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GUIDE TO THE DESIGN OF TERRA FORCE Ll3

RETAINING WALLS

HAWKINS HAWKINS & OSBORNE Consulting Engineers

GUIDE TO THE DESIGN OF TERRAFORCE L13 RETAINING WALLS prepared for TERRAFORCE (PTY) LTD P O BOX 1453 CAPE TOWN 8000 by HAWKINS HAWKINS & OSBORN CONSULTING ENGINEERS P O BOX 244 RIVONIA 2128 300375/W G Technau October 1992


GUIDE TO THE DESIGN OF TERRAFORCE L13 RETAINING WALLS INDEX Page PART 1 : THE TERRAFORCE L13 BLOCK RETAINING WALL .................................. 3 - 10 PART 2 : USER GUIDE FOR PRACTICAL APPLICATIONS ......................................... 11 - 72 PART 3 : THEORETICAL ANALYSIS AND DESIGN PROCEDURES ......................... 73 - 90 PART 4 : WORKED EXAMPLES ....................................................................................... 91 - 110 PART 5 : REPORT ON LABORATORY TESTS ............................................................... 111–128 ANNEXURES A AND B……………………………………………………………………… 129 - 147 Copyright (c) 1992 by TERRAFORCE (PTY) LTD All rights reserved. This document or any part thereof may not be reproduced in any form without the

written permission of the publisher.


PART 1: THE TERRAFORCE L13 BLOCK RETAINING WALL INDEX Page 1.1 The System .................................................................................................................. 5 1.2 The Application .................................................................................................................. 6 1.3 The Product .................................................................................................................. 7 1.4 Statutory Provisions ............................................................................................................. 8 1.5 The Professional Service ..................................................................................................... 8 1.6 Users Responsibility ............................................................................................................ 8 1.7 Disclaimer .................................................................................................................. 9


PART 1: THE TERRAFORCE L13 BLOCK RETAINING WALL 1.1 The System Terraforce L13 provides a simple, versatile and cost effective solution to earth retaining

problems. With the blocks stacked at a predetermined inclination, the wall is able to serve as a conventional gravity retaining structure.

The unique shape of these durable precast concrete blocks allows the wall to follow virtually any

desired curvature. The bottomless pots also lend themselves ideally for the establishment of plant growth.


1.2 The Application Terraforce is adaptable to a wide range of site conditions and can be used not only for the

construction of featuresque terraces in domestic gardens, but also for purposefully designed retaining walls in the development of school and sport facilities, townships and industrial complexes.

The construction of a Terraforce Wall is labour intensive and usually does not require

sophisticated building equipment or highly skilled techniques. Practical installation guidelines and typical construction details are described and illustrated in a

separate manual, "TERRAFORCE CONSTRUCTION", obtainable on request.


1.3 The Product (a) Technical Specifications: Length = 340mm Width = 425mm Height = 222 ± 3mm Wall thickness = 50mm Units per m2 of wall = 13 Mass of empty block = 28 - 35 kg Volume of infill = 16 ltr Mass of infill: top soil = 18 kg dense sand = 27 kg concrete = 35 kg Avg. unit mass of wall = ± 760 kg Min. crushing strength of a block under in-situ loading = 8 MPa Min. frictional resistance between blocks without keys: Cf = 0,54 (b) Quality Control: Terraforce L13 blocks are available countrywide (and in other countries) from a number

of manufacturers who apply strict control on the materials used and the maintenance of the dimensional standards for product integrity in terms of their quality management system.

(c) Non-Standard Requirements Modifications can easily be made to the concrete mix design to suit specific

applications, e.g. where a wall is to be constructed in an aggressive environment. Coastal conditions in particular, require that the blocks are made of a stronger concrete to achieve improved durability.


1.4 Statutory Provisions The construction of these so-called "dry stacked" gravity retaining walls has as yet not been

covered by a particular Standard Specification. Often however, such a wall could influence the integrity of any adjoining property, building,

service or excavation. In terms of the South African National Building Regulations [1], it is therefore required that this kind of wall structure shall be designed by a competent person to provide strength, stability, serviceability and durability in accordance with accepted principles of structural design.

1.5 The Professional Service a) Design: The structural design for the safety and stability of the wall under most common

applications is provided in these guidelines. The suitably engineered design charts present an easy method to determine the desired inclination of the wall for a given height of embankment and back slope, taking due account of the prevailing material properties.

Extended applications which fall outside the scope of the design charts, can however,

be designed individually by a qualified engineer. b) Construction Supervision and Certification: Where a local authority requires certification of the design and construction of a

Terraforce retaining wall on a project, this service can be provided via the manufacturer by a professional engineer.

