CA FTBR PONDEROSA BRDIGE(1) Final Hydraulics Report.pdf

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This solicitation seeks proposals for two bridge projects located near Auburn, California. Ponderosa Bridge involves removing and replacing an existing single lane bridge over the American River and improving 2.4 miles of gravel road. Mountain Quarry Bridge requires replacing and grading an existing aggregate surface to address drainage issues on an existing pedestrian bridge and replacing the bridge railing to improve safety. The solicitation was issued by the United States Department of Transportation Federal Highway Administration. Proposals are due on or before the date specified in the solicitation for the design and construction of the bridge projects.

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FEDERAL HIGHWAY ADMINISTRATION

CENTRAL FEDERAL LANDS HIGHWAY DIVISION

Project No. 10205909

PONDEROSA WAY BRIDGE REPLACEMENT

FINAL HYDRAULICS REPORT

August 2021

Prepared By:

HDR Engineering, Inc.

2365 Iron Point Road, Suite 300

Folsom, CA 95630

This page intentionally left blank.

2365 Iron Point Road, Suite 300, Folsom, CA P 916-817-4700 hdrinc.com ii

Table of Contents

1 Introduction

1.1 Project Description

1.2 Purpose

1.3 Location

2 Data Collection and Site Investigation

2.1 Existing Bridge Description

2.2 Site Investigation

2.3 Ground and Bathymetry Survey

2.4 FEMA Flood Insurance Rate Map

3 Design Criteria and Computational Methods

3.1 Hydrologic and Hydraulic Design Criteria

3.2 Drainage Design Criteria

3.3 Bridge Scour Criteria and Methods

3.3.1 Pier Scour in Erodible Rock

3.3.2 Live-Bed Contraction Scour in Transportable Sediment

4 Specific Site Requirements

4.1 Floodplain Encroachment

4.2 Channel Stability

4.3 Stormwater Requirements

4.4 Other Considerations

5 Hydrologic Evaluation

5.1 Hydrologic Analysis

5.2 Hydrologic Results

6 Hydraulics Assessment

6.1 SMS Hydraulic Modeling Development

6.1.1 Terrain Development

6.1.2 Roughness Coefficients

6.1.3 Mesh Development

6.1.4 Boundary Conditions

6.1.5 Existing Condition Bridge Model Configuration

6.1.6 Proposed Condition Bridge Configuration

6.2 SRH-2D Hydraulic Results

iii

6.2.1 Existing Conditions Results

6.2.2 Proposed Conditions Results

6.3 Scour Assessment

6.3.1 Pier Scour

6.3.2 Contraction Scour

6.4 Drainage Assessment

6.4.1 North Road Approach

6.4.2 South Road Approach

6.4.3 Bridge Deck

6.5 Results Summary

7 References iv

Tables

Table 1. Design Criteria for Hydraulic Analysis of the Proposed Ponderosa Way Bridge (FHWA

PDDM Ch 7)

Table 2. Design Criteria for Drainage Structures of the Ponderosa Way Bridge (FHWA PDDM Ch 7) 7

Table 3. Exhibit 7.4-A Capacity Design, Scour Design, and Countermeasure Design Standards for

Bridges (FHWA PDDM Ch 7)

Table 4. Regional flood-frequency equations for rural ungaged streams in California. [DRNAREA, drainage area, in mi2; PRECIP, mean annual precipitation, in inches; ELEV, mean basin elevation, in feet]

Table 5. Summary of Streamstats Weighted Regional Regression Flood-Frequency Analysis

Table 6. Calculation to determine the weighted flows used in this analysis. Based on USGS gage

#11427000 and project site locations

Table 7. Existing Bridge Deck Cord Elevations Used in Pressure Flow Boundaries

Table 8. Proposed Bridge Deck Cord Elevations Used in Pressure Flow Boundaries

Table 9. SRH-2D Results for Existing Condition just Upstream of Ponderosa Bridge at Cross Section

Table 10. Steady State 1D HEC-RAS Results for the 200-YR and 500-YR flow events

Table 11. SRH-2D Results of Proposed Condition just Upstream of Ponderosa Bridge at Cross

Section 5

Table 12. Ponderosa Bridge Erodibility Index from Shannon & Wilson Rock Analysis

Table 13. Contraction Scour Results for 50-YR, 100-YR, 200-YR, & 500-YR Storm Events v

Figures Figure 1. Project Location (Map Source: California Topo; caltopo.com)

Figure 2. Project Vicinity Map (Map source: Google Earth)

Figure 3. Existing Bridge at Ponderosa Way (Photo Source: KSN Site Visit April 28th, 2020)

Figure 4 FEMA FIRMs 06061C0500H and 06061C0800H (eff. November 2, 2018)

Figure 5. Fall Velocity of Sand-Sized particles with Specific gravity of 2.65 in Metric Units

Figure 6. PeakFQ Bulletin 17B Estimate of Peak Streamflow. Confidence Intervals are shown for estimate

Figure 7. Delineated Watershed for Ponderosa Bridge Replacement

Figure 8. Terrain surface used in Ponderosa Way Bridge Hydraulic Modeling

Figure 9. Manning’s N delineation for Ponderosa Way Bridge Hydraulic Model. Associated values shown are based on Chow 1959

Figure 10. Transitional Mesh used in 2D Domain for Hydraulic Modeling of Proposed Design

Figure 11. Rating Curve Developed by SMS tool for Downstream Boundary Condition

Figure 12. Maximum WSEs for Existing Conditions of Ponderosa Bridge

Figure 13. 2-Year Proposed Condition Floodplain Compared to the Field Delineated Ordinary High-

Water Mark

Figure 14. Maximum WSEs for Proposed Conditions of Ponderosa Bridge

Figure 15. Zones of Aggradation & Degradation at and around Ponderosa Bridge per KSN Survey

Surface

Figure 16. Particle Distribution of Native Soil at Ponderosa Way Bridge (S&W 2021) vi

Appendices Appendix A Stormwater Risk Assessment for NPDES General Permit

Appendix B Streamstats Data

Appendix C USGS Gage #1427000 Data

Appendix D Plan View Velocity, Depth & WSEL 2D Hydraulic Results

Appendix E Hydraulic Calculations vii

1 Introduction

1.1 Project Description

The Central Federal Lands Highway Division (CFLHD) of the Federal Highway Administration

(FHWA) has tasked HDR to perform engineering, hydraulic, geotechnical, environmental, and project management to deliver design plans, specifications and estimate for proposed improvements for the replacement of Ponderosa Way Bridge along the North Fork of the

American River. The replacement bridge will be constructed immediately downstream of the existing bridge.

