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**FHWA-CFL/TD-06-006
November 2006
Federal Highway Administration
U.S. Department of Transportation**

Central Federal Lands Highway Division 12300 West Dakota Avenue

Lakewood, CO 80228

**Publication No. FHWA-CFL/TD-06-006
November 2006**

**Central Federal Lands Highway Division 12300 West Dakota Avenue
Lakewood, CO 80228**

The Federal Lands Highway (FLH) of the Federal Highway Administration (FHWA) promotes development and deployment of applied research and technology applicable to solving transportation-related issues on Federal lands. The FLH provides technology delivery, innovative solutions, recommended best practices, and related information and knowledge sharing to Federal agencies, Tribal governments, and other offices within the FHWA.

The objective of this study is to review existing analytical methods and construction techniques currently in use for design and construction of rockeries and to develop a unified framework for design and specification of rockeries in modem highway construction. The ultimate goal of the project is to provide designers, inspectors, and contractors with a basis for evaluating existing rockeries and specifying and constructing new rockeries.

James W. Keeley, P.E., Director of Project Delivery

Federal Highway Administration

Central Federal Lands
Highway Division

This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document. This report does not constitute a standard, specification, or regulation.

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the objective of the document.

The Federal Highway Administration (FHWA) provides high-quality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.

1. Report No.FHWA-CFL/TD-06-006 |
2. Government Accession No. |
3. Recipient's Catalog No. |
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4. Title and Subtitle Rockery Design And Construction Guidelines |
5. Report DateNovember 2006 |
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6. Performing Organization Code |
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7. Author(s)Darren A. Mack, P.E., Steven H. Sanders, P.E., William L. Millhone, P.E., Renée L. Fippin, P.E., Drew G. Kennedy, P.G. |
8. Performing Organization Report No. |
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9. Performing Organization Name and AddressSanders & Associates Geostructural Engineering, Inc. (SAGE) 4180 Douglas Boulevard, Suite 100 Granite Bay, California 95746 |
10. Work Unit No. (TRAIS) |
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11. Contract or Grant No.DTFH68-05-P-00120 |
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12. Sponsoring Agency Name and AddressFederal Highway Administration Central Federal Lands Highway Division 12300 W. Dakota Avenue, Suite 210 Lakewood, CO 80228 |
13. Type of Report and Period Covered
Final Report April 2006 to November 2006 |
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14. Sponsoring Agency CodeHFTS-16.4 |
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15. Supplementary NotesCOTR: Khamis Haramy, FHWA-CFLHD; Advisory Panel Members: Scott Anderson, FHWA-FLH; Daniel Alzamora, FHWA-RC; Rich Barrows, FHWA-WFLHD; Khalid Mohamed, FHWA-EFLHD; and Roger Surdahl, FHWA-CFLHD. This project was funded under the FHWA Federal Lands Highway Technology Deployment Initiatives and Partnership Program (TDIPP). |
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16. AbstractRockeries consist of earth retaining and/or protection structures comprised of interlocking, dry-stacked rocks without mortar or steel reinforcement. They have been used for thousands of years and rely on the weight, size, and shape of individual rocks to provide overall stability. Some of the earliest rockeries constructed by the Federal Government date back to 1918. Within the private sector, commercially built rockeries have been constructed in the Pacific Northwest for at least the last four decades and in Northern California and Nevada for at least the last 10 years. As rockery design procedures tend to vary regionally, studies were performed to determine the methods by which rockeries are designed and constructed in various regions throughout the western United States. These design methods were then compared using several typical rockery design loading conditions to determine how the resulting rockery designs differ and which methods are most appropriate for a proposed design for the FHWA's FLH Divisions. Based on the research performed, a rational design methodology, which evaluates rockery stability as a function of the rockery geometry (height, base width, and batter), rock properties and placement, and lateral pressure imposed by the backfill materials, was developed. A sample design problem is included. Recommendations for specifying and constructing rockeries that are consistent with the design methodology are also provided. |
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17. Key WordsROCKERY, ROCKERIES, EARTH RETENTION, ROCK WALLS, LATERAL EARTH PRESSURE, GEOPHYSICAL EVALUATION METHODS |
18. Distribution StatementNo restriction. This document is available to the public from the sponsoring agency at the website http://www.cflhd.gov. |
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19. Security Classif. (of this report)Unclassified |
20. Security Classif. (of this page)Unclassified |
21. No. of Pages178 |
22. Price |

