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Auto ren
D r . - l n g . B e r n h a r d O d e n w a l d D i p l . - I n g . O l i v e r Stelzer Bundesanstalt f ü r Wasserbau ( B A W ) A b t e i l u n g G e o t e c h n i k K u B m a u l s t r a B e 17 D - 7 6 1 8 7 K a r l s r u h e T e l . : + 4 9 ( 0 ) 7 2 1 - 9 7 2 6 / 3 6 2 0 , + 4 9 ( 0 ) 7 2 1 - 9 7 2 6 / 3 1 7 0 Fax: + 4 9 ( 0 ) 7 2 1 - 9 7 2 6 / 4 8 3 0 e - m a i l : b e m h a r d . o d e n w a l d @ b a w . d e , o l i v e r . s t e l z e r @ b a w . d e W e b : w w w . b a w . d eO n the use of finite element models for geotechnical design
R o n a l d B . J . B r i n k g r e v e , M a r k Post
Abstract: The Finite Element Method is primarily meant f o r serviceability l i m i t state (SLS) calculations, but it also offers possibilities f o r ultimate l i m i t state ( U L S ) calculations in geo-technical design. The combined use o f SLS and U L S calculations w i t h partial safety factors according to the different design approaches in the Eurocode 7 can be time-consuming and prone to en-or. In this contribution a Design Approaches facility is presented f o r an efficient use o f partial safety factors in a finite element environment. In addition to a description o f t h e methods used in this faciiit>'. an example is elaborated involving the geotechnical design o f an embedded sheet pile wall using different design approaches.
K u r z f a s s u n g : Die Finite Elemente Methode w i r d i m Bereich der Geotechnik vorrangig f ü r Nachweise i m Grenzzustand der Gebrauchstauglichkeit (GZG) verwendeL sie bietet dariiber hinaus jedoch auch M ö g l i c h k e i t e n zum Nachweis des Grenzzustandes der Tragfahigkeit (GZT). D i e Kombination von G Z G und G Z T Berechnungen mit den Teilsicherheitsfaktoren der verschiedenen Nachweisverfahren des Eurocode 7 kann jedoch sehr zeitaufwandig und fehleranfallig sein. In diesem Beitrag w i r d ein Werkzeug zur effizienten Verwendung von Teilsicherheitsfaktoren i m Rahmen der Finiten Elemente Methode vorgestellt. Die verwendeten Methoden werden eriSutert und die Nachweisfuhrung mit den verschiedenen Nachweisverfahren w i r d am Beispiel einer eingespannten Spundwand dargestellt.
1 Introduction
In the past decennia t h e F i n i t e E l e m e n t M e t h o d ( F E M ) has been used i n c r e a s i n g l y f o r t h e analysis o f stress, d e f o r m a t i o n , s t r u c t u r a l f o r c e s , b e a r i n g capacity, s t a b i l i t y a n d g r o u n d w a t e r f l o w i n geotechnical e n g i n e e r i n g a p p l i c a t i o n s . Besides developments related t o t h e m e t h o d itself (e.g. n e w c o n s t i t u t i v e m o d e l s f o r s o i l and r o c k , n e w n u m e r i c a l procedures a n d c a l c u l a -tion methods), the r o l e o f the F E M has e v o l v e d f r o m a research t o o l i n t o a d a i l y e n g i n e e r i n g .look T h e m e t h o d has obtained a p o s i t i o n next t o c o n v e n t i o n a l design m e t h o d s , and o f f e r s s i g
-nificant advantages i n c o m p l e x situations.
Regarding t h e use o f the F E M i n g e o t e c h n i c a l d e s i g n , methods h a v e been d e v e l o p e d t o deal with the requirements o f design codes. F o r decades, t h e m e t h o d o f strength r e d u c t i o n w a s t h e way to evaluate g l o b a l g e o t e c h n i c a l safety f a c t o r s . T h e i n t r o d u c t i o n o f E u r o c o d e 7 i n f e r r e d the need t o i n c o r p o r a t e p a r t i a l f a c t o r s f o r A c t i o n s , M a t e r i a l s a n d Resistances. S o m e o f t h i s is d i f f i c u l t to h a n d l e i n the F E M , w h e r e actions and resistances f r o m t h e s o i l are a result o f the equilibrium s o l u t i o n rather t h a n a p r i o r i i n p u t data. A l t e r n a t i v e l y , E u r o c o d e 7 a l l o w s f o r par-tial factors o n ' A c t i o n e f f e c t s ' , w h i c h o f f e r s p o s s i b i l i t i e s f o r the F E M .
M e a n w h i l e , some authors h a v e p u b l i s h e d examples o f finite e l e m e n t calculations a c c o r d i n g to t h e d i f f e r e n t design approaches i n E u r o c o d e 7, w i t h emphasis o n t h e d i f f e r e n c e s i n results and t h e i n f l u e n c e o f t h e s o i l c o n s t i t u t i v e m o d e l b e i n g used (e.g. S c h w e i g e r , 2 0 1 0 ) . T h e purpose ol t h e current c o n t r i b u t i o n is t o describe a D e s i g n A p p r o a c h e s f a c i l i t y f o r an e f f i c i e n t use o f par-t i a l safepar-ty f a c par-t o r s i n a finipar-te elemenpar-t e n v i r o n m e n par-t . Chappar-ter 2 describes hov. parpar-tial f a c par-t o r s can b e t a k e n i n t o account u s i n g t h e D e s i g n A p p r o a c h e s f a c i l i t y a n d h o w t o deal w i t h design calcu-lations i n r e l a t i o n t o s e r v i c e a b i l i t y state c a l c u l a t i o n s . Chapter 3 demonstrates an elaborated e x a m p l e o f an embedded sheet p i l e w a l l . A t t h e end o f t h i s c o n t r i b u t i o n some conclusions are d r a w n .
