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111 CHAPTER 13 CONCLUSIONS AND RECOMMENDATIONS 13.1 CONCLUSIONS Shelby tube); placing it through a tight-fitting opening in the bottom of a rectangular cross-section conduit; pushing a 13.1.1 General small protrusion of soil into the conduit; sending flowing water over the top of the sample at a chosen velocity; and The topic addressed is the prediction of the scour depth recording the corresponding erosion rate. This is repeated around a bridge pier founded in cohesive soils and subjected for several velocities and the erosion function for each is to water flow. The scour components considered are complex obtained in that fashion. pier scour and contraction scour. The proposed method, which is based on 42 useful flume tests and 49 useful numerical sim- ulations, is a further development of the method formulated 13.1.4 SRICOS-EFA Method earlier for simple pier scour (cylindrical pier in deep water). for Cylindrical Piers in Deep Water SRICOS stands for Scour Rate In COhesive Soils. Since the 13.1.2 Erodibility of Cohesive Soils method makes use of the erosion function measured in the EFA, the method is referred to as the SRICOS-EFA Method. It is emphasized that erodibility is not an index but a rela- The SRICOS-EFA Method (program) gives the scour depth as tionship or function between the water velocity (or, better, the a function of time for the period covered by the hydrograph for shear stress at the water-soil interface) and the erosion rate of a given velocity hydrograph at a bridge, a given multilayered the soil. Erodibility is represented by the erosion function. soil stratigraphy with an erosion function defined for each Two important parameters help describe the erosion function: layer, and a given cylindrical pier in deep water (water depth the critical shear stress and the initial slope of the erosion func- larger than 1.6 times the pier diameter). tion. It is found that, although the critical shear stress of a cohe- The method is based on the calculation of two basic param- sive soil is not related to its mean grain size, the common range eters: the maximum depth of pier scour and the initial rate of of critical shear stress values for cohesive soils (0.5 N/m2 to scour. The maximum depth of scour is based on an equation 5 N/m2) is comparable to the range obtained in sands. This obtained from flume tests and the initial rate is based on an explains why the maximum scour depth in cohesive soils is equation giving the initial shear stress obtained from numeri- comparable to the one obtained in sands. The initial slope of cal simulations. The initial rate of scour is read on the EFA the erosion function can be many times less than the one in erosion function at the corresponding value of the calculated sand (e.g., 1,000 times less) and, therefore, the scour depth can shear stress. A hyperbola is used to connect the initial scour develop very slowly in some cohesive soils. There lies the rate to the maximum or asymptotic scour depth and describes the complete scour depth versus time curve. Robust algo- advantage of developing a method that can predict scour depth rithms are used to incorporate the effect of varying velocities as a function of time for a given hydrograph (cohesive soil) and multilayered soil systems. This earlier method was devel- rather than a maximum depth of scour for a design flood oped by the authors under TxDOT sponsorship and was ver- (sands). This was the goal of this project. It also was found that ified by satisfactory comparison between predicted scour and the critical shear stress and the initial slope were not related to measured scour at eight bridges in Texas. soil properties because the R2 of the regressions were all very low. To obtain the erosion function this study recommends using the Erosion Function Apparatus (EFA). 13.1.5 SRICOS-EFA Method for Maximum Scour Depth at Complex Piers 13.1.3 EFA A set of flume experiments was conducted to study the This EFA was developed in the early 1990s to obtain the maximum depth of scour for a pier including the effect of erosion function. A soil sample is retrieved from a bridge shallow water depth, the effect of rectangular shapes, the site using an ASTM standard, thin-wall steel tube (i.e., a effect of the angle of attack on rectangular shapes, and the

