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

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 Copyright ASCE 2010 International Conference on Scour and Erosion 2010 (ICSE-5) 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. H C L B B (1) Where B L is the creep length that is measured along the bottom face of the weir, B C is Bligh's creep ratio which varies depending on the type of the foundation soil, and H is the water head. For example the fine sand B C is 15. The critical head is CB H when CB B B H C L . The second method is Lane's method. H C L L L (2) Where L L is the weighted creep length. h h v v L l k k l L / (3) Where, v l is the creep length of vertical direction (inclination angle of more than 45 degrees), h l is the creep length of horizontal direction (inclination angle of lower than 45 degrees). v k is the vertical coefficient of permeability and v k is the horizontal coefficient of permeability. However, h v k k / has been used 1/3 customarily. L C is Lane's creep ratio which varies depending on the type of the foundation soils. For example the fine sand L C is 7.0. H is the water head. The critical head is CL H , when CL L L H C L . SCOUR AND EROSION 561 Copyright ASCE 2010 International Conference on Scour and Erosion 2010 (ICSE-5) 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 (Figure1). The first group was named “Depth group” to change penetration depth of the weir: Weir1, 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 Weir5. 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 Table1 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 562 Copyright ASCE 2010 International Conference on Scour and Erosion 2010 (ICSE-5) 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 10mm 40mm 10mm 40mm 5mm 5mm 10mm 40mm Position group Weir 4 Weir 1 Weir 5 10mm 30mm 10mm 30mm 10mm 10mm 5mm 5mm 5mm 5mm Two cut-off group Weir 6 Weir 7 Depth group Weir 1 Weir 2 Weir 3 20mm 30mm 10mm 40mm 80mm 50mm Relative Density Critical water head Piping / Boiling Average of critical water head % mm mm 82 80 Piping 86.3 90 Piping 83.6 90 Piping 84.7 140 Piping 86.1 145 Boiling 84.5 125 Piping 88.9 250 Boiling 85.1 251 Boiling 81.4 271 Boiling 87.4 70 Piping 81.2 75 Piping 81.5 75 Piping 82.6 155 Boiling 83.1 175 Boiling 87.4 180 Boiling 86.6 130 Boiling 84.5 135 Boiling 82.6 135 Boiling 83.6 145 Boiling 82.3 165 Boiling Weir1 Weir4 Weir3 Weir2 Pattern