Development of a Rock Fall Hazard Rating Matrix for the ... · Development of a Rock Fall Hazard Rating Matrix for the State of Ohio Martin J. Woodard Michael Baker Jr., Inc. Dr.

Development of a Rock Fall Hazard Rating Matrix for the State of Ohio

Martin J. WoodardMichael Baker Jr., Inc.

Dr. Abdul ShakoorGeology Department, Kent State University

Dr. Rachael CraigNational Science Foundation

Previous WorkOregon Rock Fall Rating SystemNew York State DOT Rock Slope Rating SystemWashington DOT Unstable Slope Rating System

Oregon Rating System

Points 3 Points 9 Points 27 Points 8125 feet 50 feet 75 feet 100 feetGood catchment

Moderate catchment

Limited catchment No catchment

25% of time 50% of time 75% of time 100% of timeAdequate sight distance, 100%

of low design value

Moderate sight distance, 80% of low design

value

Limited sight distance, 60% of low design

value

Very limited sight distance,

40% of low design value

44 feet 36 feet 28 feet 20 feet

Structural condition

Discontinuous joints, favorable

orientation

Discontinous joints, random

orientation

Discontinuous joints, adverse

orientation

Continuous joints, adverse

orientation

Rock FrictionRough, Irregular Undulating Planar

Clay infilling, or slickensided

Structural condition

Few differential erosion features

Occasional erosion features

Many ersosion features

Major erosion features

Differences in Erosion Rates

Small difference

Moderate difference Large difference

Extreme difference

1 foot/ 3 cubic yards

2 footr/ 6 cubic yards

3 foot/ 9 cubic yards

4 feet/ 12 cubic yards

Low to moderate

precipitation; no freezing periods; no

water on slope

Moderate precipitation or short freezing

periods or intermittent

water on slope

High precipitation or long freezing

periods or continual water

on slope

High precipitation

and long freezing periods

or continual water on slope

and long freezing periods

Few falls Occasional falls Many falls Constant falls

Block Size/Quantity of Rockfall/Event

Climate and Presence of Water on Slope

Rockfall History

Category

Cas

e 1

Cas

e 2

Roadway Width Including Paved Shoulders

Geo

logi

c C

hara

cter

Slope Height

Ditch Effectiveness

Average Vehical Risk

Percent of Decision Sight Distance

Rating Criteria and Score

Previous WorkNew York Rock slope rating system

Three categories! Geological Factor

• Multiple geologic conditions• Exponential Scoring System

! Section Factor• Ritchie Ditch Criteria

! Human Impact Factor

1 Point 3 Points 9 Points 27 Points 81 Points1a Geology

(Xtal.)Massive, no

fractures dipping out of

slope

Discontinuous fractures, random

orientation

Fractures that form wedges

Discontinuous fractures dipping out

of slope

Continuous fractures dipping out of slope

1b Geology (Sed.) Horizontal to

slightly dipping

Raveling, occasional small

blocks

Small overhangs or columns,

numerous small blocks

Overhangs, some large unstable blocks, high

columns

Bedding or joints dipping out of slope, over-steepened cut

face

2 Block Size 150 mm 150 to 300 mm 0.3 to 0.6 m 0.6 to 1.5 m 1.5 m or more

3 Rock Friction

Rough, irregular

Undulating Planar Smooth, slickensided

Clay, gouge-faulted

4 Water/IceDry Some seepage

Moderate seepage High seepage/brush

High seepage with long backslope/brush

5 Rock Fall No falls Occasional minor falls Occasional falls Regular falls Major falls/slides

6 Backslope Above Cut Flat to gentle

slope (up to 15 º)

Moderate slope (15º - 25º)

Steep slope (25º - 35º)

Very steep slope (>35º) or steep slope (25º - 35º)

with boulders

Very steep slope (>35º) with boulders

Categories for Geologic Factor

G.F. = Σ (each category/ 10)