1.6 User Responsibility Like any other manufactured product which is commercially available, Terraforce L13 is

designed for a specific range of applications. Although very wide, the range does have natural limitations.

The design guides presented here can only cover general application cases and it is therefore the

responsibility of the user to ensure that his (or her) particular application has had the requisite engineering input.


1.7 Disclaimer Although every reasonable effort has been made to ensure that the technical information and the

design procedures presented in this Guide are correct, neither Terraforce (Pty) Ltd and any manufacturer of the product, nor their consultants, who have contributed to the preparation of these guidelines, will be held liable for any loss or damage, either direct or consequential, arising from any failure or collapse of a wall of any description constructed with Terraforce L13 precast concrete blocks.

As with any structure, the design of Terraforce retaining walls should only be undertaken by

suitably qualified and experienced designers with due cognisance being taken of the specific geotechnical conditions and vital soil parameters pertaining to the site.


PART 2: USER GUIDE FOR PRACTICAL APPLICATIONS


PART 2: USER GUIDE FOR PRACTICAL APPLICATIONS INDEX Page 2.1 Notation .................................................................................................................. 13 2.2 Principles of Gravity Retaining Wall Design ........................................................ 4 - 15 2.3 Choice of Design Parameters ................................................................................. 16 2.4 Design Charts and their Applications .................................................................... 17 - 19 2.5 Shear Keys ............................................................................................................. 20 - 21 2.6 Wall Foundations ................................................................................................... 22 - 23 2.7 Drainage ................................................................................................................. 24 - 25 2.8 Practical Limitations .............................................................................................. 26 2.9 Examples of Extended Applications ..................................................................... 27 - 33 2.10 Design Charts ......................................................................................................... 34 - 71


16 PART 2: USER GUIDE FOR PRACTICAL APPLICATIONS 2.1 Notation H = total height of wall (m) HO = height of wall without keys (m) HK = portion of wall height with keys (m) w = unit weight of wall (kN/m2) W = total weight of wall (kN/m) ß = inclination of wall (deg) i = slope of backfill (deg) φ = angle of internal friction of backfill (deg) δ = angle of friction between backfill and wall (deg) Cf = coefficient of friction between blocks b = width of block (m) γ = bulk density of backfill (kN/m3) ka = coefficient of active earth pressure P = total active thrust of retained material (kN/m) PH = horizontal component of active thrust (kN/m) PV = vertical component of active thrust (kN/m) a = lever arm of wall weight around toe (m) c = lever arm of earth pressure around toe (m) x = distance of resultant from toe (m) R = total resultant at base (kN/m) RH = horizontal component of resultant (kN/m) RV = vertical component of resultant (kN/m) SFO = safety factor against overturning SFS = safety factor against sliding DF = depth of foundation below final ground level (m) SB = horizontal setback of blocks related to wall inclination (mm) y = height above base where P is applied (m) po = intensity of uniformly distributed surcharge (kN/m2) C = cohesion factor RK = resistance produced by shear keys (kN/m) σb = block bearing stress (MPa) pb = min. crushing strength of blocks (MPa) tan μ = friction factor for base concrete on foundation material Rf = frictional resistance produced by founding material (kN/m)


2.2 Principles of Gravity Retaining Wall Design In the context of the described application, the Terraforce L13 wall is acting as a gravity

retaining wall. As such it is designed to resist, solely by its own weight and profile, within stipulated stability criteria, the thrust caused by the lateral earth pressure of the material retained (see Fig. 2.1).

The applicable earth pressures are determined by the classic soil mechanic theories developed

centuries ago by Coulomb and Rankine. The formulas established at the time for the evaluation of lateral earth pressures, today still form the basis of any retaining wall design.

The theory applies the principle that the structure has to resist the forces which are activated by a

nominal displacement of the failure wedge in the retained material. The displacement occurs once the wall is allowed to tilt or move outwards by a small amount. Under these conditions, the resultant forces acting on the wall are deflected by wall friction, which could be as large as the internal friction of the retained material.

The active earth pressure in this case is often called the "equivalent fluid pressure" and the

pressure distribution is assumed to be increasing linearly over the height of the wall. Coulomb's analysis of this principle and his formulation of the pressure coefficient ka, and the total thrust P, on the wall, have been adopted in the design procedures incorporated in these guidelines (see Fig. 2.1).