The existing Ponderosa Way truss bridge, built in 1935, has reached the end of its service life and is exhibiting deterioration, pier scour, and undermining. The bridge was originally constructed for fire control access and is still utilized by CALFIRE.

1.2 Purpose

The purpose of this report is to summarize the hydrologic and hydraulic approach and modeling results at Ponderosa Way Bridge to inform the 95% design package.

This report includes:

• Documentation of data collection and site investigation

• Documentation of approved hydrologic and hydraulic design criteria and methodology

• Identification of floodplain encroachment, channel stability issues and stormwater requirements

• Environmental support findings in the areas of water quality, wetlands, fish passage and stream restoration

• Hydrologic, hydraulic bridge scour, and drainage computational methods, assumptions and results

1.3 Location

The existing Ponderosa Way Bridge is in Placer County, California, three miles east of

Applegate crossing over the North Fork American River. The project site location is shown in

Figure 1 and the vicinity map is shown on Figure 2.

Figure 1. Project Location (Map Source: California Topo; caltopo.com)

Project Site

Figure 2. Project Vicinity Map (Map source: Google Earth)

2 Data Collection and Site Investigation

2.1 Existing Bridge Description

The existing bridge is a 13-ft-wide by 256-ft-long one-lane steel truss bridge with a failing wood deck. The piers and abutments are concrete that have been constructed into bedrock. The existing bridge’s North concrete pier foundation has slowly shown signs of scour and undermining. The existing bridge is shown in Figure 3 taken on April 28, 2020 during the survey collection field visit.

Figure 3. Existing Bridge at Ponderosa Way (Photo Source: KSN Site Visit April 28th, 2020)

2.2 Site Investigation

The project site was visited by the project design team on June 19, 2019. Hydraulic flow conditions at the existing bridge crossing the North Fork American River were evaluated. Land use conditions and erosion potential were also evaluated upstream and downstream of the bridge. The geotechnical site evaluation and rock borings were collected by Shannon & Wilson

Geotechnical and Environmental Consultants.

2.3 Ground and Bathymetry Survey

Ground and bathymetry survey information was gathered by KSN Inc. on April 28, 2020.

Bathymetry data was captured along 10 cross sections with additional points captured in between the cross sections. The study reach extended approximately 570 feet upstream from the existing bridge and 500 feet downstream from the bridge. The terrain coverage was supplemented on the floodplain fringe with additional LiDAR data retrieved from USGS 3DEP services. This data has an average spacing of 0.7 meters and was part of the LiDAR collection performed in July 2018 for the California NorCal Wildfires B1 data collection series. Additional information regarding the terrain development is included in Section 6.1.1 – Terrain

Development.

The horizontal datum is projected in the North American Datum of 1983 (NAD83) California

State Plane II and the vertical datum is North American Vertical Datum 1988 (NAVD88). All elevations provided in this report are provided in vertical datum NAVD88.

2.4 FEMA Flood Insurance Rate Map

The Ponderosa Way Bridge is located within a Federal Emergency Management Agency

(FEMA) Flood Insurance Hazard Area, Approximate Zone A. The North Fork American River spans two Flood Insurance Rate Maps (FIRM) 06061C0500H and 06061C0800H, both dated

Novembers 2, 2018. An Approximate Zone A is defined as an area inundated by 1% annual chance flooding and was determined by approximate methods, for which no BFEs have been determined. The FIRMs are shown in Figure 4 below.

Based upon recently collected topography and aerial imagery, it is easily noted that the effective

FEMA A Zone is a gross representation of the 1% annual chance floodplain and does not accurately follow actual topography within the vicinity of the bridge.

Figure 4 FEMA FIRMs 06061C0500H and 06061C0800H (eff. November 2, 2018)

3 Design Criteria and Computational Methods The following sections outline the relevant design criteria and analyses methods for the project site. Design criteria for the Ponderosa Way crossing follows guidelines set forth by the Federal

Highway Administration, Central Division. The Project Development and Design Manual

(PDDM) has been referenced to identify requirements for the hydraulic design, drainage design, scour assessment, and outlet protection of the proposed crossing.

3.1 Hydrologic and Hydraulic Design Criteria

The PDDM requires a minimum of two feet of freeboard from the low cord of the bridge to the design flood. Under this rural setting the 50-year flood event is selected as the design flood.

Check floods for the 100-yr, 200-yr, and 500-yr flood to evaluate the potential for bridge events have been added to determine the potential of overtopping. The hydraulic criteria required for the

Ponderosa Way Bridge replacement are included in Table 1 below.

The hydraulic analysis has been developed using the Surface Modeling Software (SMS version

13.0.14) interface along with the U.S. Bureau of Reclamation Sedimentation and River

Hydraulic 2-Dimensional (SRH-2D) hydraulic computational software. The SMS interface generates flexible and hybrid (quadrilateral and triangular cell combination) mesh domains which provide the most suitable conditions for modeling with the SRH-2D hydraulic modeling software. The SRH-2D hydraulic model utilizes an implicit solution to the finite-volume numerical method that uses the 2D depth-averaged dynamic wave equations. This solution method is particularly useful for problems that need to evaluate 2D effects and local flow patterns through in-stream structures.

Table 1. Design Criteria for Hydraulic Analysis of the Proposed Ponderosa Way Bridge (FHWA PDDM Ch 7)

3.2 Drainage Design Criteria

Design criteria for roadway structures are split into two categories, High-Standard and Low-

Standard Roads, and are defined from the PDDM as follows:

• High-Standard Road – A roadway will be classified as a high-standard road if any of the following conditions apply to any section of the project:

o Design Speed > 45 mph o Design Average Daily Traffic (ADT) > 1500 o Designated as critical access road

• Low-Standard Road – All others.

The proposed Ponderosa Way crossing is defined as a “High-Standard” road by designation as a critical fire access road. This crossing was scoped as a type 3R project with a design speed of

15 mph. The hydraulic criteria used for the Ponderosa bridge drainage plan can be viewed in

Table 2 below.