APPROXIMATE CONVERSIONS TO SI UNITS | ||||
---|---|---|---|---|

Symbol | When You Know | Multiply By | To Find | Symbol |

LENGTH |
||||

in | inches | 25.4 | millimeters | mm |

ft | feet | 0.305 | meters | m |

yd | yards | 0.914 | meters | m |

mi | miles | 1.61 | kilometers | km |

AREA |
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in^{2} |
square inches | 645.2 | square millimeters | mm^{2} |

ft^{2} |
square feet | 0.093 | square meters | m^{2} |

yd^{2} |
square yard | 0.836 | square meters | m^{2} |

ac | acres | 0.405 | hectares | ha |

mi^{2} |
square miles | 2.59 | square kilometers | km^{2} |

VOLUME |
||||

fl oz | fluid ounces | 29.57 | milliliters | mL |

gal | gallons | 3.785 | liters | L |

ft^{3} |
cubic feet | 0.028 | cubic meters | m^{3} |

yd^{3} |
cubic yards | 0.765 | cubic meters
NOTE: volumes greater than 1000 L shall be shown in m |
m^{3} |

MASS |
||||

oz | ounces | 28.35 | grams | g |

lb | pounds | 0.454 | kilograms | kg |

T | short tons (2000 lb) | 0.907 | megagrams (or "metric ton") | Mg (or "t") |

TEMPERATURE (exact degrees) |
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°F | Fahrenheit | 5 (F-32)/9 or (F-32)/1.8 | Celsius | °C |

ILLUMINATION |
||||

fc | foot-candles | 10.76 | lux | lx |

fl | foot-Lamberts | 3.426 | candela/m^{2 } |
cd/m^{2} |

FORCE and PRESSURE or STRESS |
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lbf | poundforce | 4.45 | newtons | N |

lbf/in^{2} |
poundforce per square inch | 6.89 | kilopascals | kPa |

APPROXIMATE CONVERSIONS FROM SI UNITS | ||||

Symbol |
When You Know |
Multiply By |
To Find |
Symbol |

LENGTH |
||||

mm | millimeters | 0.039 | inches | in |

m | meters | 3.28 | feet | ft |

m | meters | 1.09 | yards | yd |

km | kilometers | 0.621 | miles | mi |

AREA |
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mm^{2} |
square millimeters | 0.0016 | square inches | in^{2} |

m^{2} |
square meters | 10.764 | square feet | ft^{2} |

m^{2} |
square meters | 1.195 | square yards | yd^{2 } |

ha | hectares | 2.47 | acres | ac |

km^{2} |
square kilometers | 0.386 | square miles | mi^{2} |

VOLUME |
||||

mL | milliliters | 0.034 | fluid ounces | fl oz |

L | liters | 0.264 | gallons | gal |

m^{3} |
cubic meters | 35.314 | cubic feet | ft^{3} |

m^{3} |
cubic meters | 1.307 | cubic yards | yd^{3} |

MASS |
||||

g | grams | 0.035 | ounces | oz |

kg | kilograms | 2.202 | pounds | lb |

Mg (or "t") | megagrams (or "metric ton") | 1.103 | short tons (2000 lb) | T |

TEMPERATURE (exact degrees) |
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°C | Celsius | 1.8C+32 | Fahrenheit | °F |

