# Rock riprap for protection of bridge abutments located at the flood plain.

Introduction

Bridge abutments commonly contract the free flow of water in the channel and flood plains through the bridge opening during high flows. During high flow events, the abutments are subject to strong erosive currents that are forced to pass through the bridge opening. These currents undermine the streambed at the toe of the abutments and beyond. This phenomenon, known as local scour at the abutments, in turn causes acceleration of flow deflected by the abutments. The development of a vortex system induced by the obstruction is the principal mechanism for the development of local scour. The strength of the vorticity generated by the deflection is related to the depth of flow, abutment depth and shape, alignment of the abutment with respect to the flow, size of bed material, rate of bed material transportation, and ice or drift accumulation.

Laboratory measurements indicate that average point velocities away from the abutment area are not influenced by the abutment's presence. Consequently, scour at abutments is considered a local phenomena that is not significantly related to the overall geometry of the flow. (1) [1]

A common method for protecting the stream bed from erosive currents is to place a rock riprap apron. To determine the size of rock riprap needed to prevent local scouring at abutments, it is necessary to study the stability of the rock as it is exposed to the erosive currents in the channel and flood plain.

This study was conducted at a hydraulic flume of the Federal Highway Administration TurnerFairbank Highway Research Center. Results of this study are presented in this article. Complete results of the study are presented elsewhere. (2,3)

Literature Review

Many researchers have developed equations based on average velocity that relate the critical conditions affecting stability. Isbash presented an equation that can be expressed as: (4)

[N.sub.sc] = [E.sup.2] * 2 (1)

where:

[N.sub.sc] = sediment number representing the ratio of approach flow inertial energy at critical conditions to the stabilizing potential created by the submerged rock weight. (5)

For loose stone lying on top of the fill, [N.sub.sc is expressed as:

[N.sub.sc]=[V.sup.2]/g*[D.sub.50]*(SG-1)] (2)

where:

V = flow velocity that will remove the loose stones m/s(ft/s)

[D.sub.50] = characteristic median rock size m(ft)

SG = Specific Gravity of the rock

g = gravitational acceleration 9.8m/[s.sub.2](32.2 ft/[s.sup.2])

E = 0.86 for loose stone lying on top of the fill

For stones deposited into flowing water that roll (due to the force of water acting over them) until they find a "seat" and a support, E = 1.2.

Rearranging equation 2 in terms of [D.sub.50] for E = 1.2, we obtain:

[D.sub.50] =0.347 * [V.sup.2]/(g*(SG-1) (3)

Equation (3) is a rearranged form of the Isbash equation.

Neill established a relation for "first displacement" of uniform graded gravel based on uniform parameters. (6) The following expresses conservative design curve: Mathematical Expression Omitted

where:

[D.sub.g] = characteristic rock size on the approach flow bed m(ft)

d = depth of the approach flow m(ft)

Parola conducted experiments using Neill's criteria for first displacement and found good agreement. (5) Figure 1 shows the sediment number curve, [N.sub.sc], based on Neill's and Parola's experiments for unobstructed flow--no obstruction to the free flow of water.

Pagan developed the following regression equation for an average sediment number design curve based on Neill's and Parola's experiments for undisturbed flow: (2) Mathematical Expression Omitted

Framework of Experiments

The parameters that characterize the disturbed flow are:

[V.sub.cc] = average velocity of the contracted flow at observed incipient motion of the rock at the contraction m(ft/s)

[d.sub.cc] = average depth of the contracted flow at observed incipient motion of rock at the contraction m(ft)

[W.sub.a] = width of the approach flow m(ft)

[W.sub.t-c] = width of the contraction m(ft)

[D.sub.50] = characteristic median rock size on the contraction flow bed m(ft)

AS = factor associated with the abutment shape

K = roughness of the bed upstream

[K.sub.s] = roughness of the bed surrounding the obstruction

g = gravitational acceleration 9.8 m/[s.sup.2] (32.2ft/[s.sup.2])

[rho] = fluid density 998.2 kg/[m.sup.3] (1.93 slugs/f[t.sup.3]) @20[degrees]C

[rho.sub.s] = rock density (kg//[m.sup.3] )

[Micro] = dynamic viscosity of fluid kg/m-s(slug/ft-s)

The effect of displacement due to leaching of fines through the armored apron of gravel in the observation area near the toe of the abutment and flood plain was not studied. The size of the bed material, [D.sub.50], in the obstructed area and the roughness in the vicinity of the obstruction, [K.sub.s], are dependent variables. For the purpose of the experiments, [K.sub.s] was assumed to be adequately represented by [D.sub.50].

The characteristic parameters can be arranged into a functional equation that describes the critical condition for the initial motion of the rock as follows:

0=f([W.sub.a' [W.sub.t-c'] [d.sub.cc'] [D.sub.50'] [V.sub.cc'] AS, K, G, [rho],[[rho.sub.s],[Micro] (6)

The parameter, g, must appear in combination with [rho] and [[rho.sub.s] as follows:

[gamma]=g*([[rho.sub.s]-[rho]) (7)

Combining equations (6) and (7)in nondimensional form yields the following: Mathematical Expression Omitted

where:

[N.sub.sc] is defined in equation (1)

[Nu]= [Micro]/[rho]

D = characteristic rock size (assumed to be adequately represented by [D.sub.50]).

Yalin stated that ([rho.sub.s]/[rho]) "can be important only with regard to the properties associated with the `ballistics' of an individual grain." (6)

In case of highly turbulent flows needed to cause the initial motion of the rock protection, the influence of the obstruction particle Reynolds number-the effect of viscosity relative to inertia, [V.sub.cc] *(D/[Nu]), was considered to be negligible because it was greater than [10.sup.3], which is well beyond the range that Shields and other researchers found to be no longer a factor.