2 The use of partial safety factors in F E M
D e s i g n codes p r i m a r i l y deal w i t h u l t i m a t e l i m i t state ( U L S ) design, i.e. s t a b i l i t y issues, bear-i n g capacbear-ity and f a bear-i l u r e , whereas t h e F E M bear-is p r bear-i m a r bear-i l y used f o r stress and d e f o r m a t bear-i o n analy-sis at g i v e n w o r k i n g l o a d c o n d i t i o n s . T h e latter is m o r e c l o s e l y related w i t h s e r v i c e a b i l i t j l i m i t state ( S L S ) design rather than U L S d e s i g n . I n u r b a n p r o j e c t s a n d other situations where d e f o r m a t i o n s are c r i t i c a l , S L S requirements are o f t e n considered i n a d d i t i o n t o U L S require-ments. T h i s has c o n t r i b u t e d t o t h e i n c r e a s i n g r o l e o f t h e F E M i n geotechnical design i n the last decades.
P e r f o r m i n g S L S and U L S analysis u s i n g the same m o d e l is e f f i c i e n t and b e n e f i c i a l f o r all parties i n v o l v e d i n the design process. T h i s has s t i m u l a t e d t h e d e v e l o p m e n t o f finite elemeni based methods t o d e f i n e safety i n a g e o t e c h n i c a l c o n t e x t , such as t h e m e t l i o d o f p h i - c reduc-t i o n o r sreduc-trengreduc-th r e d u c reduc-t i o n ( B r i n k g r e v e & B a k k e r , 1 9 9 1 ; G r i f f i reduc-t h & L a n e . 1999) reduc-t o calculareduc-te E global f a c t o r o f safety. T h i s m e t h o d has p r o v e n its usefulness over t h e last decades. T h e in-t r o d u c in-t i o n o f E u r o c o d e 7 has i n f e r r e d in-t h e need in-t o i n c o r p o r a in-t e d i f f e r e n in-t c o m b i n a in-t i o n s o f par-tial safety f a c t o r s f o r A c t i o n s ( l o a d s ) . M a t e r i a l s and Resistances, a c c o r d i n g to the v a r i o u s de-sign approaches as d e f i n e d i n E u r o c o d e 7. I n the F E M , external loads and materials are con-sidered i n p u t data. T h e use o f p a r t i a l f a c t o r s f o r loads and m a t e r i a l properties can s i m p l y be dealt w i t h at i n p u t l e v e l . A c t i o n s and resistances f r o m t h e s o i l , o n the other hand, are noi k n o w n a p r i o r i . T h e y depend o n t h e l o c a l stress c o n d i t i o n s and m a y change d u r i n g t h e analy-sis. T h i s m a k e s i t d i f f i c u l t t o a p p l y partial f a c t o r s o n actions a n d resistances c o m i n g f r o m the s o i l . A l t e r n a t i v e l y , E u r o c o d e 7 a l l o w s f o r p a r t i a l f a c t o r s o n ' A c t i o n e f f e c t s ' , w h i c h can be interpreted as t h e r e s u l t i n g structural f o r c e s ( f o r c e s i n anchors a n d struts, b e n d i n g m o m e n t s in w a l l s , etc.). I n t h i s w a y , i t is f e a s i b l e t o use p a r t i a l f a c t o r s a c c o r d i n g t o the d i f f e r e n t design approaches u s i n g t h e F E M .
T h e t i m e t h a t geotechnical engineers o n l y w o r k i n l o c a l areas w i t h one design code is f a r be-h i n d us. T be-h e w o r k be-has become i n t e r n a t i o n a l . T be-h e i n t r o d u c t i o n o f E u r o c o d e 7 is a first step t o w a r d s h a r m o n i z a t i o n . H o w e v e r , d i f f e r e n t countries have selected dilTerent design ap-proaches and d e f i n e d d i f f e r e n t sets o f p a r t i a l f a c t o r s i n t h e i r n a t i o n a l annexes. T h i s makes the use o f p a r t i a l f a c t o r s i n d a i l y design c a l c u l a t i o n s error prone, i n p a r t i c u l a r w h e n u s i n g the F E M . T o o v e r c o m e t h i s , t h e finite e l e m e n t s o f t w a r e m a y p r o v i d e f a c i l i t i e s to e f f i c i e n t l y man-age t h e d i f f e r e n t design approaches w i t h coherent sets o f p a r t i a l factors, to assign the f a c t o r t o t h e v a r i o u s components o f the finite element m o d e l , t o d i s t i n g u i s h betv\een S L S and U i . -c a l -c u l a t i o n s , and t o assist users i n s e l e -c t i n g t h e r e q u i r e d design approa-ch f o r the U L S -cal-cula- calculat i o n s i n calculat h e i r p r o j e c calculat . I n calculathe f o l l o w i n g paragraph i calculat is described h o w calculat h i s process can be f a c i l i -t a -t e d .
2.1 Workflow and calculation schemes for ULS calculations
The t y p i c a l w o r k flow i n a ' s t a n d a r d ' finite element analysis is the f o l l o w i n g :1. Create g e o m e t r y and b o u n d a r y c o n d i t i o n s 2 . S p e c i f y and assign m a t e r i a l properties 3. Generate finite element mesh 4 . Generate i n i t i a l c o n d i t i o n s 5. D e f i n e c a l c u l a t i o n phases 6. P e r f o r m c a l c u l a t i o n s 7. Inspect results
In t h i s respect, the w o r k flow f o r U L S c a l c u l a t i o n s is n o t d i f f e r e n t t h a n f o r S L S c a l c u l a t i o n s . H o w e v e r , one need t o decide o n h o w and w h e n t o change the loads and properties w h e n g o i n g f r o m S L S calculations t o U L S c a l c u l a t i o n s f o r the same m o d e l . H e r e , i t is suggested t o first complete t h e ' n o r m a l ' w o r k flow w i t h characteristic values o f i n p u t parameters ( S L S ) b e f o r e c o n s i d e r i n g U L S c o n d i t i o n s .