ILLUMINATION |
||||

lx | lux | 0.0929 | foot-candles | fc |

cd/m^{2} |
candela/m^{2} |
0.2919 | foot-Lamberts | fl |

FORCE and PRESSURE or STRESS | ||||

N | newtons | 0.225 | poundforce | lbf |

kPa | kilopascals | 0.145 | poundforce per square inch | lbf/in^{2} |

- EXECUTIVE SUMMARY
- CHAPTER 1 - INTRODUCTION
- CHAPTER 2 - SURVEY OF EXISTING DESIGN METHODS
- CHAPTER 3 - COMPARISON OF EXISTING DESIGN METHODS
- CHAPTER 4 - RECOMMENDED ROCKERY DESIGN GUIDELINES
- CHAPTER 5 - ROCKERY CONSTRUCTION GUIDELINES
- CHAPTER 6 - CONSTRUCTION INSPECTION GUIDELINES
- CHAPTER 7 - EVALUATION OF EXISTING ROCKERIES
- CHAPTER 8 - GUIDE SPECIFICATIONS
- REFERENCES
**LIST OF FIGURES**- Figure 1. Photograph. Failure of non-engineered rockery in El Dorado Hills, California, 2004
- Figure 2. Graphic. Diagram showing definitions of height (H), base width (B), face batter, and relative rock sizes
- Figure 3. Photograph. Hadrian's Wall, Scotland
- Figure 4. Photograph. Rockery construction at Machu Picchu, Peru
- Figure 5. Photograph. Approximately 9.1-m-tall (30-ft-tall) rockery outside La Grange, California, dating from the late 1800s
- Figure 6. Graphic. Typical rockery section from Guanella Pass bid documents
- Figure 7. Graphic. Typical rockery schedule from Guanella Pass bid documents
- Figure 8. Photograph. Completed rockery for Guanella Pass Road, Colorado, 2005
- Figure 9. Chart. Critical height-to-base-width (H/B) ratios for poorly constructed rockeries (PCRs) and well-constructed rockeries (WCRs), after Hendron
- Figure 10. Graphic. Sample calculation from the Hemphill report demonstrating application of the Hemphill design method
- Figure 11. Photograph. Single-tier, 3-m (10-ft) rockery, Military Road at Enchanted Parkway, Federal Way, Washington (Site 1)
- Figure 12. Photograph. Two-tier, 7.3-m (24-ft) rockery, 15th Avenue at 12th Street, Puyallup, Washington (Site 2), with guy wire anchored at base of rockery
- Figure 13. Photograph. Single-tier, 1.2-m (4-ft) rockery near state capital building, Olympia, Washington (Site 3)
- Figure 14. Photograph. Single-tier, 2.4-m (8-ft) rockery, Nisqually National Wildlife Refuge, Washington (Site 4)
- Figure 15. Photograph. Single-tier, 7.6-m (25-ft) rockery in Tacoma, Washington (Site 5)
- Figure 16. Equation. Height-to-base-width (H/B) as a function of factor of safety, rockery inclination, backslope inclination, and soil and rock properties, from Gray & Sotir
- Figure 17. Equation. Definition of the term "b" in Figure 16
- Figure 18. Graphic. Assumed geometric relationships to be used for equations shown in Figures 16 and 17
- Figure 19. Photograph. Single-tier rockery constructed in cut condition, El Dorado Hills, California (2001)
- Figure 20. Photograph. "Protecting" rockery used as a facing for a 9.1-m-high (30- ft-high) MSE wall with a 5.5-m (18-ft) maximum tier height in Henderson, Nevada (2001)
- Figure 21. Photograph. "Protecting" rockery used as a facing material for a two-tier, 7.6-m-high (25-ft-high) soil-nail wall in Rocklin, California (1999)
- Figure 22. Photograph. Three-tier, 9.1-m-high (30-ft-high) MSE slope with protecting rockery facing, in Folsom, California (2003)
- Figure 23. Graphic. Design geometry for example design Cases #1 and #2
- Figure 24. Graphic. Design geometry for example design Cases #3 and #4
- Figure 25. Equation. Computation of active earth pressure coefficient (K
_{A}) by the Coulomb method - Figure 26. Equation. Corrected equation for height-to-base-width (H/B) ratio for use with Gray & Sotir analysis method
- Figure 27. Equation. Corrected definition of the term "b" in Figure 18
- Figure 28. Graphic. Assumed geometric relationships to be used for equations shown in Figures 25, 26, and 27
- Figure 29. Chart. Typical chart plotting slope inclination (a) vs. height-to-base- width (H/B) ratio using the Gray & Sotir method. Chart developed for φ = 32º, γ = 18.8 kN/m
^{3}(120 pcf), and FS = 2 - Figure 30. Graphic. Schematic rockery section showing critical dimensions and parameters to be determined for design
- Figure 31. Equation. Determination of lateral earth pressure coefficient, KA, using the Coulomb method
- Figure 32. Equation. Horizontal force on back of rockery, equal to the sum of the lateral earth pressure and any surcharge loads
- Figure 33. Graphic. Estimation of rockery weight and centroidal distances
- Figure 34. Equation. Computation of frictional resistance along the base of the rockery