Table 2. Design Criteria for Drainage Structures of the Ponderosa Way Bridge (FHWA PDDM Ch 7)

3.3 Bridge Scour Criteria and Methods

Reference for the scour and stream stability analysis from the PDDM does not define CFLHD standard or criteria but referenced methods from the Hydraulic Engineering Circulars (HEC) 18

Evaluating Scour at Bridges, HEC 20 Stream Stability at Highway Structures, HEC 23 Bridge

Scour and Stream Instability Countermeasures Volumes 1 & 2, and Hydraulic Design Series

(HDS) 6 River Engineering for Highway Encroachments. Methods described in HEC 18 and

HEC 20 were used to assess the scour potential and stream instability of the project area at the

Ponderosa Way crossing.

3.3.1 Pier Scour in Erodible Rock

Near a bridge pier, the downward flow at the upstream face of the pier creates additional local turbulence in the form of the horseshoe vortex. As scour occurs, the stream power 𝑃 at the bottom of the scour hole decreases as the scour hole becomes deeper. Scour will continue until the stream power at the bottom of the scour hole becomes less than the critical stream power

𝑃𝐶, at which point the scouring process can no longer be sustained. The relationship relating the relative depth of the scour hole to the stream power at the bottom of the hole for a variety of pier shapes can be expressed as:

𝑃

𝑃𝑎 = 8.42𝑒

−0.712( 𝑦𝑠 𝑏

(1)

Where:

𝑃 = stream power at bottom of scour hole, W/m2

𝑃𝑎= stream power of approach flow near stream bed, W/m2 𝑦𝑠 = depth of scour hole, m 𝑏 = pier width perpendicular to flow direction, m

As developed by Annandale (2006), the stream power of the approach flow upstream of a bridge pier (i.e., at a location not affected by turbulence caused by the pier itself) is calculated by considering the turbulence production near the bed of the stream:

𝑃𝑎 = 7.853𝜌 ( 𝜏 𝜌

1.5 (2)

Where:

𝜌 = mass density of water = 1000 kg/m3 𝜏 = bed shear stress of approach flow, Pascal = N/m2

The critical stream power 𝑃𝐶 for initiating quarrying and plucking is related to rock Erodibility

Index K as given by Annandale (2006):

𝑃𝐶 = 𝐾0.75 (3)

Where:

𝐾 = Erodibility Index

𝑃𝐶 = critical stream power necessary to initiate scour, kW/m2

The Erodibility Index 𝐾 is calculated as:

𝐾 = 𝑀𝑆 ∙ 𝐾𝐵 ∙ 𝐾𝐷 ∙ 𝐽𝑆 (4)

Where:

𝑀𝑆 = intact rock mass strength parameter

𝐾𝐵 = rock block size parameter

𝐾𝐷 = rock shear strength parameter

𝐽𝑆 = rock relative orientation parameter

Generally, rock masses on which bridge piers are founded typically exhibit Erodibility Index 𝐾 values ranging from 0.1 (very poor rock) up to 10,000 or greater (very good rock).

3.3.2 Live-Bed Contraction Scour in Transportable Sediment

The constriction of flow through a bridge opening causes irregular flow patterns to develop across the streambed at the bridge. Contraction scour is the lowering of the streambed by removal of bed material across all or part of the channel width. The reduction in flow area caused by contraction of the channel width results in increased velocities and shear stress on the channel bottom. Bed material is transported by erosive forces until the natural bed elevation is lowered enough to cause equilibrium of these erosive forces. Live-bed contraction scour is the movement of material due to the contraction at the bridge opening. Predicting average scour depths due to live-bed contraction is represented by the relationship of average depth to flow and bottom width of the channel upstream and inside the contraction section and expressed as:

𝑦2 𝑦1

𝑄2

𝑄1

6/7

𝑊1

𝑊2 𝑘1

(5)

Where:

𝑦1 = Average depth in upstream main channel, ft (m) 𝑦2 = Average depth in contracted section, ft (m) 𝑦𝑜 = Existing depth in the contracted section before scour, ft (m)

𝑄1 = Flow in the upstream channel transporting sediment, ft3/s (m3/s)

𝑄2 = Flow in the contracted channel, ft3/s (m3/s)

𝑊1 = Bottom width of the upstream main channel that is transporting bed material, ft (m)

𝑊2 = Bottom width of main channel in contracted section less pier width(s), ft (m) 𝑘1 = Exponent determined below

𝑉 ∗ 𝑇⁄ 𝑘1 Mode of Bed Material Transport

< 0.50 0.59 Mostly contact bed material discharge

0.50 to 2.0 0.64 Some suspended bed material discharge

> 2.0 0.69 Mostly suspended bed material discharge

𝑉 ∗ = √𝜗𝑜 ∆⁄ = √𝑔𝑦1𝑆1, shear velocity in upstream section, ft/s (m/s)

𝑇 = Fall velocity of bed material based on the D50, m/s (Figure 5) For fall velocity in English units (ft/s) multiply T in m/s by 3.28 𝑔 = Acceleration of gravity (32.2 ft/s2) (9.81 m/s2)

𝑆1 = Slope of energy grade line of main channel, ft/ft (m/m) 𝜗𝑜 = Shear stress on the bed, (lb/ft2) (Pa (N/m2))

∆ = Density of water (1.94 slugs/ft3) (1000 kg/m3)

Fall velocity of sand-sized particles has a relationship to the D50 particle size of the bed material.

HEC-18 provides a graphical relationship of fall velocity and the diameter of 50% of the bed material and can be viewed in Figure 5 below.

Figure 5. Fall Velocity of Sand-Sized particles with Specific gravity of 2.65 in Metric Units

Critical velocity for particle uplift is defined as a relationship to depth and particle size and is expressed as:

𝑉𝑐 = 𝐾𝑢𝑦1/6𝐷1/3 (6)

Where:

𝑉𝑐 = Critical velocity above which bed material of size D & smaller will be transported, ft/s (m/s) 𝑦 = Average depth of flow upstream of the bridge, ft (m)

𝐷 = Particle size for Vc, ft (m)

𝐷50 = Particle size in mixture of which 50 percent are smaller, ft (m)

𝐾𝑢 = 6.19 (SI Units), 11.17 (English Units)

Critical velocity is used to determine whether the selected D50 particle will experience uplift and to properly select the k1 coefficient value from Equation 5.