Therefore, by applying the preceding considerations and confining the research to subcritical flow, the effect of ([rho.sub.s]/[rho]), and [[V.sub.cc] * (D/[Nu])] can be discounted. Thus, equation (8) can be reduced as follows: Mathematical Expression Omitted

By using the contracted velocity in [N.sub.sc], the effect of [d.sub.cc]/[W.sub.t-c'] [W.sub.a]/[W.sub.t-c'], and K are negligible. Thus, equation (9) reduces to: Mathematical Expression Omitted

Equation 10 provides the framework used to determine the stability of rock riprap to protect the toe of an abutment at the flood plain. The quantity [N.sub.sc] is defined in equation (1). The parameter [D.sub.50]/[d.sub.cc] represents the relative roughness of the contracted flow.

Experimental Model

Two small scaled abutment models, vertical-wail and spill-through, were used to study the impact of the abutments on time-averaged contraction velocities and the stability of gravel placed around the toe of the abutment and flood plain. The length of the abutment was varied to investigate the effect of the contraction to the flow on the flood plain. For the vertical-wall abutment model, the length ranged from 127 to 508 mm (5 to 20 in); for the spill-through abutment model, the length ranged from 635 to 1016 mm (25 to 40 in). The total width of the vertical-wall and spill-through abutment was 152.4 and 1168.4 mm (6 to 46 in), respectively. Flow depths ranged from 46.7 to 266.7 mm (1.84 to 10.5 in).

Observation Area

An observation area was defined in the hydraulic flume for each abutment model to visualize the failure of gravel for a given flow. These areas are illustrated in figures 2 and 3.

Gravel Placement

Two different sizes of gravel were used in the experiments: [D.sub.50]= 7.62 mm (0.30 in) and 10.2 mm (0.40 in). The gravel were angular particles that passed one sieve and were retained on the next standard size so they were intended to be uniform in size. The gravel was placed in the observation area to a depth of 38.1 mm (1.5 in)in three nonuniform layers. The intermediate layer was spraypainted red to help visualize the failure or motion of the upper gravel layer. Figures 4 and 5 illustrates a typical gravel setup for each abutment model. Gradation and layer thickness were not variables in these experiments.

Experimental Procedure

The experimental procedure for each run was as follows:

1. Discharge was set to a constant.

2. Tailgate was raised to develop a velocity past the observation section slightly below the expected incipient velocity of the rock riprap failure.

3. Tailgate was gradually lowered until a discernible patch of surface rock moved in the observation section. This was determined by looking for a visible section of the colored underlying layer of rock.

4. Flow and the tailgate setting were then held constant while a grid of depth and velocity measurements were taken. This generally took approximately one and a half hours. Very few additional particles moved during this data collection period; so, it was felt that longer run times would not have changed the results.

Experimental Results

Independent experiments were conducted with each abutment model to determine the vulnerable zone for the gravel failure within the observation area at different discharges and flow depths. An initial zone of failure thus was identified for each model.

Previous research have demonstrated that the scour hole pattern in an unprotected channel and flood plain being obstructed by either a vertical-wall or spill-through abutment normal to the flow occurs at the upstream corner of the abutment. (7) Pagan demonstrated that the failure zone in an armored flood plain surrounding the abutment normal to the flow is a function of the abutment shape. (2,3)

For the vertical-wall abutment model the initial failure zone was consistently observed at the upstream corner of the abutment in the armored flood plain (figure 6). The zone then expands downstream toward the abutment and away from it with time and increase in discharge.

For the spill-through abutment model, the initial failure zone was consistently observed at the downstream radius of the model just away from its toe (figure 7). The zone then expands downstream and upstream toward the toe of the abutment and away from it into the flood plain with time and increase in discharge.

Velocity-Based Criteria

Three equally spaced average point velocities were measured within the contraction zone. For the smooth bed experiments (no gravel placed within the observation area)it was learned that the readings of average point velocities near the face of the abutment parallel to the flow were severely affected by the flow turbulence. Consequently, low velocity readings were measured near the face of the abutment. The same result was obtained in the obstructed flow experiments (free flow of water obstructed by an abutment) with gravel placed in the observation area. However, the gravel was failing at the upstream corner of the vertical-wail abutment (figure 6) and downstream near the toe for the spill-through abutment (figure 7). Thus, although the flow turbulence affected the velocity readings near the abutment models, that velocity has to be much higher than those measured during the experiments to cause the initial motion of the gravel near the toe of the abutment models.

Vertical-Wall Abutment

The vulnerable zone for incipient motion for this abutment model was observed at the upstream corner of the abutment (figure 6). The separation of flow created by the contraction of the abutment caused a strong turbulence, particularly for deeper flows. With the flow depth and velocity at the approach and for a computed discharge representing the design discharge, the velocity and flow depth were computed at the contraction of the abutment in the flood plain using Bernoulli's energy equation without elevation terms (11) and Continuity equation (12). The energy equation is as follows: Mathematical Expression Omitted

where:

[V.sub.am] = measured average point velocity at the approach m (ft/s)

[d.sub.a] = measured average depth at the approach m (ft)

[V.sub.cc] = computed average point velocity at the contraction for disturbed flow m/s (ft/s)

[d.sub.cc] = computed average depth at the contraction for obstructed flow m (ft)

[h.sub.L]= energy losses (assumed to be negligible) m(ft)

g = gravitational acceleration 9.8 m/[s.sup.2](32.2 ft/[s.sup.2])

The Continuity equation is as follows:

[Q.sub.cc] = [V.sub.cc] * [W.sub.t-c]*[d.sub.cc] (12)

where:

[Q.sub.cc] = computed discharge (cfs)

[W.sub.t-c]= horizontal distance (ft) from the toe of the abutment to the channel boundary as shown in figures 6 and 7

Using equation (2), the sediment number, [N.sub.sc], was computed for [V.sub.cc]. The values of [N.sub.sc] were plotted against the [D.sub.50]/[d.sub.cc] ratio. Figure 8 shows a plot of the individual computed sediment number curve for the vertical-wall abutment model for [D.sub.50] = 7.62 mm (0.30 in) and 10.16 mm (0.40 in) for obstructed flow.