- Figure 35. Equation. Evaluation of passive resistance at the rockery toe
- Figure 36. Equation. Expression for factor of safety against sliding (FS
_{SL}) - Figure 37. Equation. Determination of overturning moments about the toe of the rockery
- Figure 38. Equation. Determination of resisting moments about the toe of the rockery
- Figure 39. Equation. Determination of factor of safety against overturning
- Figure 40. Equation. Calculation of internal overturning moment at a distance H' from the base of the rockery
- Figure 41. Equation. Calculation of internal resisting moment at a distance H' from the base of the rockery, with outermost bearing distance x' from the face of rockery
- Figure 42. Graphic. Geometric relationships for determination of internal stability
- Figure 43. Equation. Determination of eccentricity, e, about the center of a base rock of width B
- Figure 44. Equation. Determination of maximum bearing pressure (qmax) applied at the toe of the base rock
- Figure 45. Equation. Determination of the term q for computation of KAE by the Mononobe-Okabe procedure
- Figure 46. Equation. Determination of term KAE in accordance with the Mononobe- Okabe procedure
- Figure 47. Equation. Determination of total thrust (seismic plus static) on rockery in accordance with the Mononobe-Okabe procedure
- Figure 48. Equation. Vertical distance (z) from the base of the rockery to the point of application of F
_{AE}along the back of the rockery - Figure 49. Equation. Determining overturning moment for seismic conditions
- Figure 50. Equation. Determining resisting moment for seismic conditions
- Figure 51. Equation. Determining horizontal driving force to check sliding for seismic conditions
- Figure 52. Equation. Determining horizontal resisting force to check sliding for seismic conditions
- Figure 53. Equation. Determining eccentricity under seismic conditions
- Figure 54. Equation. Determining maximum applied bearing pressure under seismic conditions
- Figure 55. Graphic. Minimum embedment required for a sloping toe condition
- Figure 56. Graphic. Example of embedment requirements for a rockery adjacent to a roadway with a drainage ditch subject to potential scour
- Figure 57. Graphic. Typical gravel leveling pad beneath base rocks (partial elevation)
- Figure 58. Graphic. Typical step in rockery foundation (partial elevation)
- Figure 59. Graphic. Typical planar failure on an adversely oriented discontinuity that daylights in the back cut
- Figure 60. Graphic. Typical wedge failure on two intersecting discontinuities with a line of intersection that daylights in the back cut
- Figure 61. Graphic. "Rectangular" and "matched irregular" facing rocks (partial elevation)
- Figure 62. Photograph. Hydraulic excavator with a clamshell constructing a rockery
- Figure 63. Photograph. Placement of facing rocks using an excavator with a "thumb."
- Figure 64. Graphic. Base rock tolerances and use of two base rocks to achieve "B" (partial plan view)
- Figure 65. Graphic. Examples of acceptable and unacceptable rockery alignment
- Figure 66. Graphic. Examples of improper rock placement (partial elevation)
- Figure 67. Photograph. Example of a relatively well constructed rockery
- Figure 68. Photograph. Example of an unacceptable rock bearing
- Figure 69. Photograph. Example of improper rock bearing and lack of chinking
- Figure 70. Graphic. Backdrain components (partial section)
- Figure 71. Photograph. Example of crushed rock placed behind rockery
- Figure 72. Photograph. Placement of drain blanket and non-woven geotextile behind rockery
- Figure 73. Graphic. V-Ditch and impermeable cap at top of rockery (partial section)
- Figure 74. Photograph. Example of proper layout, interlock, and chinking of variable shape and size rocks
- Figure 75. Photograph. Example of improper rockery layout evidences by vertical seams and rocks inclined out of face
- Figure 76. Photograph. Example of improper rockery layout evidenced by several vertical seams
- Figure 77. Equation. Determination of horizontal seismic coefficient, kh (Δ in inches)
- Figure 78. Equation. Computation of inertial thrust coefficient
- Figure 79. Equation. Computation of weight required to resist seismic forces
- Figure 80. Equation. Seismic factor of safety with regard to wall movement
- Figure 81. Graphic. Assumed Geometry for Example Problem - 2400 mm (8 ft) rockery retaining medium dense clayey sand and subjected to a vehicle surcharge.