A f t e r a successful S L S c a l c u l a t i o n , partial f a c t o r s m a y be d e f i n e d ( i f n o t y e t a v a i l a b l e ) and applied t o t h e c o r r e s p o n d i n g loads and m a t e r i a l s i n the m o d e l . Partial f a c t o r s f o r a c t i o n e f f e c t s (structural f o r c e s ) o n l y need t o be a p p l i e d a f t e r the c a l c u l a t i o n . Partial f a c t o r s t h a t are n o t exp l i c i f l y d e f i n e d are equal t o u n i t y , such t h a t characteristic values are used f o r t h e c o r r e s exp o n d ing p r o p e r t i e s . Coherent sets o f p a r t i a l f a c t o r s a c c o r d i n g t o a p a r t i c u l a r design code ( c o u n t r y -dependent) ( h e r e i n named a ' D e s i g n A p p r o a c h ' ; see F i g u r e 1) m a y be assembled and stored under a u n i q u e and r e c o g n i z a b l e name i n a g l o b a l data base. Once a D e s i g n A p p r o a c h has - j e n d e f i n e d and stored, i t can be re-used i n other projects t h a t are g o v e r n e d b y t h e same de-sign code.
Partial factors f o r loads
Design Approach
Partial factors f o r materials Partial factors f o r structural forces
Figure 1: Schematic ovei-view of a Design Approach (coherent set ofpartial factors)
Regarding p a r t i a l f a c t o r s f o r loads, d i s t i n c t i o n s h o u l d be m a d e between d i f f e r e n t ' l o a d f a c -t o r s ' . E u r o c o d e 7 d i f f e r e n -t i a -t e s b e -t w e e n Permanen-t and Variable ac-tions; b o -t h can be Unfavourable o r FaUnfavourable. W i t h i n a D e s i g n A p p r o a c h , d i f f e r e n t l o a d f a c t o r s m a y be d e f i n e d -w i t h a u n i q u e and r e c o g n i z a b l e d e s c r i p t i o n (a ' l a b e l ' ; f o r e x a m p l e Permanent unfavourable). In the finite element m o d e l , ' l o a d labels' s h o u l d be assigned t o a l l external loads, r e f e r r i n g t o
t h e a p p l i c a b l e l o a d f a c t o r , such t h a t t h e y [ a u t o m a t i c a l l y ] o b t a i n t h e r i g l i t partial f a c t o r from the applicable D e s i g n A p p r o a c h w h e n U L S c a l c u l a t i o n s are p e r f o r m e d . It s h o u l d be realised t h a t the e f f e c t o f a load ( f a v o u r a b l e o r u n f a v o u r a b l e ) m a y d i f f e r f r o m one c a l c u l a t i o n phase tc another. T h e r e f o r e , l o a d labels that are assigned t o external loads d u r i n g ihe creation o f the finite element m o d e l m a y need t o be changed as p a r t o f t h e d e f i n i t i o n o f a c a l c u l a t i o n phase.
R e g a r d i n g p a r t i a l f a c t o r s f o r m a t e r i a l s , i t is assumed t h a t m a t e r i a l prorjeriies f o r i n d i v i d u a l s o i l layers are stored as m o d e l parameters i n m a t e r i a l data sets. T h e use c f p a r t i a l f a c t o r s on m a t e r i a l s m a y lead t o the [ a u t o m a t i c ] creation o f ' s h a d o w ' m a t e r i a l data sets that are [auto-m a t i c a l l y ] used i n U L S c a l c u l a t i o n s instead o f t h e o r i g i n a l ones, a s s u [auto-m i n g that the original data sets have been created u s i n g characteristic values o f m o d e l parameters. I n the f r a m e w o r k o f t h e D e s i g n A p p r o a c h concept, partial f a c t o r s f o r m o d e l parameters ( ' m a t e r i a l f a c t o r s ' ) are d e f i n e d w i t h a u n i q u e and r e c o g n i z a b l e d e s c r i p t i o n . I n t h e m a t e r i a l data sets, ' m a t e r i a l labels' s h o u l d be assigned t o a l l m o d e l parameters, r e f e r r i n g t o t h e c o r r e s p o n d i n g m a t e r i a l f a c t o r .
L e t ' s consider t h e use o f t h e s i m p l e linear-elastic p e r f e c t l y - p l a s t i c m o d e l w i t h M o h r - C o u l o m t f a i l u r e c o n t o u r t o describe the b e h a v i o u r o f a soil layer. I n p r i n c i p l e , d i f f e r e n t m a t e r i a l labels can be d e f i n e d f o r each o f t h e parameters. W e can i d e n t i f y general properties (7), elasticity properties ( £ , v ) a n d strength propertiies ( c , cp, \)/). D i f f e r e n t m a t e r i a l labels can be d e f i n e d for t h e cohesion c and t h e friction angle cp. H o w e v e r , t h e strength parameters can be used as ef-f e c t i v e strength properties ( c ' , <p', v) i n an e f f e c t i v e stress approach, o r as undrained sfrength properties (c = s„; cp = \|/ = 0 ° ) i n an u n d r a i n e d t o t a l stress approach. T h e latter case is actually k n o w n as the Tresca m o d e l , b u t t h i s can be regarded as a special case o f M o h r C o u l o m b . A c -c o r d i n g t o E u r o -c o d e 7, d i f f e r e n t p a r t i a l f a -c t o r s are d e f i n e d f o r -c ' a n d s„. Hen-ce, a f u r t h e r dis-tinction s h o u l d be m a d e i n m a t e r i a l f a c t o r s and labels w h e n d e f i n i n g partial f a c t o r s f o r the M o h r - C o u l o m b m o d e l parameters, d e p e n d i n g on w h e t h e r the c-parameter is used as an effec-t i v e cohesion c' o r as an u n d r a i n e d shear seffec-trengeffec-th s„.