A secondary check for the live-bed contraction scour depths will be the HIRE Abutment Scour relationship between Froude number and the scour depth ratio and is expressed as:

𝑦𝑠 𝑦1

= 4𝐹𝑅0.33 𝐾1

0.55 𝐾2 (7)

Where:

𝑦𝑠 = Scour Depth, ft (m) 𝑦1 = Depth of Flow at the abutment on the overbank or the main channel, ft (m)

𝐹𝑅 = Froude number based on the velocity and depth adjacent to and upstream of the abutment

𝐾1 = Abutment shape coefficient

𝐾2 = Coefficient for skew angle of abutment to flow calculation as for Frohlich’s equation 𝜃 = Skew angle of abutment

𝐾2 = ( 𝜃

0.13

Description K1

Vertical-wall abutment 1.00

Vertical-wall abutment with wingwalls 0.82

Spill-through abutment 0.55

4 Specific Site Requirements

4.1 Floodplain Encroachment

Per Title 44 Code of Federal Regulations 60.3.c.10, a water surface elevation rise determination is required. Since the project is located within a FEMA designated Approximate A Zone, with no designated floodway or BFEs, the review must demonstrate that the cumulative effect of the proposed development, when combined with all other existing and anticipated development, will not increase the WSE of the base flood more than one foot at any point within the community.

It is assumed that other existing and anticipated development has not and/or will not contribute to the rise in base flood more than one foot.

Additionally, per Federal Lands Highway’s PDDM, Section 7.4.1.5 – Design Guidance, an encroachment upon a base floodplain identified on FEMA’s FIRMs, for which no regulatory floodway has been established, will be designed to cause no more than 1.0 ft rise in the base flood profile, unless more strict local criteria are applicable and appropriate.

4.2 Channel Stability

Per Shannon & Wilson’s Geotechnical Evaluations Memorandum of Ponderosa Way Bridge, dated May 29, 2020:

The North Fork American River is located at the bottom of a deeply incised, V-shape gorge about 1,450 feet below adjacent ridges. Canyon sidewalls are steep with overall slopes on the order of 50-70%. Bedrock is exposed along the river below the bridge deck and is exposed in cuts along the road at either end of the bridge. The hillside slopes in the site vicinity appear to be underlain by rock at shallow depth and generally stable based upon visual observations.

The slopes are generally well vegetated with conifers and hardwoods, and scattered open areas of grass and brush, particularly on the south-facing hill side north of the river.

Reviewing Google historical aerial imagery dating back to 1993, the aerial imagery shows no lateral movement of the channel or channel banks. Upon inspection of the survey surface, areas have been identified with scour holes on the channel bottom upstream and downstream of the existing bridge. These scour developments are typical of contraction scour. Since there is no lateral movement of channel banks, it was assumed that the vertical and lateral movement of the channel occurs only at the bottom width of the river where bedrock was not observed and would not impact proposed bridge structures. Stability design standards from Federal Lands

Highway’s PDDM, Exhibit 7.4-A, were followed when assessing the stability design of the proposed bridge foundation. Refer to the Bridge Layout Report (TS&L) for stability design of the bridge substructure per recommendations from this report and the Final Geotechnical Report.

Table 3. Exhibit 7.4-A Capacity Design, Scour Design, and Countermeasure Design Standards for Bridges (FHWA PDDM Ch 7)

4.3 Stormwater Requirements

Construction activity resulting in a land disturbance of one acre or more must obtain the

Construction Activities Storm Water General Permit. Owners of new construction are required to file a complete Notice of Intent (NOI) package and develop a Storm Water Pollution Prevention

Plan (SWPPP) in accordance with Section A of the General Permit prior to the commencement of soil disturbing activities.

A risk assessment has been performed to determine the site-specific requirement during construction. The risk assessment considers:

• Receiving Water Quality, per Caltrans Water Quality Planning Tool:

o North Fork American River is not listed as a 303(d) listed waterbody impaired by sediment or has a USEPA approved TMDL implementation plan for sediment. A

TMDL is required for the pollutant of mercury.

o North Fork American River has designated beneficial uses for fish including spawning habitat and cold freshwater habitat but does not support migration

(due to both Folsom and Clementine Dams).

▪ Fish passage is not a design consideration at Ponderosa Way bridge

▪ Low receiving water risk is computed at Ponderosa Way bridge

• Sediment Risk Factor:

o R Factor, erosivity factor dependent upon the facility location and an assumed construction Start Date of 03/01/2022 and End Date of 02/01/2023, is 84.81 o K Factor, susceptibility of soil or surface material to erosion factor is low for the site, 0.2 o LS Factor, effects of topography on erosion factor is 10.84

▪ High sediment risk is computed at Ponderosa Way bridge

For the Ponderosa Way bridge site, a Risk Level 2 has been computed and is included in

Appendix A. See the Stormwater Pollution Prevention Plan (SWPPP) for additional information.

4.4 Other Considerations

Wetland impacts and stream restoration were considered but are not applicable to this project.

5 Hydrologic Evaluation The hydrologic analysis conducted for the Ponderosa Way Bridge includes flow determination of selected storms on the North Fork American River downstream and at the project site.

Recommended design flows were based on a statistical analysis done on the historical data at

USGS gage station #11427000 on the North Fork American River. Analysis was based on

Bulletin 17B using USGS PeakFQ tool. Results of analysis were transposed to project site based on a ratio that was based on regional regression equations retrieved from Streamstats.

The regional regression equations utilized from Streamstats are shown in Table 3 (USGS 2012).

Table 4. Regional flood-frequency equations for rural ungaged streams in California. [DRNAREA, drainage area, in mi2; PRECIP, mean annual precipitation, in inches; ELEV, mean basin elevation, in feet]

5.1 Hydrologic Analysis

The 2-YR, 10-YR, 50-YR, 100-YR, 200-YR, and 500-YR flood-frequency storm events were calculated at the bridge site using the USGS PeakFQ calculator and Streamstats (regional regression equations calculator). Table 5 shows flood flow data retrieved from Streamstats at the USGS gage and project locations incorporated into the hydrologic analysis as a basis for determining weighted flood-frequency flow ratios.

USGS gage #11427000 data was imported into the USGS PeakFQ software to calculate these flood-frequency events. Bulletin 17B and at-site estimate Station skew coefficients of -0.244 and

-0.495, respectively, were used to determine the 2-YR, 10-YR, 50-YR, 100-YR, 200-YR and

500-YR peak flow rates. The length of peak flow record retrieved from USGS gage #1147000 was 78 years, which is significantly lengthier than the recommended 30 years of record to provide a reasonable result. The PeakFQ Bulletin 17B estimate for peak streamflow from the

USGS gage #11427000 can be viewed in Figure 6.