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112 effect of spacing between piers positioned in a row perpen- uncontracted channel after scour has occurred; VHEC (m/s) is dicularly to the flow. The proposed equation for the maxi- the mean depth water velocity at the location of the pier in mum depth of scour is in the form of the equation for the the contracted channel; c (N/m2) is the critical shear stress cylindrical pier in deep water with correction factors based of the soil; (kg/m3) is the mass density of water; g (m/s2) is on the results of the flume tests. the acceleration due to gravity; n is the Manning's Coeffi- cient (s/m1/3); and the K factors take the transition and the con- Zmax ( Pier ) in mm = K w Ksp Ksh (0.18 Re 0.635 ) tracted channel length into account. Note that the parenthe- sis in the equation is a factored difference between the Froude Where Zmax(Pier) is the maximum depth of pier scour in milli- Number and the critical Froude Number. Equations also are meters; Re is the Reynolds Number equal to VB/v, proposed for the uniform contraction scour depth as well as V (m/s) being the mean depth velocity at the location of the the location of the scour depths. pier if the bridge were not there; the K factors take into account the shallow water depth, spacing, shape, and angle of attack being considered through the use of the projected 13.1.8 SRICOS-EFA Method for Initial Contraction Scour Rate width B (m) in the calculation of the Reynolds Number. A set of numerical simulations was performed to study the 13.1.6 SRICOS-EFA Method maximum shear stress around the contraction of a channel for Initial Scour Rate at Complex Piers including the effects of the ratio of the contracted channel width over the approach channel width, the transition angle, A set of numerical simulations was performed to study the the water depth, and the contracted channel length. The pro- maximum shear stress around a pier including the effect of posed equation for the maximum shear stress is in the form shallow water depth, rectangular shapes, angle of attack on of the equation for the shear stress at the bottom of an open rectangular shapes, and spacing between piers positioned in and uncontracted channel with correction factors based on a row perpendicularly to the flow. The proposed equation for the results of the numerical simulations. the maximum shear stress is in the form of the equation for the cylindrical pier in deep water with correction factors based on the results of the numerical simulations. ( - max (Cont ) = kc - R kc - kc - H kc - L n 2 V 2 Rh 3 1 ) where max(Cont) (N/m2) is the maximum shear stress along max ( Pier ) = kw ksh ksp k 0.094 V 2 - 1 1 the centerline of the contracted channel; is the unit weight log Re 10 of water (kN/m3); n is the Manning's Coefficient (s/m1/3); V (m/s) is the upstream mean depth velocity; Rh (m) is the where max(Pier) (kN/m2) is the maximum shear stress around hydraulic radius defined as the cross-section area of the flow the pier; Re is the Reynolds Number equal to VB/v, V (m/s) divided by the wetted perimeter; and the k factors take the being the mean depth velocity at the location of the pier if the contraction ratio, the transition angle, the water depth effect, bridge were not there; B (m) is the pier diameter or pier and the contracted length into account. Equations also are width; (kg/m3) is the mass density of water; the k factors proposed for the location of the maximum shear stress. take the shallow water depth, pier shape, pier spacing, and attack angle into account. 13.1.9 SRICOS-EFA Method for Complex Pier Scour 13.1.7 SRICOS-EFA Method and Contraction Scour for Maximum Contraction Scour Depth in Cohesive Soils A set of flume experiments was conducted to study the Once the equations were established, the SRICOS-EFA depth of scour associated with the contraction of a channel Method was assembled. Care was taken not to simply add including the effects of the ratio of the contracted channel complex pier scour and contraction scour to get total pier width over the approach channel width, the contracted chan- scour. Instead, advantage was taken of the fact that at the end nel length, and the transition angle. The proposed equation of the maximum contraction scour, the velocity is at the crit- for the maximum depth of contraction scour is ical velocity and the maximum pier scour should be calcu- lated using the critical velocity of the soil and not the initial c 0.5 velocity in the contracted channel. In addition, the rules of 1.49VHEC accumulation due to the hydrograph and the multilayer sys- Zmax (Cont ) = K KL 1.90 H1 - 0 gH1 gnH11 3 tem developed for the simple pier scour method were adapted for the complex pier and contraction scour method. The Where Zmax(Cont) (m) is the maximum depth of contraction superposition and accumulation reasoning lead to the fol- scour; H1 (m) is the water depth along the center line of the lowing steps for the SRICOS-EFA Method for predicting the