This figure also shows that the curves for the two gravel sizes, which were derived by regression, were close to one curve and almost parallel to the unobstructed flow curve (figure 1 ). The velocity, [V.sub.cc], is the computed average contracted velocity within the flood plain for the obstructed flow, but observed failure is for any discernible area of particular movement in that opening.

Figure 9 shows the combined sediment number curve for the two gravel sizes. This plot reveals that the slope of the combined curve follows that of the unobstructed flow curve. For the gravel to fail at the toe of the abutment upstream of the constriction, the local effective velocity must have been close to that that would have caused failure for the unobstructed flow curve.

Flow at the upstream corner of the abutment where the initial failure of rock riprap occured was highly rotational and was difficult to quantify with the electromagnetic probe sensor, the instrumentation available for this study. The so called "local effective velocity" is defined as the velocity that would have moved the rock in unobstructed flow.

To determine the stable size of rock riprap, equation (2) should be rearranged as follows: Mathematical Expression Omitted

where:

[V.sub.cc] = computed average velocity at the contraction within the flood plain m/s (ft/s)

By regression analysis of the combined sediment number curve (figure 9), [N.sub.sc] is obtained as: Mathematical Expression Omitted

Substituting equation (14)into equation (13) yields: Mathematical Expression Omitted

Although equation (15)is not dimensionless as written, it is dimensionally homogeneous--i.e., can be reduced to the same units on both sides. It can be used with either the International System of units (SI) or English units as long as consistent units are used in all of the terms.

Figure 10 presents a plot of [V.sub.cp] /[V.sub.cc] versus [X,sub.t]/[W.sub.t-c] The velocity ratio, [V.sub.cp] /[V.sub.cc], represents the effective computed local velocity (near the abutment face at which the rock failed) to the computed average contracted velocity in the flood plain within the contraction.

The ratio of [V.sub.cp] /[V.sub.cc] also represents the indirect method--or "simple multiplier"--that should be applied to the computed average contracted velocity in the contraction within the flood plain to obtain the velocity near the abutment face that caused the gravel's incipient motion.

[V.sub.cp] is the computed average point velocity at the contraction for undisturbed flow, in fids. [V.sub.cc] is the average computed point velocity at various distances, [X.sub.t], from the toe of the abutment for disturbed flow. [W.sub.t-c] is the horizontal distance from the toe of the abutment to the channel boundary, in m (ft). Both [X.sub.t] and [W.sub.t-c] are shown in figures 6 and 7.

At [X.sub.t ]/[W.sub.t-c]=0, and for 95 percent of the of the computations, the ratio, [V.sub.cp] /[V.sub.cc] fell near 2.0. At [X.sub.t ]/[W.sub.t-c] =0, and for 5 percent of the computations, the ratio reached 2.304.

The local effective velocity had no resemblance to what actually occurred around the abutment, but it was a convenient parameter to use in developing a simple multiplier ( [V.sub.cp] /[V.sub.cc]= 2.0) for the velocity term in the rearranged Isbash equation [equation (3)]. The velocity term within equation (3) can be multiplied by 2.0 to compute the rock riprap size for the vertical-wall abutment model.

The discharge was increased 1.7 times the discharge that caused the incipient motion of the gravel to observe the extent of the failure zone. The multiplier, 1.7, is suggested to approximate [Q.sub.500] from [Q.sub.100](8) This demonstrated that the rock riprap apron should be extended along the entire length of the abutment, both upstream and downstream, and to the parallel face of the abutment to the flow.

Figure 10 also illustrates that the velocity amplification decays rapidly with distance from the toe of the abutment and that the effect of the abutment occurs in a small portion of the contracted area. Therefore, it would be reasonable to limit the rock riprap apron to a relative small portion of the constriction. However, additional data analysis needs to be made to determine the extent of the rock riprap apron.

Spill-through Abutment

The observed vulnerable zone for incipient motion for this model was observed downstream of the contraction near the toe of the abutment (figure 7). The acceleration of flow through the slope of the spill face of the abutment parallel to the flow and the turbulence developed at the most contracted section of a stream jet are believed to have influenced the gravel failure at the mentioned zone. With the flow depth and velocity measured at the approach and for a computed discharge at the approach representing the design discharge, the velocity and flow depth were also computed at the contracted zone in the flood plain using equations (11) and (12). Using equation (2), the sediment number, [N.sub.sc], was computed with [V.sub.cc]. The values of [N.sub.sc] were plotted versus the [D.sub.50]/[d.sub.cc]ratio. Figure 11 shows a plot of the individual computed sediment numbers curve for the spill-through abutment for [D.sub.50] = 7.62 mm (0.30 in) and 10.16 mm (0.40 in)for obstructed flow.

Because of the adverse slope obtained by regression analysis and the insufficient data at [D.sub.50]/ [d.sub.cc] ratio smaller than 0.03, an average [N.sub.sc] of 2.09 and 1.67 was taken for [D.sub.50] = 7.62 mm (0.30 in) and 10.16 mm (0.40 in), respectively. A combined sediment number curve was obtained by averaging all the computed [N.sub.sc] values for the two gravel sizes used during the experiments (figure 12). As a result, the average value of [N.sub.sc] was found to be 1.87.

Although the scatter of data on the vertical wall and spill-through experiments is similar, the effect of [D.sub.50]/[d.sub.cc] was found to be less significant for the spill-through abutment.

Figure 12 also indicates that for the spill-through model, depth is an important factor in determining the stability of the rock riprap when compared to the unobstructed flow curve. This figure also indicates that for the spill-through abutment, the velocity that caused the incipient motion of the gravel in the flood plain near the toe of the abut* ment should have been at least that for the unobstructed flow.