Weighted flood-frequency ratios were calculated by taking the ratio of the Streamstats flow from the project site and USGS gage locations. Streamstats flow information at the project site and

USGS gage location can be viewed in Appendix B.

Table 5. Summary of Streamstats Weighted Regional Regression Flood-Frequency Analysis

Gaging Station ID

Gaging Station Name

Drainage Area (Sq.

Miles)

Discharge for each respective storm event (cfs)

2-YR 10-YR 50-YR 100-YR 200-YR 500-YR

11427000 North Fork American River @ North Fork Dam, CA

0.53 11,200 30,400 54,600 67,600 81,700 103,000

N/A Project Site* 0.51 11,000 29,700 53,500 66,200 80,100 101,000

*- Streamstats uses the Regional Weighted Regression Method for all ungaged sites from USGS SIR 2012-5113

The contributing watershed from the USGS gage #11427000 can be seen in Figure 7 below.

The gage location was used as the contributing watershed to verify a conservative hydrologic result was achieved through this analysis.

Figure 6. PeakFQ Bulletin 17B Estimate of Peak Streamflow. Confidence Intervals are shown for estimate.

Figure 7. Delineated Watershed for Ponderosa Bridge Replacement

5.2 Hydrologic Results

Final weighted flows at project site were calculated based on the ratio of the project site location and the USGS gage # 11427000 location. Table 6 summarizes the flows used in this analysis.

Additional hydrologic analyses data is included in Appendix C.

Table 6. Calculation to determine the weighted flows used in this analysis. Based on USGS gage #11427000 and project site locations.

Event Streamstats

Result Ratio1

PeakFQ Flow Result at USGS Gage #1142700 (cfs)

Recommended Flow at Project site (cfs)

2-YR 0.982 13,010 12,778

10-YR 0.977 39,910 38,991

50-YR 0.980 74,070 72,578

100-YR 0.979 91,220 89,331

200-YR 0.980 109,900 107,748

500-YR 0.981 136,900 134,242

1 Result Ratio is the Streamstats flow at the project site divided by the USGS gage location flow at #1142700. RR = Project Site flow / USGS gage station flow

6 Hydraulics Assessment The hydraulic analysis of the North Fork of the American River at Ponderosa Way Bridge was conducted utilizing Bureau of Reclamation SRH-2D hydraulic software. The Aquaveo Surface

Water Modeling Software (SMS Version 13.0.14) was used as modeling interface for developing model parameters and plugged into an SRH-2D hydraulic calculator included with the SMS software. The scour analysis was completed using hand calculations from the HEC methods described in Section 3.

6.1 SMS Hydraulic Modeling Development

6.1.1 Terrain Development

Survey information gathered from the KSN Inc. survey on April 28, 2020 was used in the development of the hydraulic model. Figure 5 shows the collection of survey points and bathymetry data used for the terrain surface. The terrain coverage was supplemented on the floodplain fringe with additional LiDAR data retrieved from USGS 3DEP services. Figure 8 shows the extension of the terrain surface using the available 2018 California Wildfire LiDAR set.

Figure 8. Terrain surface used in Ponderosa Way Bridge Hydraulic Modeling

6.1.2 Roughness Coefficients

Manning roughness coefficient were developed based on the aerial imagery and assigned values according to the Open-Channel Hydraulics book written by Ven Te Chow (1959). Site

Bathymetry Cross Sections

2018 Ca NoCAL Wildfire LiDAR

2020 KSN Survey

XS1

XS10

XS9

XS8

XS7

XS6

XS5

XS4

XS3

XS2

visit photographs were also used to confirm the assigned values into the model. Figure 9 shows the values assigned to each delineated area.

Chow does not provide values specific for bridge deck modeling and other sources were checked (including Henderson as well as Brater& King). The truss substructure provides resistance to flow on the existing configuration under the main span. Existing abutment spans were set to 0.05, owing to typical values of existing wood deck and concrete being 0.020. By raising the value from 0.02 to 0.05 (abutments) & 0.07 (main span), the model captures the resistance due to truss and railing impedance. Proposed bridge deck manning values have remained modeled at 0.05 for all spans due to the removal of larger truss section on superstructure and the continued use of railing.

Figure 9. Manning’s N delineation for Ponderosa Way Bridge Hydraulic Model. Associated values shown are based on Chow 1959

6.1.3 Mesh Development

The 2D domain was split into multiple polygons to create a transitional mesh to improve the quality of the SRH-2D simulation result. Average element size ranges from 5 ft to 15 ft, where the 15 ft elements are seen at the upstream and downstream boundaries. A quadrilateral mesh of 5 ft elements was used at the bridge to verify pressure flow calculations, velocities, eddies, and lateral/vertical movement of water. Figure 10 captures the 2D domain configuration for the proposed bridge model with the terrain surface elevations assigned to each element according to closest triangle of the surface.

Figure 10. Transitional Mesh used in 2D Domain for Hydraulic Modeling of Proposed Design

6.1.4 Boundary Conditions

Upstream and downstream boundary conditions were set for each respective storm event. The upstream boundary condition was modeled as an unsteady step time series hydrograph for each storm event. Ramp-up for each respective flow was incorporated to maintain model stability. The downstream boundary was assigned a subcritical normal depth rating curve which was created from the SMS exit boundary tool. Assigning the most downstream hydraulic cross section as the boundary, the SMS tool created a synthetic rating curve based on average bed slope (s = 0.00505), downstream cross section geometry, and composite Manning’s n value (n

= 0.052) of the entire reach. The downstream rating curve can be viewed in Figure 11 below.

To verify that the downstream rating curve was a valid boundary input, a 1D HEC-RAS simulation was run using the same average bed slope (s = 0.00505) to compare WSEL results at the downstream end of the model domain. The percent difference in water surface results for all events ranged from 0.07%-0.14%. This small range of percent different gave confidence that the SRH-2D results were valid for use in design.

Figure 11. Rating Curve Developed by SMS tool for Downstream Boundary Condition

6.1.5 Existing Condition Bridge Model Configuration

The existing bridge piers and abutments were incorporated into the model by making voids into the terrain surface. The bridge deck was added as a pressure flow boundary across the length of the bridge alignment. Low and high cord elevations were set using surveyed elevations and are included in Table 7 below. The bridge deck was model as a flat, broad-crested, paved weir.