I n a s i m i l a r w a y , a m a t e r i a l f a c t o r can be d e f i n e d f o r u n i t w e i g h t (y) f o r materials that are p r i m a r i l y used as external loads. N o t e t h a t m a t e r i a l f a c t o r s are t y p i c a l l y used t o decrease pa-rameter values whereas load f a c t o r s are t y p i c a l l y used t o increase values, so i n this case the m a t e r i a l f a c t o r s h o u l d correspond t o the inverse o f t h e a p p l i c a b l e f a c t o r f o r external l o a d .
I t s h o u l d be noted t h a t some advanced m o d e l s have parameter-dependencies and there are l i m i t a t i o n s i n t h e values o r ratios t h a t those parameters can have. T h e r e f o r e , i t has t o be checked that a p p l y i n g m a t e r i a l f a c t o r s does n o t lead t o i m p o s s i b l e U L S parameter values 01 r a t i o s .
R e g a r d i n g p a r t i a l f a c t o r s f o r structural f o r c e s , i n p r i n c i p l e o n l y one ' s t r u c t u r a l f a c t o r ' is needed w h i c h is a p p l i e d t o a l l structural f o r c e s . H o w e v e r , t h e D e s i g n A p p r o a c h concept al-l o w s f o r d i f f e r e n t structuraal-l f a c t o r s t o be d e f i n e d w i t h a u n i q u e and recognizabal-le name ( ' s f r u c t u r a l l a b e l ' ) . I n t h a t case, each ( t y p e o f ) structure o r structural f o r c e i n t h e finite ele-m e n t ele-m o d e l s h o u l d be assigned a s t r u c t u r a l l a b e l , r e f e r r i n g t o t h e c o r r e s p o n d i n g p a r t i a l factoi f o r structural f o r c e s .
I n order t o p e r f o r m design c a l c u l a t i o n s , n e w c a l c u l a t i o n phases need t o be d e f i n e d i n addition t o t h e S L S phases. T o indicate w h e t h e r a c a l c u l a t i o n phase is a design c a l c u l a t i o n ( U L S ) , the a p p l i c a b l e D e s i g n A p p r o a c h needs t o be selected f o r t h a t phase. I n such phases t h e
corre-; p o n d m g load factors are [ a u t o m a t i c a l l y ] a p p l i e d t o the loads and t h e m a t e r i a l f a c t o r s are [ a u t o m a t i c a l l y ] apphed t o the m o d e l parameters ( u s i n g the ' s h a d o w ' m a t e r i a l data sets) based on t l i e i r labels, whereas phases f o r w h i c h no D e s i g n A p p r o a c h has been selected use the o r i g m a l (characteristic) values. O n c e t h e d i f f e r e n t D e s i g n A p p r o a c h e s as w e l l as the 'labelshave been property d e f i n e d , c h a n g i n g f r o m one design approach t o another is easy and v i r t u -ally free o f error.
f h e r e are t w o possible schemes to p e r f o r m U L S c a l c u l a t i o n s i n r e l a t i o n to S L S c a l c u l a t i o n s ( B a u d u i n et a l , 2 0 0 0 ) . Scheme I: 0. I n i t i a l state 1. Phase 1 ( S L S ) > 4 . Phase 4 ( U L S ) .•!. Phase 2 ( S L S ) > 5. Phase 5 ( U L S ) .1. Phase 3 ( S L S ) > 6. Phase 6 ( U L S )
In t h e first scheme t h e design c a l c u l a t i o n s ( U L S ) are p e r f b r m e d f o r each s e r v i c e a b i l i t y state c a l c u l a t i o n separately. T h i s means t h a t Phase 4 starts f r o m the r e s u l t i n g sti-ess state o f Phase 1, Phase 5 starts from Phase 2 , etc. N o t e t h a t i n tiiis case a p a r t i a l f a c t o r o n a m a t e r i a l s t i f f n e s s parameter is o n l y used to calculate additional displacements as a result o f stress r e d i s t r i b u -tions due t o t h e f a c t o r e d ( h i g h e r ) loads and the f a c t o r e d (reduced) strength parameters. I t is a n y h o w questionable w h a t the m e a n i n g is o f displacements o b t a i n e d f r o m U L S c a l c u l a t i o n s .
<cheme 2:
0. I n i t i a l state > 4. Phase 4 ( U L S ) > 5. Phase 5 ( U L S ) > 6. Phase 6 ( U L S ) 1. P h a s e l ( S L S ) ^ ' 2. Phase 2 ( S L S )
.V Phase 3 ( S L S )
In t h i s scheme, the design c a l c u l a t i o n s ( U L S ) start from the i n i t i a l s i t u a t i o n and are p e r f o r m e d subsequentiy. T h i s means that Phase 4 starts from the I n i t i a l state. Phase 5 starts from the re-s u l t i n g re-sfrere-sre-s re-state o f Phare-se 4. etc. I n general, i t ire-s r e c o m m e n d e d t o ere-stablire-sh t h e i n i t i a l re-strere-sre-s field f r o m characteristic values o f Ko ( h o w e v e r , some e x c e p t i o n s m a y o c c u r ) - see also Frank et a l . ( 2 0 0 4 ) .