Therefore, to determine the stable size of rock riprap, equation (2) should be used as follows: Mathematical Expression Omitted

Figure 13 presents a plot of [V.sub.cp]/[V.sub.cc]versus [X.sub.t]/[W.sub.t-c] The velocity ratio, [V.sub.cp]/[V.sub.cc'], and [V.sub.cc'][V.sub.cp'][X.sub.t] and [W.sub.t-c] remain as previously defined. The plot shows that the effect of the abutment diminishes quickly with distance from the abutment.

At [X.sub.t]/[W.sub.t-c] =0, and for 97 percent of the computations, the ratio of [V.sub.cp]/[V.sub.cc fell near 2.0. At [X.sub.t]/[W.sub.t-c= 0, and for 3 percent of the computations, the ratio of [V.sub.cp]/[V.sub.cc reached 2.135.

The ratio of [V.sub.cp]/[V.sub.cc] also represents the indirect method--or "simple multiplier"--that should be applied to the averaged computed contracted velocity in the contraction within the flood plain to obtain the velocity near the abutment face that caused the incipient motion of the gravel.

The local effective velocity had no resemblance to what actually occured around the abutment, but it was a convenient parameter to use in developing a simple multiplier ( [V.sub.cp]/[V.sub.cc] = 2.0) for the velocity term in the rearranged Isbash equation (equation 3). Similarly to vertical-wall abutment, the velocity term within equation (3) can be multiplied by 2.0 to compute the rock riprap size for the spill-through abutment.

As with the other model, the discharge was also increased by 1.7 times the discharge that caused the incipient motion of the gravel to observe the extent of the failure zone. (8) This demonstrated that the rock riprap apron should be extended along the entire length of the abutment, both upstream and downstream, and to the parallel face of the abutment to the flow.

Figure 13 also illustrates that the velocity amplification decays rapidly with distance from the toe of the abutment and that the effect of the abutment occurs in a small portion of the contracted area. Therefore, as with the vertical-wall abutment, it would be reasonable to limit the rock riprap apron to a relative small portion of the constriction. Again, however, additional data analysis is needed to determine the extent of the rock riprap apron for this model.

Conclusions

The location for the most critical failure zone on an abutment encroaching the free flow of water on an armored flood plain depends on the abutment shape. For the vertical-wall abutment model, the critical failure zone occurs at the upstream corner of the abutment and expands downstream towards the abutment and away from the toe with time and increase in discharge. For the spill-through abutment model, the critical failure zone is located downstream of the contraction near the toe and "grows" downstream and upstream of the constriction expanding to the toe and away from the abutment.

The turbulence of flow and vorticity generated near the face of the abutment are the causes of rock riprap failure. The velocities diminish in intensity and stabilize as distance from the toe of the abutment increases.

Equation (15) can be used to determine a stable rock riprap size to protect the toe of the verticalwall abutment. Equation (16)can be used for spill-through abutment. (Note that use of these equations are limited to abutments encroachments up to 28 percent onto the flood plain for vertical-wall abutment shapes and 56 percent for spill-through abutment shapes--without counting the dimension of the main channel.)

The recommended rock riprap thickness should be equivalent to two times [D.sub.50]. The average velocity in the flood plain within the constricted section should be used in equations (15) and (16).

The velocity multipliers found in this research for the vertical-wall and spill-through abutments, respectively, can be applied to the velocity term in the rearranged Isbash equation (equation 3) for sizing a stable rock riprap size for abutment protection.

Further data analysis is needed to determine the extension of the rock riprap apron for both vertical-wall and spill-through abutments.

Further research is needed to investigate the effect of:

* A greater encroachment onto the flood plain on the stability of the rock riprap.

* The abutments in a skew to the flow.

* The main channel in the stability of the rock riprap.

References

(1) H.K. Liu, F.M. Chang, M.M. Skinner. "Effect of Bridge Constriction on Scour and Backwater," Colorado State University, Fort Collins, CO, February 1961.

(2) Jorge E. Pagan-Ortiz. "Stability of Rock Riprap for Protection at the Toe of Abutments Located at the Flood Plain." Publication No. FHWA-RD-91-057, Federal Highway Administration, September 1991.

(3) Jorge E. Pagan-Ortiz. "Stability of Rock Riprap for Protection at the Toe of Abutments Located at the Flood Plain," masters thesis, The George Washington University, Washington, DC, December 1990.

(4) S.V. Isbash. "Construction of Dams by Depositing Rock in Running Water," Communication No. 3, Second Congress on Large Dams, Washington, DC, 1936.

(5) Arthur Parola, Jr. "The Stability of Riprap Used to Protect Bridge Piers," doctoral dissertation, State College, Pennsylvania State University, May 1990.

(6) Charles R. Neill and M. Selim Yalin. "Quantitative Definition of Beginning of Bed Movement," Journal of the Hydraulics Division, Proceedings of the American Society of Civil Engineers, Volume 95, No. HY1, January 1969.

(7) Scour Around Bridges, Research Report No, 13-B, Highway Research Board, Washington, DC, 1951.

(8) E.V. Richardson, Lawrence J. Harrison, and Stanley R. Davis. "Evaluating Scour at Bridges," Hydraulic Engineering Circular No. 18, Federal Highway Administration, Washington, DC, February 1991. List of figures

Jorge E. Pagan-Ortiz is a hydraulic engineer, Federal Highway Administration, Bridge Division, Hydraulics and Geotechnical Branch. He has presented FHWA guidelines and related microcomputer software in Latin America and is a member of the Pan American Institute of Highways. Mr. Pagan-Ortiz's received a masters degree in Civil Engineering with concentration in Water Resources Engineering. His thesis involved the determination of stability of rock riprap for the protection at the toe of abutments located in flood plains.