Section Factor

S.F.= (DR + WR)/(DA + WA); where

DR = ditch depth in meters (Ritchie Graph)WR = ditch width in meters (Ritchie Graph)DA = actual ditch depth in meters (measured in field)WA = actual offset distance in meters (measured in field)

NY DOT Rockfall Rating SystemHuman Effect

Active Condition:! Fa = AADT x [(L + SSD)/(V x 24,000)]

Passive Condition:! Fp = log10 (AADT) x log10(L)[a/(SSD - a)]

Human Effect Factor (HEF)! H.E.F. = (Fa + Fp)/3

Total Relative Risk = GF x SF x HEF

Previous workWashington Unstable Slope Rating System

Accounts for both Rock slopes and Landslides! Exponential scoring system! Economic factor

Criterion Points = 3 Points = 9 Points = 27 Points = 81

Problem Type Soil Cut or Fill Slope Erosion

Settlement or Piping Slow Moving Landslides

Rapid Landslides or Debris Flows

Problem Type Rock Minor Rockfall Good Catchment

Moderate Rockfall Fair Catchments

Major Rockfall Limited Catchment

Major Rockfall No Catchment

Average Daily Traffic < 5000 5,000 - 20,000 20,000 - 40,000 > 40,000Decision Site Distance Adequate Moderate Limited Very LimitedImpact of Failure on Roadway

< 50 ft 50 - 200 ft 200 - 500 ft > 500 ft

Roadway Impedance Shoulder Only 1/2 Roadway 3/4 Roadway Full Roadway

Average Vehicle Risk 25% of the Time 25 - 50% of the Time 50 - 75% of the Time > 100% of the Time

Pavement Damage Minor-Not Noticeable

Moderate-Driver Must Slow

Severe-Driver Must Stop

Extreme-Not Traversible

Failure Frequency No Failures in Last 5 Years

One Failure in Last 5 Years

One Failure Each Year

More Than One Failure Each Year

Annual Maintenance Costs

< $5,000 per Year $5,000 - $10,000 per Year

$10,000 - $50,000 per Year

> $50,000 per Year

Economic Factor No Detours Required

Short Detours < 3 Miles

Long Detours > 3 Miles

Sole Access No Detours

Accidents in Last 10 Years 1 2-3 4-5 >5

WASHDOT Rating System for Unstable Slopes

Valley Stress Relief Joint

Why Develop a New Rating SystemGeology

All previous rating systems deal with multiple geological conditionsOhio region has one predominant geological condition

Site Locations

108 sites

Geologic ParametersCompetent Bedding ThicknessCompetent Discontinuity SpacingSlake DurabilityMaximum Amount of UndercuttingTypical Amount of UndercuttingBlock SizeRecharge AreaAnnual RainfallAnnual DrainageOregon RFHRS Climate

Geometric ParametersSlope OrientationSlope LengthSloe HeightSlope AngleBackslope AngleBackslope ConditionDitch Depth Ditch WidthDitch Angle

Ritchie Depth Ritchie WidthRitchie ScoreCRSP outputOregon Ditch ScoreNew Oregon Catchment Ditch Evaluation

Traffic ParametersRoadway widthDecision Sight DistanceStopping Sight DistanceAverage Daily TrafficPosted Speed LimitOregon RFHRS Vehicle RiskNYDOT RFRS Active Condition

Laboratory MethodologiesSlake Durability IndexColorado Rockfall Simulation Program (CRSP 4.0)

Rockfall AnalysisROCKPACK III

Kinematic Stereonet Analysis

Creating the Matrix for the State of Ohio

Is the exponential scoring system appropriate?Difficulties

Lack of an independent variable to assess systemCluster Analysis

Normalized data

Statistical ProceduresPurpose-Reason Conclusions

Univariate StatisticsFrequency-distribution histograms QQ-plots Summary statistics

Bivariate Statistics

x-y scatter plots Correlation coefficients (R2)

Cluster AnalysisK-means Analysis of variance

Determine significant variables Group or cluster data

Significant variables obtained for geology and geometry

What was done

Examine different slope mechanics

Geology Geometry

TrafficDivide into groups

Check for outliers (errors in data) Test for normality

Raw or natural log data indicate normality

Check for outliers (reapply Univariate Statistics) Identify variables that provide independent information

Cleaned data rechecked through univariate statistics. Some data provided similar information (maximum and typical amount of undercutting)

Slak

e D

urab

ility

Inde

x

Max

. Am

t. O

f Und

ercu

t.

log

Max

. Am

t. U

nder

cut.