The aforementioned stability criteria which have to be satisfied in the design procedures are the

following: • The wall has to resist the overturning forces with a safety factor of equal to or

greater than 1,5. • The wall has to resist the horizontal sliding forces with a safety factor equal to or

greater than 1,30, assuming a friction coefficient of 0,54 between the wall elements. • The base of the wall has to be in compression over its full width, which is proven

when the resultant of the resisting forces acts inside the middle third of the base. Not only must these stability requirements be satisfied at the base, but also throughout the height

of the wall, which could feature flowerboxes, terraces, etc.


2 3

where


2.3 Choice of Design Parameters This manual covers the design of Terraforce L13 retaining walls when constructed under

conditions where: • the wall retains cohesionless material • water pressure build up is prevented in the embankment fill • no additional surcharge to the sloping backfill is placed on the embankment • the embankment fill is unreinforced • the resistance to the horizontal sliding forces is provided by suitable shear keys

where the inter-block sliding resistance is exceeded. These are considered to be the basic wall conditions for which the general engineering design is

provided by means of the enclosed design charts. These have been developed from multiple calculations governed by the stipulated stability criteria using the selected values of the varying material properties.

The theoretical formulations and detailed design procedures are explained in Part 3. The design for extended application under conditions where, for example:

• the wall has to retain backfill which is inundated for prolonged periods • the wall has to retain cohesive material • a surcharge, e.g. traffic or stored material, is placed on top of the embankment • a portion of the retained material is reinforced by means of stabilization or geofabrics

falls outside the scope of these guidelines. These cases can, however, be evaluated but require

substantial additional engineering input (see also Section 2.9).


2.4 Design Charts and their Applications The charts are designed to display the required wall inclination, ß, for the vertical wall height, H,

and the slope of the retained material, i. Both H and i are usually established values, having been initially determined from a survey of the terrain.

The top half of the chart displays the total height, H, while the bottom half shows the associated

portional height, HO, which does not require shear keys for the designed conditions. The height to which keys have to be incorporated in the wall, HK, is derived simply by subtracting HO from H (see the general design chart, Fig. 2.2).

Where i is supplied from the survey data as a ratio of the unit height to the horizontal length of

the incline, or alternatively as a percentage rise, this has to first be converted into degrees for further use in the charts.

The material properties which have a marked influence on the design are: • the angle of internal friction of the retained material, φ • the angle of friction between the surface of the wall and the retained material, δ • the moist density of the retained material, γ • the unit weight of the wall, w • the coefficient of friction between blocks, Cf. These critical material properties however, vary considerably under natural conditions in the

field. It is thus important that the in-situ properties are accurately assessed by a competent person prior to construction. This will enable the designer to choose the chart with the most suitable property combination for their design, or establish the wall inclination and height requiring keys for un-charted conditions by individual calculations using the basic theory (see Part 3).

Sets of commonly applicable values have been chosen and a number of charts have thus been

produced to display the effects of different combinations on the design of the wall (see Section 2.10).

The main chart (Fig. 2.2) is considered to represent situations which commonly occur in the

Witwatersrand area. The values chosen for the controlling properties in this case are: φ = 30 deg. being applicable for most silty sands, δ = 27 deg. being applicable under conditions where the backface of the wall is

in direct contact with the fill, γ = 19 kN/m3 being applicable to a material with a dry density of 16,5 kN/m3

and a moisture content of approximately 15%, w = 6 kN/m2 being applicable under conditions where the blocks are filled with

top soil only.


It will be observed that the graph lines in the charts are not uniformly spaced and deviate at

certain points. This is due to the following reasons: • In Range (1), the stability criterion of the resistance against overturning is the

governing factor in the design for the required wall inclination ß, for a given wall height H, with back slope i.

• In Range (2), the proof of no open joint at the base becomes more critical in the

determination of ß in terms of stability than for the previous criterion. • In Range (3), the key-less height HO is equal to the total height H of the wall and the

resistance against sliding is safely provided by the own weight of the wall. • In Range (4), the resultant of the applied forces is located in the middle third of the

base width of the wall. Under these conditions, the full weight of the wall, together with the installed shear keys over height HK, is providing the necessary resistance against sliding.

• In Range (5), the resultant of the applied forces is located beyond the middle third of

the base and extends even into the fill. This is brought about by applying the governing safety factor against overturning in the design for ß. The effect of this procedure is that the wall is shedding a portion of its own load onto the fill, in this height range. The resulting loss of vertical reaction at the base of the wall increases the requirement of the horizontal resistance which now has to be supplied by a greater number of shear keys in a proportionately higher HK section.