1 Italic numbers in parentheses indentify refrences on pages 30-31

Bridge abutments commonly contract the free flow of water in the channel and flood plains through the bridge opening during high flows. During high flow events, the abutments are subject to strong erosive currents that are forced to pass through the bridge opening. These currents undermine the streambed at the toe of the abutments and beyond. This phenomenon, known as local scour at the abutments, in turn causes acceleration of flow deflected by the abutments. The development of a vortex system induced by the obstruction is the principal mechanism for the development of local scour. The strength of the vorticity generated by the deflection is related to the depth of flow, abutment depth and shape, alignment of the abutment with respect to the flow, size of bed material, rate of bed material transportation, and ice or drift accumulation.

Laboratory measurements indicate that average point velocities away from the abutment area are not influenced by the abutment's presence. Consequently, scour at abutments is considered a local phenomena that is not significantly related to the overall geometry of the flow. (1) [1]

A common method for protecting the stream bed from erosive currents is to place a rock riprap apron. To determine the size of rock riprap needed to prevent local scouring at abutments, it is necessary to study the stability of the rock as it is exposed to the erosive currents in the channel and flood plain.

This study was conducted at a hydraulic flume of the Federal Highway Administration TurnerFairbank Highway Research Center. Results of this study are presented in this article. Complete results of the study are presented elsewhere. (2,3)

Literature Review

Many researchers have developed equations based on average velocity that relate the critical conditions affecting stability. Isbash presented an equation that can be expressed as: (4)

[N.sub.sc] = [E.sup.2] * 2 (1)

where:

[N.sub.sc] = sediment number representing the ratio of approach flow inertial energy at critical conditions to the stabilizing potential created by the submerged rock weight. (5)

For loose stone lying on top of the fill, [N.sub.sc is expressed as:

[N.sub.sc]=[V.sup.2]/g*[D.sub.50]*(SG-1)] (2)

where:

V = flow velocity that will remove the loose stones m/s(ft/s)

[D.sub.50] = characteristic median rock size m(ft)

SG = Specific Gravity of the rock

g = gravitational acceleration 9.8m/[s.sub.2](32.2 ft/[s.sup.2])

E = 0.86 for loose stone lying on top of the fill

For stones deposited into flowing water that roll (due to the force of water acting over them) until they find a "seat" and a support, E = 1.2.

Rearranging equation 2 in terms of [D.sub.50] for E = 1.2, we obtain:

[D.sub.50] =0.347 * [V.sup.2]/(g*(SG-1) (3)

Equation (3) is a rearranged form of the Isbash equation.

Neill established a relation for "first displacement" of uniform graded gravel based on uniform parameters. (6) The following expresses conservative design curve: Mathematical Expression Omitted

where:

[D.sub.g] = characteristic rock size on the approach flow bed m(ft)

d = depth of the approach flow m(ft)

Parola conducted experiments using Neill's criteria for first displacement and found good agreement. (5) Figure 1 shows the sediment number curve, [N.sub.sc], based on Neill's and Parola's experiments for unobstructed flow--no obstruction to the free flow of water.

Pagan developed the following regression equation for an average sediment number design curve based on Neill's and Parola's experiments for undisturbed flow: (2) Mathematical Expression Omitted

Framework of Experiments

The parameters that characterize the disturbed flow are:

[V.sub.cc] = average velocity of the contracted flow at observed incipient motion of the rock at the contraction m(ft/s)

[d.sub.cc] = average depth of the contracted flow at observed incipient motion of rock at the contraction m(ft)

[W.sub.a] = width of the approach flow m(ft)

[W.sub.t-c] = width of the contraction m(ft)

[D.sub.50] = characteristic median rock size on the contraction flow bed m(ft)

AS = factor associated with the abutment shape

K = roughness of the bed upstream

[K.sub.s] = roughness of the bed surrounding the obstruction

g = gravitational acceleration 9.8 m/[s.sup.2] (32.2ft/[s.sup.2])

[rho] = fluid density 998.2 kg/[m.sup.3] (1.93 slugs/f[t.sup.3]) @20[degrees]C

[rho.sub.s] = rock density (kg//[m.sup.3] )

[Micro] = dynamic viscosity of fluid kg/m-s(slug/ft-s)

The effect of displacement due to leaching of fines through the armored apron of gravel in the observation area near the toe of the abutment and flood plain was not studied. The size of the bed material, [D.sub.50], in the obstructed area and the roughness in the vicinity of the obstruction, [K.sub.s], are dependent variables. For the purpose of the experiments, [K.sub.s] was assumed to be adequately represented by [D.sub.50].

The characteristic parameters can be arranged into a functional equation that describes the critical condition for the initial motion of the rock as follows:

0=f([W.sub.a' [W.sub.t-c'] [d.sub.cc'] [D.sub.50'] [V.sub.cc'] AS, K, G, [rho],[[rho.sub.s],[Micro] (6)

The parameter, g, must appear in combination with [rho] and [[rho.sub.s] as follows:

[gamma]=g*([[rho.sub.s]-[rho]) (7)

Combining equations (6) and (7)in nondimensional form yields the following: Mathematical Expression Omitted

where:

[N.sub.sc] is defined in equation (1)

[Nu]= [Micro]/[rho]

D = characteristic rock size (assumed to be adequately represented by [D.sub.50]).

Yalin stated that ([rho.sub.s]/[rho]) "can be important only with regard to the properties associated with the `ballistics' of an individual grain." (6)

In case of highly turbulent flows needed to cause the initial motion of the rock protection, the influence of the obstruction particle Reynolds number-the effect of viscosity relative to inertia, [V.sub.cc] *(D/[Nu]), was considered to be negligible because it was greater than [10.sup.3], which is well beyond the range that Shields and other researchers found to be no longer a factor.