Avg

. Am

t. O

f Und

ercu

t

log

Avg

. Am

t. U

nder

cut.

Bloc

k Si

ze

log

Bloc

k Si

ze

Hyd

rolo

gic

Valu

e

log

Hyd

rolo

gic

Valu

e

Slop

e O

rient

atio

n

Dev

iatif

rom

due

sout

h

Mean 81.7 2.7 1.1 1.3 0.3 718.0 4.8 985011 13.4 120.3 91.6Standard

Deviation24.1 2.0 0.6 1.0 0.7 3104.6 1.6 1053837 0.9 87.2 51.8

coefficient of variation

0.30 0.75 0.57 0.80 2.23 4.32 0.33 1.07 0.07 0.72 0.57

standardized skewness

-0.99 0.14 -0.44 0.25 -0.28 3.49 0.37 -0.06 0.33 0.07

standardized kurtosis

1.49 -0.41 0.19 -0.33 -0.15 23.84 0.88 5.71 20.26 -0.07 -0.40

Geology Summary Statistics

Statistical AnalysisStep 2: Bi-variant analysis

x-y scatter plotsSecond check for errors in data baseEnsuring that variables used in analysis will provide independent information! Correlation coefficient

Geology Correlation Coefficients (R2)Variables

Slake Durability Index (%)

Max. Amt. of

Undercut. (ft)

log Max. Amt. of

Undercut. (ft)

Avg. Amt. of

Undercut. (ft)

log Avg. Amt. of

Undercut. (ft)

log Block Size (lbs)

log Hydro. Value (ft3)

Slope Orient.

(degree)

Slake Durability Index (%)

1

Max. Amt. of Undercut. (ft)

0.06 1

log Max. Amt. of Undercut. (ft)

0.04 0.89 1

Avg. Amt. of Undercut. (ft)

0.03 0.82 0.65 1

log Avg. Amt. of Undercut. (ft)

0.01 0.70 0.78 0.90 1

log Block Size (lbs)

3.7E-03 0.03 0.04 0.03 0.04 1

log Hydrologic Value (ft3)

3.2E-04 0.01 4.6E-04 0.01 6.7E-04 0.08 1

Slope Orient. (degree)

1.8E-04 2.9E-03 1.1E-05 0.01 1.7E-03 1.4E-03 1.8E-04 1

x-y scatter plots

R2=0.82

Geometric Correlation Coefficients (R2)Variables

log Slope Length

(ft)

log Slope Height

(ft)

Slope Angle (angle)

log Backslope

(angle)

Ditch Depth

(ft)

Ditch Width

(ft)

Ritchie Score

log Slope Length (ft)

1

log Slope Height (ft)

0.07 1

Slope Angle (angle)

0.01 0.06 1

log Backslope (angle)

0.03 0.02 0.0003 1

Ditch Depth (ft)

0.00 0.02 0.00 0.03 1

Ditch Width (ft)

0.10 0.11 0.03 0.04 0.068 1

Ritchie Score

0.04 0.02 0.01 0.01 0.101 0.285 1

Traffic Correlation Coefficients (R2)

VariablesRoadway Width (ft)

log Avg. Daily

Traffic

Posted Speed Limit (mph)

log Oregon Vehicle

Risk

% Decision

Site Distance

Roadway Width (ft)

1

log Avg. Daily Traffic

0.15 1

Posted Speed Limit (mph)