Design c a l c u l a t i o n s t h a t finish s u c c e s s f u l l y ( w i t h o u t f a i l u r e ) can be regarded as ' f u l f i l l i n g t h e requirements o f the design c o d e ' ; at least w i t h respect to t h e p a r t i a l f a c t o r s i n U L S d e s i g n . H o w e v e r , a c a r e f u l check o n t h e results remains necessary.
In t h e post-processing a f t e r t h e design calculations, the s t r u c h i r a l f a c t o r s are [ a u t o m a t i c a l l y ] applied t o the calculated values o f structural f o r c e s i n order to o b t a i n t h e i r design values. N o t e that S L S r e q u i r e m e n t s s h o u l d be checked on the basis o f t h e c o r r e s p o n d i n g S L S c a l c u l a t i o n -asults rather than from t h e U L S results.
In this section i t has been i n d i c a t e d [ i n square brackets] w h e r e t h e D e s i g n A p p r o a c h e s c o n -cept can be automated i n finite e l e m e n t s o f t w a r e . I f t h a t is done, i t is essential f o r the user t o be able t o v i e w w h i c h values o f loads, m a t e r i a l properties and structural forces are a c t u a l l y
used i n the U L S c a l c u l a t i o n . T r a n s p a r e n c y is necess.ary s u c h that the us -r (geotechnical er neer) can c h e c k those v a l u e s and maintains his / iic-r responsibility f o r thi- geotechnical desi
3 Case: ULS design of an embedded sheet pile wall
T h i s e x a m p l e presents the c a l c u l a t i o n o f the Struciiiral and G r o u n d L i n it State o f an en • ded sheet-pile w a l l . T h e c a s e is based on example 9.2 f r o m the E u r o c o i i e 7 document ( E i - ' . pean C o m m i t t e e for S t a n d a r d i z a t i o n . 2 0 0 4 ) . T h e geometry o f the situati >n is s h o w n in Fieurc 2. T h e w a l l has a n o m i n a l e x c a v a t i o n depth o f 5 m. and an additional excavation depth o f 0.4 m (due to accidental over-dig) is foreseen. T h e w a l l is supported by one row o f anchors at an elevation level o f -1.0 m ( a n c h o r a g e inclination is 10 degrees downw;!rd). T h e free ai . length is 11 m a n d the length o f the a n c h o r body is approximately 6.5 m .
q _ k = 10 kPa
T a b l e 1: C h a r a c t e r i s t i c soil properties
F i g u r e 2: G e o m e t r y o f t h e emliedded sheet pile w a l '
T h e ground p r o f i l e consists o f t w o layers. A r e l a t i v e l y soft soil layer Is overlain by a 4 -t h i c k s-tiffer layer. T h e charac-teris-tic proper-ties o f -these l a y e r s in -terms o f model parame-ters for the H a r d e n i n g S o i l m o d e l are presented in T a b l e 1. T h e initial phret t i c level is 1.0 m bel o w ground s u r f a c e . I n this e x a m p bel e the belong term situation is a n a bel y s e d S(' o n bel y drained beh; -lour is considered and e f f e c t i v e stress parameters are presented. F o r th different layers we u s e the f o l l o w i n g water conditions:
• L a y e r A & B : H y d r o s t a t i c , a c c o r d i n g to i n i t i a l phreatic level at g r - i u n d s u r f a c e -1 m • In the phases w i t h dewatering: Steady-slate situation (calcul.ited by steady-stale
groundwater f l o w based on the h e a d d i f f e r e n c e as a result o f tlu lowered water tab -inside the e x c a v a t i o n ) , a s s u m i n g the lov\er-ed water table is eqeal to the excavation level in each phase, the sheet p i l e w a l l is impermeable and the h t t o m o f t h e model c l o s e d f o r f l o w .
Parameter Layer A Layer B Unit
Material model Hardening Soil Hardening Soil
Behaviour Drained Drained
Unit weight y„,„„r/yM/ 18/20 2 0 / 2 0 IcN/m'
20000 12000 20000 8000 IcN/m^ E,„"' •> 60000 36000 kN/m^ Power m 0.5 0-8 -Poisson's ratio v 0.2 0.2 -Cohesion c' 1.0 5-0 kN/m^ Friction angle 9 35 24 -Dilatancy angle ^ 0 0 Normally-consolidated stress ratio K,"^ 0.50 0.59 -Failure ratio Jt/ 0-9 0-9 -Tensile strength cr, 0.0 0-0 kN/m^
Interface strength ratio 0.67 0.67
-Initial stress ratio A'u 0-50 0.95
-Permeability 1.0 0-001 m/day
^0 Reference stiffiiess at a reference stress level of 100 kN/m^
Other parameters used in the c a l c u l a t i o n are:
o V a r i a b l e surcharge load o f 10 k N / m " on the a c t i v e side o f the w a l l
» E m b e d m e n t depth o f the sheet-pile w a l l pre-determined a t - 1 2 m ( w a l l length 12 m ) " Steel sheetpile w a l l : E A = 3 ; 6 7 5 1 0 ' k N / m , E I = SIO** k N m V m . no c o r r o s i o n c o n s i d
-ered, w e i g h t 1.4 k N / m / m
« A n c h o r stiffness: E A = 16.5-10^ k N / m
« A n c h o r pre-stress f o r c e , applied only w h e n the a n c h o r is installed: 100 k N / m
The geometry used to create the f i n i t e element model is presented in F i g u r e 3 .
