Iida, Toshiaki

Magara, N.

Okajima, Kenji

English

Hydraulic Engineering Repository

Conference Paper, Published VersionOkajima, Kenji; Magara, N.; Iida, ToshiakiReexamination of Creep Theory in the Foundation of Weirsby Model Experiments and Elasto-Plastic FEMVerfügbar unter/Available at: https://hdl.handle.net/20.500.11970/100269Vorgeschlagene Zitierweise/Suggested citation:Okajima, Kenji; Magara, N.; Iida, Toshiaki (2010): Reexamination of Creep Theory in theFoundation of Weirs by Model Experiments and Elasto-Plastic FEM. In: Burns, Susan E.;Bhatia, Shobha K.; Avila, Catherine M. C.; Hunt, Beatrice E. (Hg.): Proceedings 5thInternational Conference on Scour and Erosion (ICSE-5), November 7-10, 2010, SanFrancisco, USA. Reston, Va.: American Society of Civil Engineers. S. 560-569.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.Reexamination of Creep Theory in the Foundation of Weirs by Model Experiments and Elasto-Plastic FEM K. Okajima l , N. Magara l and T. Iida l ILaboratory of Water Environmental Engineering, Department of Biological and Environmental Engineering, Graduate School of Agricultural and Life Sciences, The University of Tokyo, Zip code 113-8657, Tokyo, Bunkyo-ku Yayoi I- I-I; PH(+81 )3-5841 -5349; email: aokajim@mail.ecc.u-tokyo.ac.jp ABSTRACT Creep flow theories that are Bligh 's and Lane's equation have been used as the safety criteria against piping under foundation of weirs. These methods were reexamined by model experiments and finite element analyses in this study. These model experiments were carried out in six patterns and had same creep length by changing the installation position and length of cut-off wall. These critical water heads of model experiments were different from each pattern. It was clear that creep flow theories were not able to predict these differences. Our FEM predicted these critical water heads of model experiments. Maximum shear strain contour line by our finite element analysis indicated that shear strain concentrated in similar soil mass as Terzaghi assumed in the seepage failure equation. It was suggested that Terzaghi's method was more effective than the creep theory to calculate the critical water head if the soil mass was defined properly. INTRODUCTION Creep flow theories are applied to the design criteria against piping of foundation of a weir. Bligh's creep flow theory was developed as the empirical equation for the design of floating type weirs in permeable layer through many experiences in 1910 (Bligh). After suggestion of this theory it was indicated that vertical sections of the creep length contribute more to reduce the danger of piping than horizontal sections of the length. In the response to this, Lane (1935) suggested the weighted creep flow theory. These creep flow theories were based on the assumption that the cause of piping was erosion along the contact surface between soils and weir. The purpose of this study is the reexamination of these practical safety criteria 560 SCOUR AND EROSION 561 against seepage failure. We conducted a series of model experiments, and then evaluated these practical safety criteria and the validity of the elasto-plastic FEM by applying to the experiments. CREEP FLOW THEORIES To prevent piping at the down-stream side of a weir, practical manuals indicate that a safe creep length have to be ensured under the surface of the weir and along the side of the weir. The creep length to be ensured must be larger than the values calculated by two methods. The first method is Bligh's method. (I) Where LB is the creep length that is measured along the bottom face of the weir, C B is Bligh's creep ratio which varies depending on the type of the foundation soil, and t;f{ is the water head. For example the fine sand C B is 15. The critical head is t;f{ CB when Ls = C Bt;f{ CB . The second method is Lane's method. (2) Where LL is the weighted creep length. Where, Iv is the creep length of vertical direction (inclination angle of more than 45 degrees), I" is the creep length of horizontal direction (inclination angle of lower than 45 degrees). k,. is the vertical coefficient of permeability and kv is the horizontal coefficient of permeability. However, kv / k" has been used 1/3 customarily. CL is Lane's creep ratio which varies depending on the type of the foundation soils. For example the fine sand C L is 7.0. t;f{ is the water head. The criticalheadis t;f{cL , when LL =CLt;f{CL. 562 SCOUR AND EROSION MODEL EXPERIMENTS AND REEXAMINATION OF CREEP FLOW THEORIES Layout of Model Experiments The experimental apparatus was consisted of a glass-walled sand box. The size was 1000mm long, 500mm high and 200mm wide. The permeable layers in these model experiments were made by using clean sand. The sand was the Toyoura sand with a specific gravity of 2.64, a mean diameter (D50) of 0.16 mm and a uniformity coefficient of 1.46. The