Therefore, by applying the preceding considerations and confining the research to subcritical flow, the effect of ([rho.sub.s]/[rho]), and [[V.sub.cc] * (D/[Nu])] can be discounted. Thus, equation (8) can be reduced as follows: Mathematical Expression Omitted

By using the contracted velocity in [N.sub.sc], the effect of [d.sub.cc]/[W.sub.t-c'] [W.sub.a]/[W.sub.t-c'], and K are negligible. Thus, equation (9) reduces to: Mathematical Expression Omitted

Equation 10 provides the framework used to determine the stability of rock riprap to protect the toe of an abutment at the flood plain. The quantity [N.sub.sc] is defined in equation (1). The parameter [D.sub.50]/[d.sub.cc] represents the relative roughness of the contracted flow.

Experimental Model

Two small scaled abutment models, vertical-wail and spill-through, were used to study the impact of the abutments on time-averaged contraction velocities and the stability of gravel placed around the toe of the abutment and flood plain. The length of the abutment was varied to investigate the effect of the contraction to the flow on the flood plain. For the vertical-wall abutment model, the length ranged from 127 to 508 mm (5 to 20 in); for the spill-through abutment model, the length ranged from 635 to 1016 mm (25 to 40 in). The total width of the vertical-wall and spill-through abutment was 152.4 and 1168.4 mm (6 to 46 in), respectively. Flow depths ranged from 46.7 to 266.7 mm (1.84 to 10.5 in).

Observation Area

An observation area was defined in the hydraulic flume for each abutment model to visualize the failure of gravel for a given flow. These areas are illustrated in figures 2 and 3.

Gravel Placement

Two different sizes of gravel were used in the experiments: [D.sub.50]= 7.62 mm (0.30 in) and 10.2 mm (0.40 in). The gravel were angular particles that passed one sieve and were retained on the next standard size so they were intended to be uniform in size. The gravel was placed in the observation area to a depth of 38.1 mm (1.5 in)in three nonuniform layers. The intermediate layer was spraypainted red to help visualize the failure or motion of the upper gravel layer. Figures 4 and 5 illustrates a typical gravel setup for each abutment model. Gradation and layer thickness were not variables in these experiments.

Experimental Procedure

The experimental procedure for each run was as follows:

1. Discharge was set to a constant.

2. Tailgate was raised to develop a velocity past the observation section slightly below the expected incipient velocity of the rock riprap failure.

3. Tailgate was gradually lowered until a discernible patch of surface rock moved in the observation section. This was determined by looking for a visible section of the colored underlying layer of rock.

4. Flow and the tailgate setting were then held constant while a grid of depth and velocity measurements were taken. This generally took approximately one and a half hours. Very few additional particles moved during this data collection period; so, it was felt that longer run times would not have changed the results.

Experimental Results

Independent experiments were conducted with each abutment model to determine the vulnerable zone for the gravel failure within the observation area at different discharges and flow depths. An initial zone of failure thus was identified for each model.

Previous research have demonstrated that the scour hole pattern in an unprotected channel and flood plain being obstructed by either a vertical-wall or spill-through abutment normal to the flow occurs at the upstream corner of the abutment. (7) Pagan demonstrated that the failure zone in an armored flood plain surrounding the abutment normal to the flow is a function of the abutment shape. (2,3)

For the vertical-wall abutment model the initial failure zone was consistently observed at the upstream corner of the abutment in the armored flood plain (figure 6). The zone then expands downstream toward the abutment and away from it with time and increase in discharge.

For the spill-through abutment model, the initial failure zone was consistently observed at the downstream radius of the model just away from its toe (figure 7). The zone then expands downstream and upstream toward the toe of the abutment and away from it into the flood plain with time and increase in discharge.

Velocity-Based Criteria

Three equally spaced average point velocities were measured within the contraction zone. For the smooth bed experiments (no gravel placed within the observation area)it was learned that the readings of average point velocities near the face of the abutment parallel to the flow were severely affected by the flow turbulence. Consequently, low velocity readings were measured near the face of the abutment. The same result was obtained in the obstructed flow experiments (free flow of water obstructed by an abutment) with gravel placed in the observation area. However, the gravel was failing at the upstream corner of the vertical-wail abutment (figure 6) and downstream near the toe for the spill-through abutment (figure 7). Thus, although the flow turbulence affected the velocity readings near the abutment models, that velocity has to be much higher than those measured during the experiments to cause the initial motion of the gravel near the toe of the abutment models.

Vertical-Wall Abutment

The vulnerable zone for incipient motion for this abutment model was observed at the upstream corner of the abutment (figure 6). The separation of flow created by the contraction of the abutment caused a strong turbulence, particularly for deeper flows. With the flow depth and velocity at the approach and for a computed discharge representing the design discharge, the velocity and flow depth were computed at the contraction of the abutment in the flood plain using Bernoulli's energy equation without elevation terms (11) and Continuity equation (12). The energy equation is as follows: Mathematical Expression Omitted

where:

[V.sub.am] = measured average point velocity at the approach m (ft/s)

[d.sub.a] = measured average depth at the approach m (ft)

[V.sub.cc] = computed average point velocity at the contraction for disturbed flow m/s (ft/s)

[d.sub.cc] = computed average depth at the contraction for obstructed flow m (ft)

[h.sub.L]= energy losses (assumed to be negligible) m(ft)

g = gravitational acceleration 9.8 m/[s.sup.2](32.2 ft/[s.sup.2])

The Continuity equation is as follows:

[Q.sub.cc] = [V.sub.cc] * [W.sub.t-c]*[d.sub.cc] (12)

where:

[Q.sub.cc] = computed discharge (cfs)

[W.sub.t-c]= horizontal distance (ft) from the toe of the abutment to the channel boundary as shown in figures 6 and 7

Using equation (2), the sediment number, [N.sub.sc], was computed for [V.sub.cc]. The values of [N.sub.sc] were plotted against the [D.sub.50]/[d.sub.cc] ratio. Figure 8 shows a plot of the individual computed sediment number curve for the vertical-wall abutment model for [D.sub.50] = 7.62 mm (0.30 in) and 10.16 mm (0.40 in) for obstructed flow.