Only three values of the back slope i have been included in each chart. The maximum value of

this slope is always equal to the natural angle of repose, which is assumed to be the same as the angle of internal friction, φ. Any intermediate values of i can be linearly interpolated and the resulting wall inclination would still satisfy the governing stability criteria for the given

height H. The steps to be followed in the general design procedure for ß and HO are displayed, by means of

an example, in Fig. 2.2 for a chosen set of parameters: For the case with a total wall height, H = 3,8m, (Point 1) and a slope of backfill, i = 10 deg, find

the intersection point on the interpolated slope line (Point 2) and draw a line down to the required wall inclination ß (Point 3). Go back to Point 4 on the line where it intersects with the applicable slope line in the lower half of the chart, and go across to Point 5 to find the maximum height HO, which does not require shear keys. The minimum height with keys is then derived from HK = H - HO (Point 6).


2.5 Shear Keys The shear keys form an integral part of the wall structure (see Fig. 2.3). They have to be installed

over height HK, in which the horizontal sliding force exceeds the resistance given by the inter-block friction. The suitably designed and sized precast mortar (Class I) or cast in-situ concrete (15 MPa) keys have to be placed between the blocks in the backface of the wall. The keys have to be evenly distributed at a rate of 3 per m of the wall length in the bottom row of, for example, a 6m high wall. The numbers will then decrease proportionately to the level at the top of HK, where they are no longer required.

The keys provide an essential part of the overall sliding resistance developed by the wall.

Inadequate design or inaccurate placing could therefore lead to a critical failure of the structure. A designed upstand on the wall foundation must equally be provided to prevent the bottom row

of blocks from sliding off the base (see Fig. 2.4).


4 5

FIGURE 2.3.2: DETAILS OF SHEAR KEYS


2.6 Wall Foundations a) General In most cases, the Terraforce Wall requires foundations like any other load bearing structure. As an initial conservative guide, one should look for a founding material which is also suitable

for a typical strip foundation of a normal house with walls of a similar height as the one to be constructed. In such a case the applied bearing pressures under 3m high walls of a single storey house are approximately 50 kPa, and 80 to 100 kPa under 6m high walls of a double storey house. For walls under 1,5m, it is usually sufficient to place the bottom row of blocks, filled with concrete, on a level blinding.

Suitable guidance on the bearing capacities of the most common soils is also given in the SABS

0161 - 1980 "Code of Practice for the Design of Foundations for Buildings" [2]. b) Assessment of Founding Conditions If warranted by the purpose of the wall (see Sections 1.2 and 1.4), an experienced geotechnical

engineer or engineering geologist has to be consulted to assess the properties of the foundation material which have a critical influence on the stability of the structure. The governing properties which need to be tested, if necessary, are:

• the available bearing capacity • the sliding resistance • the density • the moisture content • the angle of internal friction • the heave and collapse potential of the founding material. The overall stability of the embankment must then also be checked for a possible deep-seated

failure through a slip circle analysis under conditions where weaker strata are present under the proposed foundation level.

In cases where the bearing capacity of the founding material is suspect, the ultimate bearing

capacity of the ground has to be evaluated in relation to the effective shear strength, density parameters and depth of foundation. The applicable analysis of this aspect is given by Terzaghi and Peck [3].

c) The Design With the limiting parameters known, the engineer then has to design the shape, size and depth of

the strip foundation to suit the applied founding pressure. In this process he has to take account of the settlement and stability criteria and possible fluctuations of the ground water level.

A typical foundation design is shown in Fig. 2.4. Details of the design procedure are given in

Part 3.


6

FIGURE 2.4: TYPICAL WALL FOUNDATION


2.7 Drainage Where a high water table could intersect with the wall, the thrust on the wall would rise to more

than double that created by a dry backfill. At the same time, the angle of internal friction of the retained material, the wall friction and the friction between the blocks would be substantially reduced. The allowable bearing and sliding resistance of the foundation material would be similarly affected. The wall would become unstable under such conditions and would be bound to fail.

It is therefore essential that the subsurface water flow is specifically investigated and assessed,

and that adequate facilities be provided in the backfill to prevent the associated build-up of pore pressure in the backfill material under these circumstances (see Fig. 2.5).

In this context the effects of leaking services located close to the wall would also have to be

investigated. Suitable measures also have to be considered for the effective drainage of surface water which

could undermine the foundations and erode the backfill at the crest of the wall and on its sides (see Fig. 2.5).