weir was made of rigid acrylic plates. The weir was fixed to sand box and was sealed by silicon rubber and silicon adhesion bond to prevent water and sand from spilling out. The sandpaper was pasted on the bottom and side of the weir to prevent roofing. The cut-off wall was made of aluminum plate. The sand layers were prepared by pouring dry sand using hopper into stored water and deleting air during the soil particle falling. The high density of the sand layers was obtained: the relative density was about 85%. After setting up the water levels of both upstream and downstream side equal, the downstream water level was lowered incrementally (5mm after an hour). The deformation of the sand layer was measured. When piping or boiling occurred, the water head was defined to attain the critical water head. The data of a series of model experiments are indicated in Figure2. All patterns had same creep length in which Bligh's creep length is 180mm and Lane 's creep length is 123mm. These data were obtained by conducting 2 or 3 times in each experiment. These experiments are divided into 3 groups (Figure I). The first group was named "Depth group" to change penetration depth of the weir: Weir!, Weir2 and Weir3. From these experiments we can evaluate the influence of the depth of the weir for piping. The second group was named "Position group" to change the position of a cut-off wall: Weir4, Wei3 and WeirS. From these experiments we can evaluate the influence of the position of the cut-off wall for piping. The third group was named "Two cut-off group" to change the position and length of two cut-off walls: Weir6 and Weir7 . From these experiments we can evaluate the influence of the position of the cut-off wall for piping. Results of Model Experiments Table I shows results of model experiments that are relative density (%), critical water head, the kind of seepage failure (Piping or Boiling) and average of critical water head. Piping was observed in some patterns of model experiments. The SCOUR AND EROSION 563 heaving was observed because sand ground in down-stream side deformed. Relative densities were about 85% from 81.2% to 88.9%. Critical water heads in each pattern were similar water heads. In these model experiments the reproducibility was observed. These model experiments had same creep length. Bligh's and Lane's creep flow theories predict a critical water head with patterns. However, each critical water head was different from the other pattern. The result indicated that creep flow theories were not able to predict the critical water head. Discussions of each groups described later. Table 1 Results of model experiments Rdll i\~ Critic:>] Piping! BOiling AVC;:J.~~rO~~C:J.:[ic:J.1 Pallcm Dcn s~y w : llcrhc~d Depth group Weirl Weir 2 Weir3 % ,,~I I' 80 m.m ~ CJ " " Pi[:inl! Weir! 86.3 90 P!£ing 87 M; H6 90 P!Eing 30mm ? 84.7 ,.,1) Pi~irl\~ ,Om Weir:! l:!6.1 ,." Boiling 137 S-t.; 12S P!Einl! I lIK9 2:iO Boiling WeirS Weir) 85.1 2" Boiling 258 lll.-I 271 Boiling Position group r= 87.4 70 P!£inc Wc ir-l 1:11.2 75 P!£inc 13 81.5 75 P i~ ing ===r 82.6 155 Boilin!;: WeirS 83.1 175 Boilin~ liD M7. -I '''' Boiling r===" 1:16,6 130 Boiling Wc ir6 '" 135 Boilin!;; lJJ Two cut-off group l!2 .6 13' Boilin!:: F=f 1:1),6 '45 Boiling Wdr7 155 ».2.3 165 Boiling Figure 1 Patterns of model experiments SEEPAGE FAILURE ANALYSES BY ELASTO-PLASTIC FEM In this study the finite element analysis consisted of two steps. The first step is the seepage flow analysis by FEM. The second is the seepage failure analysis by the elasto-plastic FEM to input effective stress regarding the seepage force as the external force. Constitutive model of the elasto-plastic model The finite element analysis employs the elasto-plastic constitutive equations with a non-associated flow rule and strain hardening-softening. The constitutive equations based on the yield function of Mohr-Coulomb and the plastic potential function of Drucker-Prager. The finite element is 4-noded iso-parametric element 564 SCOUR AND EROSION with one point integration. The explicit dynamic relaxation method combined with the generalized return-mapping algorithm is applied. The elasto-plastic constitutive relations including the effect of the shear band are employed. A simplified and generalized version of mesh size-dependent softening modulus method (Tanaka and Kawamoto, 1989) is used in this study. A material model for a real granular material (i.e., Toyoura sand) with a high angle of internal friction is used with the features of nonlinear pre-peak, pressure-sensitivity of the deformation and strength characteristics of sand, non-associated flow characteristics, post-peak strain softening, and strain-localization into a shear band with a specific width (Tatsuoka et aI., 1991; Siddiquee, 1999). The material model will be briefly described in this section. Input Parameter and