior PDFs, percentage rankings
denoted by {Yjk: k =1, …, N}. Conceptually, the samples
k α\ jk In this paper, the sites of the 46 anchors in the
{ρ new\ j C (Yjk): k = 1,…, N} are the samples of the
database are taken as the representative set of soil
actual capacity of the j-th anchor Cj conditioning on the
profiles in the Taipei basin. Numerous scenarios of
data C1:46\ j, and their histogram can be regarded as the
anchor designs are considered and the corresponding
predicted PDF of Cj conditioning on the data C1:46\ j. If
η -PF* relationships are computed. It is found that the
the analysis framework is reasonable, the percentage
η -PF* relationships strongly depend on the chosen
ranking of the actual Cj among the predictive samples
α\ jk design model CD, the dominant soil types within the
{ρ new\ jC (Yjk): k =1,…, N}, defined as the ranking of
fixed end, and the length of the fixed end.
the actual Cj among the samples divided by the total
When the design model CD is chosen to be C n in
number of samples N, should be roughly uniformly
Eq. (1), the η-PF* relationships will depend on the
distributed over [0,1].
dominant soil types within the fixed end as well as the
The afore-mentioned percentage ranking is
length of the fixed end. It is evident that if the soils
calculated for all anchors in the database, and Figure 3
within the fixed end are primarily sandy, the calibrated
shows the empirical cumulative distribution function of
resistance factors are larger, while the resistance factors
the 46 percentage rankings. The dashed line indicates
are smaller if the soils are mostly clayey. The
the cumulative distribution for a uniform distribution. It
dependency of the η-PF* relationship on the soil types is
is observed that the distribution of the 46 percentage
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THE 12TH CONFERENCE ON CURRENT RESEARCHES Aug. 29-31 2007
IN GEOTECHNICAL ENGINEERING IN TAIWAN Chi-Tou
due to the fact that undrained shear strengths of clayey
soils are more uncertain than the shear strength of sandy
soils.
Moreover, the calibrated resistance factors are
smaller for anchors with long fixed ends and are larger
for those with short fixed ends. The dependency on the
fixed anchor length is due to the fact that the C n model
does not take the decay behavior of developed shear
resistance along the fixed end into account. Therefore,
the calibrated resistance factor will be smaller for long
fixed end than for short fixed end.
When the Cn model is adopted for designs, the
ranges of required resistance factors corresponding to
various target failure probabilities, fixed anchor lengths,
and soil types are compiled in Figure 4. Note that the
required safety factors for target failure probability 10-2
and 10-3 rarely exceed 3, the safety factor required by
most anchor codes. For target failure probability 10-2,
the required resistance factor is around 0.6 to 1.2 (safety
factor is around 0.9 to 1.7), depending on the soil type
and fixed-end length. For target failure probability 10-3,
the required resistance factor is around 0.4 to 1 (safety
factor is around 1 to 2.5). The safety factor of three
recommended by anchor codes corresponds to failure
probability less than 10-4, which is somewhat
over-conservative for flush drilled anchors in Taipei.
Note that this conclusion may not apply to different
types of anchors nor to anchors outside Taipei.
One must be careful that the recommended
resistance factors and safety factors in Figure 4 for fixed
anchor length is among 30m-40m are extrapolation
results because the longest fixed end in our database is
32m. So, cares must be taken when adopting the
resistance factors and safety factors if the designed fixed
end is longer than 32m.

7 CONCLUSIONS

A database of 46 anchors in the Taipei basin is

analyzed in this study to construct the relationship
between the resistance factor and target failure
probability of flush drilled anchors. It is found that the
safety factor of three recommended by anchor codes is
somewhat over-conservative for flush drilled anchors in Figure 4 The recommended ranges of the resistance
Taipei. This conclusion may not apply to different types factors for different design scenarios and target failure
of anchors nor to anchors outside Taipei. Again, cares probabilities based on the Taipei database when Cn is
must be taken when adopting the above resistance and adopted.
safety factors if the design fixed anchor length is longer
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IN GEOTECHNICAL ENGINEERING IN TAIWAN Chi-Tou
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