Layer A Layer B Paint =cJnt < Y m j 0 -10.0C -2a.00 IQ ^ . o o 1 -10.0C O . K ) 11 20.00 -1.00 2 ^ . o c o . c o 12 9.17 -2.91 2 •SO.OC -20.00 i : i Z 7 2 -;-00 4 2D.oa 0.00 ^a -w.oo - Ï . O 0 £ 2 0 . o d -12.00 I t -so. 00 -1.00 e 2 0 . 0 0 -13.00 Ifl 23.00 -5.00 7 20.0{ - Ï . 0 0 17 - « . 0 0 -5.00 3 -10.00 - Ï . O 0 9 20.0t — . ~ Ö
— H *
-F i g u r e 3: G e o m e t r y used t o create the finite element m o d e
T h e safety p h i l o s o p h y is i n t r o d u c e d u s i n g the f o l l o w i n g s t a r t i n g p o i n t s and assumptions: • F o r t h i s e x a m p l e i t is chosen t o use b o t h E C 7 - D A 2 as w e l l as E C 7 - D A 3 f o r the
struc-t u r a l ( S T R ) a n d g r o u n d ( G E O ) L i m i struc-t Sstruc-tastruc-te v e r i f i c a struc-t i o n . T h e parstruc-tial f a c struc-t o r s are struc-take.i fi-om E C 7 , a p p e n d i x A , as presented i n T a b l e 2 a n d 3 .
• N o p a r t i a l f a c t o r s are a p p l i e d t o t h e properties o f s t r u c t u r a l e l e m c n i s .
• I t is assumed that a l l w a t e r levels are s t r i c t l y c o n t r o l l e d , so no a d d i t i o n a l safety sui-charge is a p p l i e d o n w a t e r c o n d i t i o n s d u r i n g U L S .
• A c c i d e n t a l o v e r - d i g is t a k e n i n t o account, so an a d d i t i o n a l e x c a v a t i o n depth is applie i i n t h e U L S c a l c u l a t i o n s .
• I n t h i s e x a m p l e n o s t i f f i i e s s v a r i a t i o n f o r s o i l a n d structural elements is a p p l i e d d u r i n -t h e U L S calcula-tions.
• I n t h i s e x a m p l e o n l y an u n f a v o u r a b l e l o a d f a c t o r is used f o r the ( v a r i a b l e ) surcharg; l o a d ; i n p r a c t i c e i t m i g h t also be necessary t o investigate t h e e f f e c t o f f a v o u r a b l e loa l f a c t o r s .
T a b l e 2 : P a r t i a l f a c t o r s o n actions ( S T R / G E O L S , d e f a u l t values a c c o r d i n i ; t o E C 7 , annex A
A c t i o n E C 7 - D A 2 E C 7 - D A 3
P e r m a n e n t Unfavourable 1.35 1.00
Favourable 1.00 1.00
V a r i a b l e Unfavourable 1.50 1.30
Favourable 0.00 0.00
t a b l e 3: Factors on soil parameters ( S T R / G E O L S , d e f a u k values a c c o r d i n g t o E C 7 , a n n e x A )
Soil p a r a m e t e r E C 7 - D A 2 E C 7 - D A 3
.Angle of s h e a r i n g r e s i s t a n c e (tan tp) 1.00 1.25
E f f e c t i v e cohesion 1.00 1.25
U n d r a i n e d s h e a r s t r e n g t h 1.00 1.40
W e i g h t density 1.00 1.00
The a f o r e m e n t i o n e d D e s i g n A p p r o a c h f a c i l i t y , as i m p l e m e n t e d i n P L A X I S 2 D , has been used to elaborate t h i s case; b o t h a c c o r d i n g t o E C 7 - D A 3 and E C 7 - D A 2 . I n t h e latter case, p a r t i a l :",-.ctors are used on the action effects b y m u l t i p l y i n g the r e s u l t i n g s t r u c t u r a l f o r c e s ( o b t a i n e d
with characteristic values f o r t h e soil properties) w i t h an appropriate p a r t i a l f a c t o r f o r the
ac-tion e f f e c t s . T h i s approach is o f t e n i n d i c a t e d as E C 7 - D A 2 * . T h e f o l l o w i n g p r a c t i c a l m e t h o d is used: A t i n p u t , a f a c t o r o f 1 is used f o r t h e p e r m a n e n t u n f a v o u r a b l e loads (instead o f 1.35) and a factor o f 1.5 / 1.35 = 1.11 is used f o r t h e v a r i a b l e u n f a v o u r a b l e loads (instead o f 1.5). F r o m the o u t p u t t h e a c t i o n e f f e c t s ( i . e . the s t r u c t u r a l f o r c e s ) are then m u l t i p l i e d b y a f a c t o r o f 1.35.