FEM mesh In the elasto-plastic finite element analysis, the material constants of Toyoura sand are as follow: relative density = 88%, residual friction angle (tP,)= 33 degree. The calibration of the other elasto-plastic parameter of air-dried Toyoura sand in the elasto-plastic constitutive model was performed using the plane strain compression tests by Tatsuoka et al (1986) . The analysis was performed using a series of finite element mesh of each model experiment, as shown in Figure2. Elements bordering on the weir were boundary elements and the friction was set to be equal to the friction between sand and weir in these elements. Weir! mesh 1111 II III II j- I ·1 II I I Ii .! · 11 .11; III (a) Weir2 mesh (b) Weir3 mesh (c) Weir4 mesh SCOUR AND EROSION I - I I ! I I : __ J ----- 1 -- . ...... (e) WeirS mesh RESULT AND DISCUSSION Critical water head I I -I I ·,·1 r-(a) Weir6 mesh Figure 2 FEM mesh 565 I III I I' I , r I-I I -il +1 -r+ ---(b) Weir7 mesh Result of model experiments and FEM in each groups are discussed about the effectiveness of FEM and the tendency of seepage failure of foundation of the weir_ Figure3 indicates the critical water head of Position group _ The critical water head gradually increases with the moving to the downstream end of the weir in Position group which has same creep length. Results of FEM predicted each critical water head well. Figure4 indicates the critical water head of Depth group. The critical water head gradually increases with the increasing the penetration depth of the weir in Depth group which has same creep length. Results of FEM predicted each critical water head well. FigureS indicates the critical water head of Two cut-off group. The critical water head varies with the number and length of cut-off walls though these critical water head was near without the point of longer cut-off wall. Results of FEM predicted each critical water head well. Results of FEM which penetration depth of weir was 10mrn and the cut-off wall was set at upstream side or middle of the length of weir were computed higher than results of model experiments (Weir! and Weir4). The reason is considered that the continuum model might not hold true when number of particle of sand (the average particle side is 0.16mrn) was about 60 at the downstream edge of the weir. Result of FEM which penetration depth of weir was 50mrn was computed lower than results of model experiment (Weir3). The reason was considered that the friction of the side glass wall influenced the water head of boiling because it was observed that larger sand mass moved during the boiling in the model experiments ofWeir3. These discussions indicated that our FEM was effective analysis to compute the critical water head. Maximum shear strain Our elasto- plastic FEM has the frictional hardening-softening functions. 566 SCOUR AND EROSION When the maximum shear strain reaches 0.1 , the frictional function changes from hardening regime to softening regime. At that time the shear band develops in these elements. Figure6 indicates that the observed shear band in model experiment at water head 180mm and computed maximum shear strain distribution by FEM at water head 170mm. The observed shear band is showed by broken line in the picture. When the shear band was compared with concentration area of the maximum shear strain, it is clear that our FEM is able to predict the position and the tilt of the shear band well. This result indicated that our FEM was able to predict the deformation by seepage failure. So we discussed the mechanism of seepage failure with these maximum shear strain distribution by our FEM. Figure7 indicates maximum shear strain distributions at the critical water head of Weirl , Weir2, Weir3 and Weir4. It is indicated that the mechanism to change the critical water head of Depth group is expanding of concentration area of maximum shear strain from Figure7 (a), (b) and (d) . It is indicated that the mechanism to change the critical water head of Position group is expanding of concentration area of maximum shear strain from Figure6 and Figure7 (d) when the cut-off wall approaches the downstream edge of weir. However the concentration areas of Figure7(c) and (d) is very similar without the position of the cut-off wall. The difference of the critical water head between Weir4 and Weir! causes the seepage force by seepage flow. These mechanisms of seepage failure indicated that Terzaghi 's method in the cut-off pile was possible to predict the critical water head in the weir. Application of Terzaghi's method Terzaghi 's method is the most famous method of a critical hydraulic gradient. Originally, Terzaghi 's method was developed to be applied to a safety criterion for sheet pile piping. This method was formulated based on experimental model tests and its effectiveness was confirmed by many sheet pile model tests.In Terzaghi 