The Manning’s coefficient used for the bridge deck ceiling was set to 0.05, simulating roughness from the railing and truss structures. The existing bridge models the main span low cord at

817.8 feet. The low cord deck extensions from the piers to the abutments were modeled at

819.8 feet. The existing bridge configuration can be viewed in Appendix D.

Table 7. Existing Bridge Deck Cord Elevations Used in Pressure Flow Boundaries

Pressure Flow Boundary Low Cord Elevation (ft) High Cord Elevation (ft)

Abutment Spans 819.8 823.6

Main Span 817.8 825.0

6.1.6 Proposed Condition Bridge Configuration

The proposed bridge was modeled as a three-span bridge with the main span extending 157 feet from the centerline of the piers. The proposed piers were designed to 3.5 ft x 5.5 ft rounded nose elongated concrete pillars and abutment spans extend 32.5 feet longer from the main span. Piers were incorporated into the terrain surface as voids and abutment wingwalls were added at a constant elevation of 824.3 ft. Low and high cord elevations were set to elevations designed from the bridge structure team and are included in Table 8 below. The main span of the bridge deck was modeled as a parabolic shape with pier elevations set to 818.7 ft. The

Manning’s coefficient used for the bridge deck ceiling was set to 0.05, simulating roughness from the railing on the bridge deck. The proposed bridge configuration can be viewed in

Appendix D.

Table 8. Proposed Bridge Deck Cord Elevations Used in Pressure Flow Boundaries

Pressure Flow Boundary Low Cord Elevation (ft) High Cord Elevation (ft)

Abutment Spans 821.6 824.3

Main Span 818.7 826.6

6.2 SRH-2D Hydraulic Results

Existing condition results of the 2-YR, 10-YR, 50-YR, and 100-YR, 200-YR and 500-YR WSEs just upstream of the existing bridge and the proposed bridge cross section (XS 5) are presented in the sections below. Two-dimensional plan view velocity, depth, and WSEL results for the 50-

YR and 100-YR events under proposed conditions are included in Appendix D.

6.2.1 Existing Conditions Results

The flow, velocity, bed stress, depth and WSE maximum results along XS 5 are included in

Table 9 below. The WSE for each storm event along XS 5 are shown in Figure 12. Negative freeboard results demonstrate that the bridge low chord has been overtopped.

Table 9. SRH-2D Results for Existing Condition just Upstream of Ponderosa Bridge at Cross Section 5

Storm Event

Flow (cfs) Max WSE (ft)

Max Depth (ft)

Max Velocity (ft/sec)

Max Bed Stress (lb/ft2)

Freeboard from Low Chord El.

817.8 (ft)

2-Year 12,778 797.3 24.1 13.1 2.3 20.5

10-Year 38,991 806.7 32.8 15.3 2.6 11.1

50-Year 72,578 816.0 41.8 17.2 3.0 1.8

100-Year 89,331 819.9 45.5 18.5 3.4 -2.1

200-Year* 107,748 823.7 49.5 18.8 3.4 -5.9*

500-Year* 134,166 833.6 60.1 16.9 3.1 -15.8*

* Results of overtopping flow shows oscillation in Max WSEL at pressure flow boundaries.

Figure 12. Maximum WSEs for Existing Conditions of Ponderosa Bridge

Results for overtopping flows on the 200-YR and 500-YR storm events from the SRH-2D hydraulic model remained unstable throughout the duration of simulations. Adjusting time step control, 2D mesh orientations, and downstream boundary conditions did not improve the hydraulic result of these overtopping flows. To verify the unstable result of overtopping flows in the SRH-2D model, a subcritical regime, steady state 1D HEC-RAS model was used to compare against the SRH-2D results. Manning’s n, bridge configuration, and hydraulic cross section information from the SRH-2D model were incorporated into the 1D HEC-RAS model.

The downstream boundary condition for the 1D model was set to normal depth slope of 0.00505 to remain consistent to SRH-2D boundary conditions. Results of the 200-YR and 500-YR steady state flows from the 1D model can be viewed in 10 below.

Table 10. Steady State 1D HEC-RAS Results for the 200-YR and 500-YR flow events

Storm Event

Flow (cfs) Max WSE (ft)

Max Depth (ft)

Max Velocity (ft/sec)

Max Bed Stress (lb/ft2)

Freeboard from Low Chord El.

817.8 (ft)

200-Year 107,800 827.2 55.7 11.6 7.1 -9.4

500-Year 134,200 831.1 59.7 12.8 7.2 -13.3

Comparison of 1D HEC-RAS and SRH-2D results show that the 200-YR has a 0.4% difference and the 500-YR has a 0.3% difference in maximum WSEL. The percent difference in WSEL from the 1D

HEC-RAS and SRH-2D result fall within a reasonable range to accept the SRH-2D result for existing conditions. It has been confirmed that the normal depth slope, based on the surface terrain, is a suitable boundary condition for developing the downstream rating curve in the SMS boundary condition creation tool.

6.2.2 Proposed Conditions Results

Results for the flow, velocity, bed stress, and WSE at XS 5 are maximum values along the delineated cross section shown in Table 11. Figure 14 shows the WSE for each respective storm event.

The computed 2-YR floodplain was also utilized to verify the field delineated Ordinary High-

Water Mark (OHW). In Figure 13 below, the 2-year proposed condition floodplain is compared to the field delineated OHWM. The delineated boundaries through the bridge structure almost matches exactly, excluding the right bank at the downstream end of the model extent.

Figure 13. 2-Year Proposed Condition Floodplain Compared to the Field Delineated Ordinary High-Water Mark

Table 11. SRH-2D Results of Proposed Condition just Upstream of Ponderosa Bridge at Cross Section 5

Storm Event

Flow (cfs)

WSE

(ft)

Depth (ft)

Velocity (ft/sec)

Bed Stress (lb/ft2)

Freeboard from Low Chord El.

818.7 (ft)

2-Year 12,778 795.9 20.7 9.5 1.2 22.7

10-Year 38,992 803.8 29.0 15.7 3.0 14.9

50-Year 72,578 812.4 37.7 18.9 3.9 6.3

100-Year 89,331 816.0 41.3 20.3 4.3 0.5

200-Year 107,748 823.7 44.9 21.1 4.5 -5.0

500-Year 134,166 828.9 49.5 22.6 5.0 -10.2

Figure 14. Maximum WSEs for Proposed Conditions of Ponderosa Bridge

In conclusion, the proposed conditions bridge is more hydraulically efficient, and therefore, produces lower water surface results for all modeled events than the existing conditions bridge structure.