0.13 0.09 1

log Oregon Vehicle Risk

0.16 0.79 0.07 1

% Decision Site Distance

0.00 0.03 0.00 0.05 1

Discrete Traffic Values

Statistical AnalysisStep 3: Cluster analysis

Compares multiple variables simultaneously! Geological Parameters! Slope Geometry Parameters! Traffic Parameters

Clusters are groupings of slopes with similar characteristics

Parameters considered in Cluster Analysis

Geologic parametersSlake DurabilityMaximum Amount of UndercuttingBlock SizeHydrologic value

Traffic ParametersRoadway WidthPosted Speed Limit

Geometric ParametersSlope HeightSlope AngleBack slope AngleDitch DepthDitch Width

Average Daily TrafficSlope Length

Geology ANOVA table

Mean Square

Degrees of

Freedom

Mean Square

Degrees of

Freedom

Slake Durability

Index27846.182 2 58.281 105 477.795 0

Max. Amt. of Undercutting

17.484 2 3.993 105 4.379 0.015

Block Size 2.25 2 2.478 105 0.908 0.406Hydrologic

Value0.825 2 0.898 105 0.919 0.402

Variables

Cluster Error

F-test Sig.

Slake Durability and Maximum Amount of Undercutting ANOVA table

Mean Square

Degrees of Freedom

Mean Square

Degrees of Freedom

Slake Durability

Index27846.182 2 58.281 105 477.795 0

Max. Amt. O f

Undercut.17.484 2 3.993 105 4.379 0.015

VariablesCluster Error

F-test Sig.

High

Moderate

Low

Geometry ANOVA table

Variables Mean Square

Degrees of Freedom

Mean Square

Degrees of Freedom

Slope Height

3.818 2 0.443 105 8.618 0

Slope Angle

8898.803 2 24.536 105 362.684 0

Back Slope Angle

0.285 2 2.248 105 0.127 0.881

Ditch Depth

0.65 2 0.737 105 0.881 0.417

Ditch Width

126.69 2 60.551 105 2.092 0.129

Cluster ErrorF-test Sig.

Slope Height and Angle ANOVA table

Mean Square

Degrees of Freedom

Mean Square

Degrees of Freedom

Slope Height

3.818 2 0.443 105 8.618 0

Slope Angle

8898.803 2 24.536 105 362.684 0

VariablesCluster Error

F-test Sig.

High

Moderate

Low

Mean Square

Degrees of

freedom

Mean Square

Degrees of

freedomlog Slope Height (ft)

4.389 2 0.432 105 10.154 0

Slope Angle 5906.073 2 81.54 105 72.431 0

Slake Durability Index (%)

22190.77 2 166.003 105 133.677 0

Max. Amt. of Undercut. (ft)

3.749 2 4.255 105 0.881 0.417

SignificanceVariables

Cluster Error

F-test

Mean Square

Degrees of

freedom

Mean Square

Degrees of

freedomlog Slope Height (ft)

4.389 2 0.432 105 10.154 0

Slope Angle 5906.073 2 81.54 105 72.431 0

Slake Durability Index (%)

22190.77 2 166.003 105 133.677 0

Variables

Cluster Error

F-test Significance

Slope Height

Slake D

urabilit

y Index

Slope Angle

3 Point/(1) 9 Points/(2) 27 Points/(3) 81 Points/(4)

90-100% 75-90% 50-75% <50%

0-1 ft 1-2 ft 2-4 ft >4 ft

Discont. joints, favorable

orientation

Discontinuous joints, random

orientation

Discontinuous joints, adverse

orientation

Continuous joints, adverse

orientation

20 15 10 5

1 ft/ 3 yd3 2 ft/ 6 yd3 3 ft/ 9 yd3 4 ft/ 12 yd3

No water seeps on slope

A few water seeps on slope

Many water seeps on slope

Numerous water seeps on

slope

<1 1-1.5 1.5-2.5 >2.5

Adequate sight distance (>100%)