's method, a piping occurs when the submerged weight of the soil prism on the down-stream side of the sheet pile equals the heaving force by excess hydrostatic pressure. In the formulation Terzaghi defined that the size of the prism was D x D / 2 in the two dimensional condition when the penetration depth is D. In this study we decided that the penetration depth D is the depth of downstream edge of the weir. F igure8 indicates the result of application of Terzaghi 's method to the weir. Terzaghi 's method was very good prediction of the critical water head. It was suggested that Terzaghi's method was more effective than the creep SCOUR AND EROSION theory to calculate the critical water head in the seepage failure of the weir. 300 o Experiments o FEM - Bligh"s creep kngth c 250 ] 200 ----- Lane's creep length o o o 300 i 250 '2 200 <> Experiments o FEM - Bligh's creep kngth ----- L:mc's creep length 567 " 150 ~ ------TI---------------~------------------------- ~ 150 ~ ] 100 8 50 ------------------------rr------------------------~ 8 u 100 U 50 8 Wt:irl I Wcir2 cr Weir3 Weir] [J I Figure 3 Critical water head of Position group Figure 4 Critical water head of Depth group lOa o Expcrimcnls I 250 o FEM - Bligh's crccpkngth " ~ 200 ----- Lanc'scn:cp kngth " 150 • .g 100 o _______ ~--------------------------------!:l--------8 50 Wcin'i \Vcir? F F=f Figure 5 Critical water head of Two cut-off group 420 440 460 480 500 520 540 560 580 600 620 Length of weir (mm) Figure 6 Shear band in model experiment at water head 180mm and maximum shear strain distribution at water head 170mm 568 SCOUR AND EROSION ~ t) ~ ' " !.I'" "-' 0 ~ ) 2 ...., ISO 140 130 120 110 100 90 80 70 60 50 440 460 480 500 510 540 560 580 Length of the weir (mm) (a) Maximum shear strain distribution at water head 140mm (Weir2) ?1 5 -··r lW ;: 14 "3' -:- 13 ~ , 12 :: I I § 10 . .:': 90 c 80 "0'0 70 £ 60 5~ -- ~ -- ~ -. --~---r--~ ~ 440 460 480 500 520 540 560 580 Length of the weir (mm) (c) Maximum shear strain distribution at water head 105mm (Weir4) ~ 1 5 § 14 5. 13 ~ 12 El l 470 490 510 530 550 570 590 Length of the we ir (mm) (b )Maximum shear strain distribution at water head 230mm (Weir3) -:::-1 5 -ilW', § 14 _ ;y-.::- 13 ;:; go 12 I I ~ '-~ i1, 70 .;:; ::r:: 60 50+- -.--~ -- -r--~ -- ~ -.-- ~ 440 460 480 500 520 540 560 580 Length of th e we ir (mm) (d) Maximum shear strain distribution at water head 115mm (Weirl) Figure 7 Maximum shear strain distribution of elasto-plastic FEM 300 0 Experiments 300 ~ 150 0 FEM 0 Experiments :.[ 250 0 FE M 0 5 6. Tcr.taghi's method () ] 200 6 Tcrzaghi's method 0 ] 200 6 ,- ISO ¥. 150 ~ ~ ] e 0 ~ $ 100 ~ ] l Oa 8 50 8 so Wcir4 Weir ] Weir5 Weirl Weir:! Weir3 r= I I I c::r D (a) Critical water head of Position group (b) Critical water head of Depth group Figure 8 Critical water head in applying Terzaghi's method SCOUR AND EROSION 569 CONCLUSION Creep flow theories were reexamined by model six patterns experiments and finite element analyses that had same creep length by changing the installation position and length of cut-off wall in this study. These critical water heads of model experiments were different from each pattern. It was clear that creep flow theories were not able to predict the critical water head. Our FEM predicted these critical water heads of model experiments. Maximum shear strain contour line by our finite element analysis indicated that shear strain concentrated in similar soil mass as Terzaghi assumed in the seepage failure equation. It was suggested that Terzaghi's method was more effective than the creep theory to calculate the critical water head if the soil mass was defined properly. REFERENCES Bligh, W. G. (1910) "The practical design of irrigation works", London Constable, 162-205 Lane, E.W. (1935) "Security from Under seepage Masonry Dams on Earth Foundations", Trans. ASCE, 100, 1234-1351 , Tanaka, T and Verruijt, A (1999) "Seepage failure of sand behind sheet piles - The mechanism and practical approach to analyze- ", Soils and Foundations, 39(3), 27-35 Tanaka, T. and Kawamoto, O. (1988) "Three dimensional finite element collapse analysis for foundations and slopes using dynamic relaxation", Proc. ofNumer. Meth. in Geomech., 1213-1218, Tatsuoka, F. , Siddiquee, M. S. A, Park, C. S., Sakamoto, M. and Abe, F. (1993) "Modeling Stress-Strain Relations of Sand", Soils and Foundations , 33(2), 60-81 Terzaghi, K. and Peck, R. B. (1948) "Soil Mechanics IN Engineering Practice" , John Wiley and Sons, 218-233 

Reexamination of Creep Theory in the Foundation of Weirs by Model Experiments and Elasto-Plastic FEM

http://henry.baw.de/bitstream/20.500.11970/100269/1/icse-5_Okajima_Magara_Iida_560-569.pdf

Reexamination of Creep Theory in the Foundation of Weirs by Model Experiments and Elasto-Plastic FEM

Abstract

Similar works

Full text

Available Versions

Hydraulic Engineering Repository