This figure also shows that the curves for the two gravel sizes, which were derived by regression, were close to one curve and almost parallel to the unobstructed flow curve (figure 1 ). The velocity, [V.sub.cc], is the computed average contracted velocity within the flood plain for the obstructed flow, but observed failure is for any discernible area of particular movement in that opening.

Figure 9 shows the combined sediment number curve for the two gravel sizes. This plot reveals that the slope of the combined curve follows that of the unobstructed flow curve. For the gravel to fail at the toe of the abutment upstream of the constriction, the local effective velocity must have been close to that that would have caused failure for the unobstructed flow curve.

Flow at the upstream corner of the abutment where the initial failure of rock riprap occured was highly rotational and was difficult to quantify with the electromagnetic probe sensor, the instrumentation available for this study. The so called "local effective velocity" is defined as the velocity that would have moved the rock in unobstructed flow.

To determine the stable size of rock riprap, equation (2) should be rearranged as follows: Mathematical Expression Omitted

where:

[V.sub.cc] = computed average velocity at the contraction within the flood plain m/s (ft/s)

By regression analysis of the combined sediment number curve (figure 9), [N.sub.sc] is obtained as: Mathematical Expression Omitted

Substituting equation (14)into equation (13) yields: Mathematical Expression Omitted

Although equation (15)is not dimensionless as written, it is dimensionally homogeneous--i.e., can be reduced to the same units on both sides. It can be used with either the International System of units (SI) or English units as long as consistent units are used in all of the terms.

Figure 10 presents a plot of [V.sub.cp] /[V.sub.cc] versus [X,sub.t]/[W.sub.t-c] The velocity ratio, [V.sub.cp] /[V.sub.cc], represents the effective computed local velocity (near the abutment face at which the rock failed) to the computed average contracted velocity in the flood plain within the contraction.

The ratio of [V.sub.cp] /[V.sub.cc] also represents the indirect method--or "simple multiplier"--that should be applied to the computed average contracted velocity in the contraction within the flood plain to obtain the velocity near the abutment face that caused the gravel's incipient motion.

[V.sub.cp] is the computed average point velocity at the contraction for undisturbed flow, in fids. [V.sub.cc] is the average computed point velocity at various distances, [X.sub.t], from the toe of the abutment for disturbed flow. [W.sub.t-c] is the horizontal distance from the toe of the abutment to the channel boundary, in m (ft). Both [X.sub.t] and [W.sub.t-c] are shown in figures 6 and 7.

At [X.sub.t ]/[W.sub.t-c]=0, and for 95 percent of the of the computations, the ratio, [V.sub.cp] /[V.sub.cc] fell near 2.0. At [X.sub.t ]/[W.sub.t-c] =0, and for 5 percent of the computations, the ratio reached 2.304.

The local effective velocity had no resemblance to what actually occurred around the abutment, but it was a convenient parameter to use in developing a simple multiplier ( [V.sub.cp] /[V.sub.cc]= 2.0) for the velocity term in the rearranged Isbash equation [equation (3)]. The velocity term within equation (3) can be multiplied by 2.0 to compute the rock riprap size for the vertical-wall abutment model.

The discharge was increased 1.7 times the discharge that caused the incipient motion of the gravel to observe the extent of the failure zone. The multiplier, 1.7, is suggested to approximate [Q.sub.500] from [Q.sub.100](8) This demonstrated that the rock riprap apron should be extended along the entire length of the abutment, both upstream and downstream, and to the parallel face of the abutment to the flow.

Figure 10 also illustrates that the velocity amplification decays rapidly with distance from the toe of the abutment and that the effect of the abutment occurs in a small portion of the contracted area. Therefore, it would be reasonable to limit the rock riprap apron to a relative small portion of the constriction. However, additional data analysis needs to be made to determine the extent of the rock riprap apron.

Spill-through Abutment

The observed vulnerable zone for incipient motion for this model was observed downstream of the contraction near the toe of the abutment (figure 7). The acceleration of flow through the slope of the spill face of the abutment parallel to the flow and the turbulence developed at the most contracted section of a stream jet are believed to have influenced the gravel failure at the mentioned zone. With the flow depth and velocity measured at the approach and for a computed discharge at the approach representing the design discharge, the velocity and flow depth were also computed at the contracted zone in the flood plain using equations (11) and (12). Using equation (2), the sediment number, [N.sub.sc], was computed with [V.sub.cc]. The values of [N.sub.sc] were plotted versus the [D.sub.50]/[d.sub.cc]ratio. Figure 11 shows a plot of the individual computed sediment numbers curve for the spill-through abutment for [D.sub.50] = 7.62 mm (0.30 in) and 10.16 mm (0.40 in)for obstructed flow.

Because of the adverse slope obtained by regression analysis and the insufficient data at [D.sub.50]/ [d.sub.cc] ratio smaller than 0.03, an average [N.sub.sc] of 2.09 and 1.67 was taken for [D.sub.50] = 7.62 mm (0.30 in) and 10.16 mm (0.40 in), respectively. A combined sediment number curve was obtained by averaging all the computed [N.sub.sc] values for the two gravel sizes used during the experiments (figure 12). As a result, the average value of [N.sub.sc] was found to be 1.87.

Although the scatter of data on the vertical wall and spill-through experiments is similar, the effect of [D.sub.50]/[d.sub.cc] was found to be less significant for the spill-through abutment.

Figure 12 also indicates that for the spill-through model, depth is an important factor in determining the stability of the rock riprap when compared to the unobstructed flow curve. This figure also indicates that for the spill-through abutment, the velocity that caused the incipient motion of the gravel in the flood plain near the toe of the abut* ment should have been at least that for the unobstructed flow.

Therefore, to determine the stable size of rock riprap, equation (2) should be used as follows: Mathematical Expression Omitted

Figure 13 presents a plot of [V.sub.cp]/[V.sub.cc]versus [X.sub.t]/[W.sub.t-c] The velocity ratio, [V.sub.cp]/[V.sub.cc'], and [V.sub.cc'][V.sub.cp'][X.sub.t] and [W.sub.t-c] remain as previously defined. The plot shows that the effect of the abutment diminishes quickly with distance from the abutment.