**LIST OF TABLES**- Table 1. Comparison of man rock definitions
- Table 2. Summary of rockery observations following the 2001 Nisqually earthquake
- Table 3. Comparison of prescriptive design methods in different cities
- Table 4. Comparison of analytical design methods
- Table 5. Soil and rockery properties used for benchmarking of analysis procedures
- Table 6. Comparison of computed base rock widths using four design methods
- Table 7. Typical friction factors for determination of FS
_{SL} - Table 8. Recommended factors of safety for static and seismic rockery design
- Table 9. Gradation Requirements for crushed rock backdrain
- Table 10. Physical properties requirements for non-woven geotextiles (from FP-03, Section 714, Type I-B geotextiles)

A - Acceleration Coefficient per AASHTO Division I-A, Section 3

A* - Amplified peak acceleration

A_{a}, A_{v} - Acceleration coefficients per ATC-3-06

AASHTO - American Association of State Highway Transportation Officials

A.D. - Latin, *Anno Domini, *current calendar epoch

AOS - Apparent Opening Size

a_{peak} - Peak spectral acceleration, gravity (g)

ARC - Associated Rockery Contractors

ASTM - American Society of Testing and Materials

ATC - Applied Technology Council

B - Base rock width, m

BMP - "Best Management Practices" as related to site erosion, sediment, and runoff control and reduction

c, c' - Total and effective soil cohesion values, respectively, in kPa. Although effective stresses are most typically used, the term "c" is commonly used throughout this report.

ca. - Latin, *circa, *meaning "about" for dates that are approximately known

CalTrans - State of California, Department of Transportation

cF, c'F - Total and effective soil cohesion values in the foundation soil, in kPa

CFLHD - Central Federal Lands Highway Division

C_{IE} - Seismic inertial coefficient

CO - Contracting Officer

d - Depth of soil to neglect when computing passive resisting force, μ d_{peak} - Peak spectral displacement, cm

D_{peak} - Embedment depth at toe of rockery, m

D* - Amplified peak displacement

e - Moment eccentricity relative to center of base rock, m

e_{s} - Moment eccentricity relative to center of base rock due to seismic forces, m

EFP - Equivalent fluid pressure applied by soil, kN/m^{3}

EPA - Effective peak acceleration, g

EPV - Effective peak velocity, cm/s

F_{A} - Active earth pressure force acting on the back of the rockery

F_{A,H} - Horizontal component of active earth pressure force kN (per meter of rockery)

F_{A,V} - Vertical component of active earth pressure force, kN (per meter of rockery)

F_{AE} - Total static plus seismic thrust acting on rockery, kN (per meter of rockery)

ΔF_{AE} - Incremental seismic thrust acting on rockery, kN (per meter of rockery)

F_{H} - Sum of static horizontal driving forces acting on rockery, kN (per meter of rockery)

F_{H,S} - Sum of static and seismic horizontal driving forces acting on rockery, kN (per meter of rockery)

FHWA - Federal Highway Administration

FLH - Federal Lands Highway

Foundation Fill - Material conforming to Section 704.01 of the FHWA Standard Specifications (FP-03)

F_{p} - Passive resisting force on toe of rockery, kN (per meter of rockery)

F_{s} - Horizontal resultant force due to application of vertical surcharge load, kN (per meter of rockery)

F_{μ} - Static resisting friction force of bottom of base rock, kN (per meter of rockery)

F_{μ,S} - Static and seismic resisting friction force of bottom of base rock, kN (per meter of rockery)

FS - Factor of safety

FS_{BC} - Factor of safety with respect to bearing capacity

FS_{OT} - Factor of safety with respect to external overturning

FS_{OT_INT} - Factor of safety with respect to internal (inter-rock) overturning

FS_{seismic}_{} - Factor of safety with respect to required rockery weight to limit rockery displacement to Δ or less

FS_{SL} - Factor of safety with respect to base sliding

GPR - Ground penetrating radar, a type of geophysical evaluation method

H - Rockery height, m

H/B - Height-to-base-width ratio

HDPE - High density polyethylene, usually referring to a type of plastic pipe

HEC - Hydraulic Engineering Circular

HP - Ultraseismic Horizontal Profiling Method, a type of geophysical surface wave method

i - Slope inclination, measured up from horizontal, per A. J. Hendron, Jr., methodology