6.3 Scour Assessment

Scour at the piers of the proposed bridge alignment was analyzed to quantify the depth of rock scour at the site. Signs of contraction scour were identified upstream and downstream in the terrain surface provided from KSN and prompted a desktop estimate of bed material determination, and analyses of contraction scour depths and channel thalweg migration. The boring samples reported show that solid rock is present down to 60.5 feet. Granular material was located at the top 6 feet of the boring sample and is described as:

“Very dense, brown, Poorly Graded Sand with Silt and Gravel with Cobbles and Boulders:

moist; fine to coarse gravel; fine to coarse sand; non-plastic fines”

For the contraction scour assessment an assumed D50 was used that represented the description of topsoil found in the boring samples.

6.3.1 Pier Scour

Shannon & Wilson (2021) determined an Erodibility Index value 𝐾=1408 (Table 12. Ponderosa

Bridge Erodibility Index) that was characteristic of the bedrock observed during the Ponderosa

Bridge field explorations and reconnaissance. The input parameters in Table 12 were determined by relating the measured data collected from rock mapping surveys and subsurface exploration against tables published in Section 4.7.2 of the Federal Highway Administration

Hydraulic Engineering Circular No. 18 (FHWA, 2018).

Table 12. Ponderosa Bridge Erodibility Index from Shannon & Wilson Rock Analysis

Based on conservative 500-year flow variables upstream of the Ponderosa Bridge (flow depth =

50 ft; velocity = 25 feet/s), the maximum pier scour YS from equation (1) is negligible, as shown below.

K = 1408 / Erodibility Index h = 15 m Approach flow depth b = 1.07 m Pier width perpendicular to flow direction

Sf = 0.0031 m/m Energy grade line slope

V = 7.62 m/s Approach velocity t = 456.17 Pa Bed shear stress of approach flow

Pt = 3.48 KW/m

Approach stream power total t*V

Pa = 2.419 KW/m2 Local stream power of approach flow per HEC-18

Pc = 229.85 KW/m

Critical stream power necessary to initiate scour K > 0.1

Pc/Pt,a = 66.13 / Maximum power ratio

Ys = 0.00 m Pier scour

This is the consequence of a large rock Erodibility Index (K = 1408), which results in the critical stream power necessary to initiate scour (𝑃𝐶 = 230 KW/m2) that is two orders of magnitude larger than the local stream power of approach flow (𝑃𝑎 = 2.4 KW/m2).

6.3.2 Contraction Scour

Based on inspection of the survey terrain provided from KSN, there are signs of typical contraction scour aggradation and degradation in the channel bed. Figure 15 depicts the signs of typical contraction scour characteristics at the Ponderosa Way Bridge crossing. The bedrock material sampled by Shannon & Wilson (2021) extends down to the toe of the channel bottom where river wash bed material is observed from site inspection and aerial imagery.

Shannon & Wilson (2021) determined the particle size distribution of the surrounding native soil from the boring samples taken at the site. Boring sample SWB-1 from Shannon & Wilson (2021) shows a distribution of erodible material in the top 6 ft of the sample, see the Final Geotechnical

Design Report for boring sample figures. The boring sample was not taken from the river channel but provides an estimate of typical material seen at the site. For the purposes of the scour assessment, the results are theoretical and provide a conservative estimate of contraction scour depths. The scour presented for the 200-YR and 500-YR flow events are under pressure conditions at the proposed bridge alignment. Figure 16 shows the distribution report of the native topsoil at Ponderosa.

Figure 15. Zones of Aggradation & Degradation at and around Ponderosa Bridge per KSN Survey Surface

Degradation

Aggradation

Figure 16. Particle Distribution of Native Soil at Ponderosa Way Bridge (S&W 2021)

The native soil at the Ponderosa Way site has a D50 of 2.57 mm and was used in the calculations of live-bed contraction scour. The scour depths calculated were compared against the terrain surface scour holes seen in Figure 15. Based on the 50-YR,100-YR, 200-YR, & 500-

YR hydraulic variables upstream and downstream of the bridge, the average scour depths, Ys, were determined and shown below in Table 16.

Table 13. Contraction Scour Results for 50-YR, 100-YR, 200-YR, & 500-YR Storm Events

Observed scour depths seen in the surface terrain range from 8 to 15 feet from the existing channel invert elevations seen upstream of the bridge contraction. The contraction scour calculations are comparative to the observed scour hole depths seen in the terrain surface.

6.4 Drainage Assessment

Drainage design for the North Approach Road, South Approach Road and Bridge Deck was developed using the design criteria established from Section 3. Refer to the design plans for plan view and profile view of proposed inlet structures, riprap armoring, and drainage culverts.

6.4.1 North Road Approach

The rainfall runoff flowing from the North Approach road will continue to bypass the proposed drainage inlet structure and flow directly towards the river downstream of the proposed bridge.

The rainfall runoff collected from the bridge deck has been estimated and the calculated 10-YR flow is 0.33 cfs. The inlet selected for the North Approach Road Abutment is a Type 5A design referenced from FHWA typical drawings. The inlet will be placed 1 foot from the end of the North

Abutment wingwall and vertically drop into a 6.8 ft deep catch basin that discharges through a

15” outlet culvert onto a riprapped apron. Drawing Standard No. 602-5 & 604-6 shows a typical design of a Type 5A inlet and grate. The Type 5A outlet culvert is sized to handle a maximum flow of 3.5 cfs.

Class II riprap will be placed at the culvert outlet in the Method B placement to prevent scour at higher flow events (50-YR and larger). The riprap area will be trenched 18” to be keyed into the existing grade. The vertical extent of the riprap will extend 24 ft and go from top of bank to the top of the bedrock layer lining the side slope of the channel. A filter layer will be place beneath the riprap layer with Subbase A aggregate and have a layer thickness of 9”.

6.4.2 South Road Approach

The rainfall runoff flowing from the South Approach Road will be routed by way of an existing but widened and deepened road ditch channel to a 24” cross-road culvert that discharges to the

East side of the existing South Abutment. The drainage channel is to be sized for a 10-YR runoff flow and the culvert to be sized to handle 50-YR runoff flow. Road ditch dimensions are a

Live-Bed Scour (Average Contracted Scour Depth)

Storm Event Y2 (ft) Yo (ft) Ys (ft)

50-YR 43.2 29.8 13.5

100-YR 46.8 33.2 13.5

200-YR 51.5 36.7 14.8

500-YR 59.9 40.2 19.7

2’ bottom width and sides slopes of 2.67:1 (H:V) to the road surface subgrade. The ditch will be lined with Class II riprap to prevent scour. The South Approach Riprap Profile drawing shows the typical cross section of the drainage channel and profile view of the 24” outlet culvert.