At [X.sub.t]/[W.sub.t-c] =0, and for 97 percent of the computations, the ratio of [V.sub.cp]/[V.sub.cc fell near 2.0. At [X.sub.t]/[W.sub.t-c= 0, and for 3 percent of the computations, the ratio of [V.sub.cp]/[V.sub.cc reached 2.135.

The ratio of [V.sub.cp]/[V.sub.cc] also represents the indirect method--or "simple multiplier"--that should be applied to the averaged computed contracted velocity in the contraction within the flood plain to obtain the velocity near the abutment face that caused the incipient motion of the gravel.

The local effective velocity had no resemblance to what actually occured around the abutment, but it was a convenient parameter to use in developing a simple multiplier ( [V.sub.cp]/[V.sub.cc] = 2.0) for the velocity term in the rearranged Isbash equation (equation 3). Similarly to vertical-wall abutment, the velocity term within equation (3) can be multiplied by 2.0 to compute the rock riprap size for the spill-through abutment.

As with the other model, the discharge was also increased by 1.7 times the discharge that caused the incipient motion of the gravel to observe the extent of the failure zone. (8) This demonstrated that the rock riprap apron should be extended along the entire length of the abutment, both upstream and downstream, and to the parallel face of the abutment to the flow.

Figure 13 also illustrates that the velocity amplification decays rapidly with distance from the toe of the abutment and that the effect of the abutment occurs in a small portion of the contracted area. Therefore, as with the vertical-wall abutment, it would be reasonable to limit the rock riprap apron to a relative small portion of the constriction. Again, however, additional data analysis is needed to determine the extent of the rock riprap apron for this model.

Conclusions

The location for the most critical failure zone on an abutment encroaching the free flow of water on an armored flood plain depends on the abutment shape. For the vertical-wall abutment model, the critical failure zone occurs at the upstream corner of the abutment and expands downstream towards the abutment and away from the toe with time and increase in discharge. For the spill-through abutment model, the critical failure zone is located downstream of the contraction near the toe and "grows" downstream and upstream of the constriction expanding to the toe and away from the abutment.

The turbulence of flow and vorticity generated near the face of the abutment are the causes of rock riprap failure. The velocities diminish in intensity and stabilize as distance from the toe of the abutment increases.

Equation (15) can be used to determine a stable rock riprap size to protect the toe of the verticalwall abutment. Equation (16)can be used for spill-through abutment. (Note that use of these equations are limited to abutments encroachments up to 28 percent onto the flood plain for vertical-wall abutment shapes and 56 percent for spill-through abutment shapes--without counting the dimension of the main channel.)

The recommended rock riprap thickness should be equivalent to two times [D.sub.50]. The average velocity in the flood plain within the constricted section should be used in equations (15) and (16).

The velocity multipliers found in this research for the vertical-wall and spill-through abutments, respectively, can be applied to the velocity term in the rearranged Isbash equation (equation 3) for sizing a stable rock riprap size for abutment protection.

Further data analysis is needed to determine the extension of the rock riprap apron for both vertical-wall and spill-through abutments.

Further research is needed to investigate the effect of:

* A greater encroachment onto the flood plain on the stability of the rock riprap.

* The abutments in a skew to the flow.

* The main channel in the stability of the rock riprap.

References

(1) H.K. Liu, F.M. Chang, M.M. Skinner. "Effect of Bridge Constriction on Scour and Backwater," Colorado State University, Fort Collins, CO, February 1961.

(2) Jorge E. Pagan-Ortiz. "Stability of Rock Riprap for Protection at the Toe of Abutments Located at the Flood Plain." Publication No. FHWA-RD-91-057, Federal Highway Administration, September 1991.

(3) Jorge E. Pagan-Ortiz. "Stability of Rock Riprap for Protection at the Toe of Abutments Located at the Flood Plain," masters thesis, The George Washington University, Washington, DC, December 1990.

(4) S.V. Isbash. "Construction of Dams by Depositing Rock in Running Water," Communication No. 3, Second Congress on Large Dams, Washington, DC, 1936.

(5) Arthur Parola, Jr. "The Stability of Riprap Used to Protect Bridge Piers," doctoral dissertation, State College, Pennsylvania State University, May 1990.

(6) Charles R. Neill and M. Selim Yalin. "Quantitative Definition of Beginning of Bed Movement," Journal of the Hydraulics Division, Proceedings of the American Society of Civil Engineers, Volume 95, No. HY1, January 1969.

(7) Scour Around Bridges, Research Report No, 13-B, Highway Research Board, Washington, DC, 1951.

(8) E.V. Richardson, Lawrence J. Harrison, and Stanley R. Davis. "Evaluating Scour at Bridges," Hydraulic Engineering Circular No. 18, Federal Highway Administration, Washington, DC, February 1991. List of figures

Jorge E. Pagan-Ortiz is a hydraulic engineer, Federal Highway Administration, Bridge Division, Hydraulics and Geotechnical Branch. He has presented FHWA guidelines and related microcomputer software in Latin America and is a member of the Pan American Institute of Highways. Mr. Pagan-Ortiz's received a masters degree in Civil Engineering with concentration in Water Resources Engineering. His thesis involved the determination of stability of rock riprap for the protection at the toe of abutments located in flood plains.

1 Italic numbers in parentheses indentify refrences on pages 30-31

Printer friendly Cite/link Email Feedback | |

Author: | Pagan-Ortiz, Jorge E. |
---|---|

Publication: | Public Roads |

Date: | Jun 1, 1992 |

Words: | 4373 |

Previous Article: | Developing a standard approach for testing new traffic control signs. |

Next Article: | The FHWA test road: construction and instrumentation. |

Topics: |