T a b l e 4 : C a l c u l a t i o n phases P h a s e State P h a s e no. S t a r t f r o m phase C a l c u l a t i o n type I n i t i a l S L S 0 Ko-procedure .Activate w a l l S L S 1 0 Elasto-plastic S u r c h a r g e 10 k P a + excavate to - l m S L S 2 1 Elasto-plastic A c t i v e a n c h o r + p r e - s t r c s s i n g 100 k N / m S L S 3 2 Elasto-plastic F u l ! excavation + d e w a t e r i n g to - 5 . 0 m S L S 4 3 Elasto-plastic F u l l excavation -f- d e w a t e r i n g to -5.4m ( i n c h i d i n g over-dig) S L S 5 4 Elasto-plastic U L S long t e r m P h a s e 2 U L S 6 2 Elasto-plastic
U L S long term P h a s e 3 U L S 7 3 Elasto-plastic
Sche i U L S long t e r m P h a s e 4 U L S 8 4 Elasto-plastic Sche i U L S long t e r m P h a s e 5 U L S 9 5 Elasto-plastic S u r c h a r g e 10 k P a + excavate to - l m • U L S 10 1 Elasto-plastic A c t i v e a n c h o r + p r e - s t r e s s i n g 100 k N / m U L S 11 10 Elasto-plastic Sclie i F u l l excavation + d e w a t e r i n g to -5.0m U L S 12 11 Elasto-plastic F u l l excavation + d e w a t e r i n g to -5.4m { i n c l u d i n g over-dig) U L S 13 12 Elasto-plastic
I n the e x a m p l e t h e d r a i n e d stress h i s t o r y is used t o analyse the S L S and U L S o f t h e structure F o r d e m o n s t r a t i o n purposes, b o t h Scheme 1 and Scheme 2 h a v e been a p p l i e d to p e r f o r m de-s i g n calculationde-s i n r e l a t i o n t o the de-s e r v i c e a b i l i t y c a l c u l a t i o n de-s . I n general, i t ide-s de-s u f f i c i e n t to choose o n l y one scheme. T h e m o d e l l e d c a l c u l a t i o n phases are l i s t e d i n T a b l e 4 . T h e results ol t h e c a l c u l a t i o n s i n t e r m s o f t h e design values o f s t r u c t u r a l f o r c e s are presented i n T a b l e 5.
T a b l e 5: C a l c u l a t i o n results P h a s e M a x . hor. w a l l def. f m m | M a x . a n c h o r f o r c e | k N / m l M a x . b e n d i n g m o m e n t | k N m / m l M a x . anclioi f o r c e I k N / m ! E C 7 - D A 2 M a x . bending moment | k N m / m | E C 7 - D A 2 " I n i t i a l -A c t i v a t e w a l l - -S u r c h a r g e 10 k P a -i- excavate to -1 m 1 - -4 A c t i v e a n c h o r + p r e - s t r e s s i n g 100 k N / m -10 100 34 F u l l excavation t d e w a t e r i n g to -5.0m 50 119 173 F u l l excavation i d e w a t e r i n g to -5.4m ( i n c l u d i n g over-dig) 70 130 215 E C 7 - D A 3 E C 7 - D A 2 ' U L S long t e r m Phase 2 - -6 - 1.35*-4 = -5
U L S long term P h a s e 3 100 36 1 . 3 5 * 1 0 0 - i:-5 1.35*34 = 46 U L S long term P h a s e 4 138 236 1 . 3 5 ' 1 2 0 = 1(2 1.35*177 = 239
U L S long term Phase 5 164 326 1.35*130 = 176 1.35*220 = 297
S u r c h a r g e 10 k P a -^ excavate to - I m - -7 - 1.35*-4 = -5 A c t i v e a n c h o r + pre-stressing 100 k N / m 100 28 1.35*100 = 1.-55 1.35*33 = 4 5 F u l l excavation + d e w a t e r i n g to -5.0m 147 261 1.35*120 = l'-2 1.35*175 = 2 3 6 F u l l excavation 1 d e w a t e r i n g to -5.4m ( i n c l u d i n g over-dig) 168 340 1.35*131 = 177 1.35*218 = 294
C o n s i d e r i n g t h e results, s o m e general observations can be m a d e :
• U s i n g scheme I o r scheme 2 g i v e s f a i r l y s i m i l a r values i n s t r u c t u r a l f o r c e s f o r h o t ! E C 7 ^ D A 2 * and E C 7 - D A 3 ( i n t h i s e x a m p l e ) . I t s h o u l d be realised t h a t d i f f e r e n c e s m a j be l a r g e r i n other situations.
• F o r a n u m b e r o f phases E C 7 - D A 2 * g i v e s r e l a t i v e l y large values f o r t h e anchor force c o m p a r e d t o E C 7 - D A 3 , w h i c h is t h e r e s u l t o f t h e f a c t that the pre-stress v a l u e is en-t e r e d as a characen-terisen-tic v a l u e i n E C 7 - D A 3 .
N o t e t h a t i n S c h w e i g e r ( 2 0 1 0 ) a s l i g h t l y d i f f e r e n t approach is presented f o r E C 7 D A 2 ' ' -w h e r e c a l c u l a t i o n s are p e r f o r m e d -w i t h o u t (case 1) and -w i t h (case 2 ) the \ ariable unfavourable l o a d . T h e design values o f structural f o r c e s are t h e n o b t a i n e d b y the sum o f t h e results f d
case 1 w i t h the partial f a c t o r f o r permanent u n f a v o u r a b l e l o a d , and t h e d i f f e r e n c e i n results between case 2 and case 1 w i t h t h e p a r t i a l f a c t o r f o r v a r i a b l e u n f a v o u r a b l e l o a d , i.e.
/^*.v,ir„ = * 1.35 + (Fcase2-F„,,,t) * 1.50 ( 1 )
The latter approach w o u l d be m o r e d i f f i c u l t to a u t o m a t e t h a n the approach d e s c r i b e d i n t h i s c o n t r i b u t i o n . It s h o u l d be n o t e d that b o t h approaches are a p p r o x i m a t i o n s o f t h e o r i g i n a l E C 7 -D A 2 .