Moderate sight distance (75%)

Limited sight distance (50%)

Very limited sight distance

(< 50%)50 feet 40 feet 30 feet 20 feet

No falls A few falls Many falls Numerous Falls

Ritchie Score

TRAFFIC PARAMETERS

EVALUATION PARAMETERS

Block Size/Volume of Rock Fall

Hydrologic Conditions

GEOLOGIC PARAMETERS

RATING SCORES FOR DIFFERENT CATEGORIES OF EVALUATION PARAMETERS

GEOMETRIC PARAMETERS

Dis

cont

inui

ty

Asp

ect

Diff

eren

tial

Wea

ther

ing

Discontinuity Extent/Orientation

Joint Roughness Coefficient

Posted Speed Limit (mph)ADT (cars/day) x Slope Length 25% of time

(very low)50% of time

(low)75% of time

(medium)100% of time

(high)

Geol

ogic

Con

ditio

nsSlake Durability

IndexMax. Amount of

Undercutting

% Decision Sight Distance

Pavement Width

ROCKFALL HISTORY

x100%

GEOLOGIC PARAMETERS

Differential Erosion

SDI (a) (g)Maximum Amount of Undercutting (b)Total (a+b) (c)

Block size (h)Discontinuities Role (i)

Discontinuity Extent/Orientation (d)Discontinuity Surface Features (e) Total (g+h+i)/4 (j)Total (d+e) (f)

GEOMETRIC PARAMETERS

Ritchie's Score (n)

TRAFFIC PARAMETERS

AVR (o)% DSD (p)Pavement Width (q)Total (o+p+q)/3 (r)

ROCK FALL HISTORY

History (s)

OVERALL SCORE

Lines (j+n+r+s)

Hydro/Climate

Greater Value (c or f)

Applying Rating Matrix to Data SetEach of the 108 sites were rated

Each site was then ranked in order from highest ranking to lowest ranking

Ratings ranged from 156 to 123Average rating was 80Median of ratings was 30

Hazard PotentialSites were assigned a hazard potential from ratings:

High Hazard potential (greater than 100)Moderate Hazard Potential (between 50 and 100)Low Hazard Potential (less than 50)

Hydrologic Overall Scores

(%)

Expo

nent

ial S

cale

(ft)

Expo

nent

ial S

cale

(ft)

Expo

nent

ial S

cale

Expo

nent

ial S

cale

Sum

Exp

onen

tial/4

exp

-sdi

/3

Ritc

hie

Scor

eEx

pone

ntia

l Sca

le w

ith

E qua

tion

Form

ula

Calc

ulat

ion

exp

Expo

nent

ial S

cale

with

e q

uatio

n(%

)

Expo

nent

ial S

cale

(ft)

exp

Expo

nent

ial S

cale

with

E q

uatio

nsu

m e

xp e

q

Sum

Exp

onen

tial/3

Sum

Exp

onen

tial/3

JEF-7-5B 91 3 6.0 81 2 27 81 48 63 2.3 70 280 81 81 100 3 33 81 31 115 38 156.6

COL-7-2.8 34 81 0.0 3 2 27 81 35 37 1.4 31 70 27 22 100 3 43 9 8 33 11 76.1

SUM-76-20 100 3 2.0 9 0.8 3 81 6 31 0.9 3 536 81 81 100 3 47 9 5 89 30 38.5

Traffic Parameter

Score

Site

Geometric Parameter

ScoreOregon Vehicle Risk

% Decision Site Distance

Roadway Width

Slake Durability

Index

Max. Amt. of Undercu

Block Diameter

Geological Parameter

Score

Examples of Ratings

Related Research ProjectsEvaluation of Catchment Ditches in the State of Ohio

Jesse Davis

Development of A Geographic Information System Data Base for Rock Fall Ratings in the State of Ohio

Carl Dokter

AcknowledgementsOhio Department of Transportation

Kirk Beech

Michael Baker Jr., Inc.