The inlet for the 24” discharge culvert will be placed at the end of the road ditch in a 2 ft deep swale armored with the same Class II riprap material as the road ditch. The rise on the culvert will be 0.63 ft and 34 feet long with end sections attached. The outlet will be conformed to the fill slope on the downstream side of the road embankment and armored with Class III riprap in a

Method B placement to prevent scour during larger flow events (50-YR and higher). The riprap area will be trenched 24” to be keyed into the existing grade. The riprap will laterally extend 16 ft up the road embankment to the end of the existing wingwall. The vertical extent of the riprap will extend 20 ft and go from top of bank to the top of the bedrock layer lining the side slope of the channel. A filter layer will be place beneath the riprap layer with Subbase A aggregate and have a layer thickness of 9”.

The final component to the South Approach drainage plan is the placement of deck drainage channel that will connect to the Class III riprap armored section for the 24” culvert outlet. The runoff flows from the bridge deck was calculated to be 0.33 cfs and can be routed by way of a 6” deep swale with road aggregate as the armored layer.

6.4.3 Bridge Deck

Cross slope on the bridge deck will be 1% and the longitudinal slope will be 2%, going from the bridge crown to the abutment ends. The gutter slope will also be 1% and creates a flow spread of 5.6’ with a max depth of 0.67” in the gutter centerline. The spread width was acceptable for this design due to the design speed of the bridge (15 mph) being less than 45 mph. With the

Type 5A inlet at the North Abutment and 6” swale channel at the South Abutment, deck drainage can be properly captured and discharged towards the river.

6.5 Results Summary

Based on the hydraulic results in Tables 12 and 13, there is a reduction in WSEs for the Design

Flow event (50-YR) and Check Flood events (100-YR, 200-YR, and 500-YR) when comparing the proposed bridge configuration against the existing bridge alignment. The proposed

Ponderosa Way Bridge is more hydraulically efficient structure than the existing bridge configuration and creates a no rise impact to the area.

The stability analysis shows that the channel does not experience lateral movement of embankments and rock scour does not occur at critical bridge structures for the design event.

Based upon assumed native material conditions, contraction scour depths will not impact the pier and abutment structures due to the depth of rock on the channel embankments.

7 References California Environmental Protection Agency, State Water Resources Control Board, 2009-0009-

DWQ Construction General Permit, https://www.waterboards.ca.gov/water_issues/programs/stormwater/constpermits.shtml.

Caltrans Water Quality Planning Tool, http://svctenvims.dot.ca.gov/wqpt/wqpt.aspx.

Central Federal Lands Highway Division, Project Development and Design Manual, July 2019.

Federal Emergency Management Agency (FEMA), Flood Map Service Center, https://msc.fema.gov/portal/home.

Federal Highway Administration (FHWA, Hydraulic Engineering Circular No. 11 (HEC-11)

Design of Riprap Revetment. Publication No. FHWA-IP-89-016. March 1989

Federal Highway Administration (FHWA, Hydraulic Engineering Circular No. 14 (HEC-14)

Hydraulic Design of Energy Dissipators for Culverts and Channels. Publication No.

FHWA-NHI-06-086. 3rd Edition, July 2006

Federal Highway Administration (FHWA, Hydraulic Engineering Circular No. 15 (HEC-15)

Design of Roadside Channels with Flexible Lining. April 1988

Federal Highway Administration (FHWA), Hydraulic Engineering Circular No. 18 (HEC-18)

Evaluating Scour at Bridges, Publication No. FHWA NHI 01-001. 4th Edition, May 2001.

Federal Highway Administration (FHWA), Hydraulic Engineering Circular No. 20 (HEC-20)

Stream Stability at Highway Structures, Publication No. FHWA-HIF-12-004, 4th Edition.

April 2012.

Federal Highway Administration (FHWA), Hydraulic Engineering Circular No. 21 (HEC-21)

Design of Bridge Deck Drainage. May 1993.

Federal Highway Administration (FHWA), Hydraulic Engineering Circular No. 22 (HEC-22)

Urban Drainage Design Manual, Publication No. FHWA-NHI-10-009. 3rd Edition. August

Federal Highway Administration (FHWA), Hydraulic Engineering Circular No. 23 (HEC-23)

Bridge Scour and Stream instability Countermeasures: Experience, Selection, and

Design Guidance Volumes 1 & 2. Publication No. FHWA-NHI-09-111 & FHWA-NHI-09-

112. 3rd Edition. September 2009.

National Cooperative Highway Research Program (NCHRP) Report 568 – Riprap Design

Criteria, Recommended Specifications, and Quality Control. Ayres Associates Inc., 2006

Shannon & Wilson (S&W) Geotechnical and Environmental Consultants, Geotechnical Design

Report, Ponderosa Way Bridge, Placer County, California, August 2021.

Title 44 Code of Federal Regulation (CFR) 60.3, Flood Plain Management Criteria for Flood-prone Areas.

https://www.waterboards.ca.gov/water_issues/programs/stormwater/constpermits.shtml http://svctenvims.dot.ca.gov/wqpt/wqpt.aspx https://msc.fema.gov/portal/home

United States Geological Survey (USGS), Methods for Determining Magnitude and Frequency of Floods in California, Based on Data through Water Year 2006, Prepared in cooperation with FEMA, Reston, VA 2012.

Appendix A – Stormwater Risk Assessment for

NPDES General Permit

Entry

84.81

0.2

10.84

Watershed Erosion Estimate (=RxKxLS) in tons/acre

Site Sediment Risk Factor

Low Sediment Risk: < 15 tons/acre

Medium Sediment Risk: >=15 and <75 tons/acre

High Sediment Risk: >= 75 tons/acre

Sediment Risk Factor Worksheet

A) R Factor

R Factor Value

B) K Factor (weighted average, by area, for all site soils)

Analyses of data indicated that when factors other than rainfall are held constant, soil loss is directly proportional to a rainfall factor composed of total storm kinetic energy (E) times the maximum 30-min intensity (I30) (Wischmeier and

Smith, 1958). The numerical value of R is the average annual sum of EI30 for storm events during a rainfall record of at least 22 years.

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