4 Conclusions
In t h i s c o n t r i b u t i o n a c o n c e p t is presented t o f a c i l i t a t e u l t i m a t e l i m i t state c a l c u l a t i o n s i n a f i n i t e e l e m e n t e n v i r o n m e n t , i n a d d i t i o n t o r e g u l a r s e r v i c e a b i l i t y state f i n i t e e l e m e n t c a l c u l a -tions. T h e f o c u s has been on a n u m b e r o f issues relevant f o r d e f i n i n g and a s s i g n i n g sets o f partial safety f a c t o r s and e x p l a i n i n g t h e w o r k fiow r e q u i r e d f o r w o r k i n g w i t h design ap-proaches. A n e x a m p l e has been elaborated i n w h i c h b o t h E C 7 - D A 2 and E C 7 - D A 3 h a v e been used i n o r d e r t o s h o w t h e p o s s i b i l i t i e s f o r w o r k i n g w i t h E u r o c o d e 7. E C 7 - D A 1 has n o t been considered, b u t t h i s can be regarded as a c o m b i n a t i o n o f the other t w o d e s i g n approaches.
The purpose o f t h i s c o n t r i b u t i o n is t o demonstrate h o w t h e D e s i g n A p p r o a c h e s f a c i l i t y can be used as an e f f i c i e n t f a c i l i t y i n finite element s o f t w a r e t o p e r f o r m g e o t e c h n i c a l u l t i m a t e l i m i t state design c a l c u l a t i o n s . I t is N O T t h e a u t h o r s ' i n t e n t i o n t o advocate a p a r t i c u l a r design ap-proach.
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Author
D r . R o n a l d B . J . B r i n k g r e v e D e l f t U n i v e r s i t y o f T e c h n o l o g y & Plaxis B V C o m p u t e r l a a n 14 2 6 2 8 X K D e l f t T e k : + 3 1 ( 0 ) 15 2 5 1 7 7 2 8 Fax: + 3 1 ( 0 ) 15 2 5 7 3 1 0 7 e - m a i l : r . b r i n k g r e v e ( g p l a x i s . n l W e b : w w w . p l a x i s . n lBodenverbesserungssaulen als Praventation der Bodenverflüssigung bei
Erdbebenbeanspruchung
J . HIeibieh, I . Herie
K u r z f a s s u n g : Die Anwendung von Schotter oder Betonsaulen zur Verhinderung von B o -d e n v e r f l ü s s i g u n g hat in -den letzten Jaliren zugenommen. Untersuchungen zu -deren Funlcti-onsweise sind jedoch kauni verhanden. Dies lasst sich damit b e g r ü n d e n , dass sowohl numeri-sche Berechnung m i t einfachen Stoffmodellen als auch kleinmaBstabliche Laborversuche problematisch sind. In diesem Beitrag w i r d die Anwendung von Bodenverbesserungssaulen als Pravention zur B o d e n v e r f l ü s s i g u n g numerisch untersucht. H i e r f ü r wurde ein hypoplastisches M o d e l l verwendet. Das Augenmerk der Untersuchung liegt dabei auf dein Einfluss von Steifigkeit und Durchlassigkeit der Saulen. Weiterhin w i r d der Unterschied z w i -schen Schotter- und Betonsaulen sowohl in 2 D - als auch in 3D-Modellen betrachtet.
A b s t r a c t : the application o f gravel or concrete columns to prevent the soil liquefaction has increased in the last few years. However, f o r understanding o f this method, detailed investi-gations are still lacking. Numerical analyses with simple constitutive models and small scale experiments are not suitable. In this paper, a numerical w i t h a hypoplastic constitutive model is presented. The influence o f stiffness and permeability o f the columns are examined sepa-rately. Furthermore, the difference between gravel and concrete columns is studied in 2D and 3D models.
1 E i n f ü h r u n g
Durch E r d b e b e n entstehen e n o r m e w i r t s c h a f t l i c h e Schaden. D i e s e Schaden s i n d o f t m i t einer B o d e n v e r f l ü s s i g u n g v e r b u n d e n . A I s i n n o v a t i v e M e t h o d e z u r V e r m i n d e r u n g der V e r f l ü s s i -gungsgefahr k a m e n i n den letzten Jahren die Bodenverbesserungssaulen z u m Einsatz. A I s Bodenverbesserungssaulen w e r d e n i n der Regel Schotter oder Betonsaulen bezeichnet. W a h -rend die Betonsaulen a l l e i n dur ch ihre hohe S t e i f i g k e i t die V e r f l ü s s i g u n g v e r h i n d e m k ö n n e n , w i r k e n die Schottersaulen gegen V e r f l ü s s i g u n g m i t verschiedenen M e c h a n i s m e n entgegen (Dranage, V e r d i c h t u n g u n d S t ü t z u n g ( M a d h a v et a l . 2 0 0 8 ) ) .
A u f g r u n d der hohen D u r c h l a s s i g k e i t der Schottersaulen i m V e r g l e i c h z u m u m l i e g e n d e n B o -den baut s i c h i n -den Saulen k a u m ein Porenwasserdruck ( P W D ) auf. D e r D r u c k u n t e r s c h i e d verursacht eine W a s s e r b e w e g u n g i n R i c h t u n g der Saulen u n d d a m i t eine A b n a h m e des P W D s im B o d e n . D a die D u r c h l a s s i g k e i t b e i m Sand u n d Schotter i n der h o r i z o n t a l e n R i c h t u n g g r o Ber als i n der v e r t i k a l e n R i c h t u n g ist, ist der E i n f l u s s der Schottersaulen n i c h t nur die A b k ü r -zung der Dranagewege, sondern auch die A n d e r u n g der W a s s e r b e w e g u n g z u der e f f e k t i v e r e n D r a n a g e r i c h t u n g zu w e c h s e l n ( M a d h a v et a l . 2 0 0 8 ) . Z u s a t z l i c h b e w i r k t der E i n b a u der