IR - Impulse Response, a type of geophysical surface wave method

K_{A} - Coefficient of active earth pressure

K_{AE} - Lateral earth coefficient for computation of static plus seismic thrust force

k_{h} - Horizontal seismic coefficient

K_{p} - Coefficient of passive earth pressure

k_{v} - Vertical seismic coefficient

LTDS - Long term design strength of geogrid reinforcement

MARV - Minimum Average Roll Values

M_{o} - External overturning moment about toe of rockery imposed by lateral earth pressure (horizontal component) and surcharge loads, kN - μ (per meter of rockery)

M_{o,s} - External overturning moment due to static and seismic loads, kN - μ (per meter of rockery)

M_{o_int} - Internal (inter-rock) overturning moment about toe of intermediate rock imposed by lateral earth pressure (horizontal component) and surcharge loads, kN - μ (per meter of rockery)

M_{r} - External resisting moment about toe of rockery imposed by rockery weight, lateral earth pressure (vertical component), and passive pressure, kN - μ (per meter of rockery)

M_{r,s} - External resisting moment about toe of rockery imposed by rockery weight and vertical components of static and seismic lateral earth pressures kN - μ (per meter of rockery)

M_{r_int} - Internal resisting moment about toe of intermediate rock imposed by partial rockery weight, lateral earth pressure (vertical component), and passive pressure, kN - μ (per meter of rockery)

MSE - Mechanically stabilized earth or embankment

OSHA - Occupational Safety and Health Administration

PCR - Poorly constructed rockery as defined by A. J. Hendron, Jr.

PGA - Peak ground acceleration, g

PS - Parallel Seismic, a type of geophysical cross-hole logging method

PVC - Polyvinyl chloride, a type of plastic pipe

q_{max} - Maximum applied bearing pressure at toe of base rock due to moment eccentricity, kPa

q_{max,s} - Maximum applied bearing pressure at toe of base rock due to moment eccentricity under seismic loading, kPa

q_{s} - Vertical surcharge pressure acting on the ground surface behind the rockery, kPa

RSP - Rock slope protection, e.g., riprap

RSS - Reinforced soil slope

SAGE - Sanders & Associates Geostructural Engineering, Inc.

SE - Sonic Echo, a type of geophysical surface wave method

T_{a} - Allowable tensile strength for geotextile soil reinforcement, equal to LTDS/FS

UBC - Uniform Building Code

U.S. - United States

UV - Ultraviolet light, such as sunlight

v_{peak} - Peak spectral velocity, cm/sec

V* - Amplified peak velocity

W - Total weight of rockery (unit width basis), kg

WCR - Well-constructed rockery as defined by A. J. Hendron, Jr.

W_{i} - Weight of rockery component (unit width basis), kg

x_{i} - Moment arm from toe of rockery to centroid of mass for rockery component, m

z - Point of application of F_{AE}, measured vertically from base of rockery, m

Δ - Tolerable rockery displacement for Richards and Elms analysis, in

ΔF_{AE} - Incremental seismic thrust acting on rockery, kN (per meter of rockery)

α - Angle, measured up from the horizontal, to the back cut or rear face of rockery, degrees. Positive angle is defined as face of back cut sloping up and away from the base of the rockery, starting from the bottom of the cut.

αA, αV, αD - Newmark and Hall amplification factors

β - Retained ground surface inclination ("backslope"), degrees. Positive angle if slope increases in height with increasing distance from the back of the rockery.

δ - Interface friction angle between retained soil and back of rockery/crushed rock backfill zone, degrees

φ, φ' - Total and effective soil friction angle / angle of internal friction, respectively. Although effective stresses are most typically used, the term "f" is commonly used throughout this report.

φCR - Friction angle (effective or total) of crushed rock backfill

φF - Friction angle (effective or total) of foundation soil and soil at toe of rockery

γ, γs - Density of retained soil, kN/m^{3}

γCR - Density of crushed rock backfill (net density, including voids), kN/m^{3}

γR - Density of rockery facing (net density, including voids), kN/m^{3}

γF - Density of foundation soil, kN/m^{3}

μ - Friction factor for sliding

ψ - Back cut inclination, degrees

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