7

FIGURE 2.5: TYPICAL DETAILS OF SUITABLE DRAINAGE MEASURES


2.8 Practical Limitations There are always some natural limitations for the application of a product. Some of the obvious

limitations for the unmodified single skin unreinforced Terraforce wall are described by the following:

a) Once a wall is designed and constructed to retain a given height and slope of

backfill, it cannot resist any additional surcharge located at its crest within a distance equal to its height, that is unaccounted for in the design.

b) The foundations of a wall must bear against undisturbed ground, which provides the

wall with the passive resistance against a sliding failure. Future services which require excavations at the toe of a wall will therefore have to be located a safe distance away from the foundation. This distance should be at least equal to three times the depth of the foundation.

c) Embankments of heaving or swelling clay should not be retained by this type of

wall. Apart from the possible build-up of critical pore pressure and the associated drainage problems, it would disturb the angle of inclination and make the wall unsafe.

d) The fill, which can never be fully compacted behind a flexible wall, is bound to

settle to some degree. It therefore prohibits the construction of rigid structures close to the top of the wall.

e) Although the flexibility of the wall is a great advantage for most applications, it can

cause uncontrolled load shedding in a rearranged matrix of blocks in cases where settlement occurs due to the failure of the weak foundation strata. The blocks are now subjected to splitting and crushing stresses which could, in the case of high walls, exceed their design strength. (This emphasises again the necessity of obtaining professional advice on the suitability of the founding conditions of a proposed wall.)


2.9 Examples of Extended Applications Very often it is found that the developer/town planner/architect has, for economic reasons of

land use, allowed only the smallest space for the positioning of a retaining wall, when required on a sloping property.

This problem can be solved to some degree, but requires certain modifications to the

configuration of the block wall, so that it can become steeper and cover less space, while still conforming to all the stability criteria.

Examples of this are: (See Fig. 2.6.) a) to increase the weight of the wall elements with concrete infill (see Chart No 142) b) to increase the leverage of the resisting forces by constructing the wall with a double

skin of blocks (see Chart No 202) c) to activate the weight of the backfill for additional overturning resistance by i) reinforcing the backfill with geotextile layers ii) stabilising the backfill with cement It must, however, be remembered that these applications influence the flexibility and plantability

aspects and also reduce the self-draining features of the wall. These effects should thus be evaluated beforehand in relation to the function of the structure. It must also be noted that the attached design charts, where applicable, present only a limited choice of variable parameters. Special cases therefore, have to be designed individually by a suitably experienced professional engineer.

Where, for example, it is anticipated that the undisturbed ground in front of the wall is to be

excavated for the laying of an underground service, measures have to be taken in advance to secure the stability of the wall. This can be achieved by constructing the foundations at a calculated level below the future excavation or by securing the then unrestricted horizontal forces with suitably designed layers of geotextiles placed in the backfill (see Fig. 2.7). In both cases the inclination of the wall would have to be redefined.

Another example of an extended application is found where one has some limited space

available and a choice of land use (see Fig. 2.8). In this case, it may be feasible to leave a portion of the embankment at its natural angle of repose

and construct a wall which is then designed for a sloping backfill. The smaller wall would clearly be less costly than a wall which has to extend to the full height of the embankment.

A further application is shown in Fig. 2.9, where a very high embankment could be suitably

covered by walls constructed on terraces.


8 9

FIGURE 2.6: EXAMPLE OF AN INCREASED WALL INCLINATION


10

FIGURE 2.7: ALTERNATIVE ARRANGEMENTS WHERE THE PLACING OF THE U/G SERVICE IS EXPECTED


11

FIGURE 2.8: A SMALLER WALL IN THE AVAILABLE SPACE


12

FIGURE 2.9: TERRACED EMBANKMENT


Finally, there is often the requirement to accommodate some kind of surcharge on the

embankment, close to the wall. This could be in the form of stored material or a defined TRAFFIC loading, which then has to be simulated by a uniformly distributed surcharge converted into an equivalent height of backfill (see Fig. 2.10).

Here it must be noted that all the Road and Rail authorities specify applicable traffic surcharge

loads, which are commonly used in bridge and retaining wall design. The TPA specifies, for example, an equivalent 0,6m height of fill as a normal traffic surcharge.

The inclination of the wall would have to be evaluated by the designer using the basic theoretical

principles. Special attention would also have to be given to the location of individual point loads, which may affect the stability of the upper rows of blocks in the wall (see Part 4: "Worked Example, Case III").


13 14

FIGURE 2.10: EXAMPLE OF AN APPLIED SURCHARGE


2.10 Design Charts The enclosed charts have been developed using the most common combination of different

material properties, and which are: φ = 25, 30, 35 deg. δ = 0,9 φ for soil in direct contact with the wall = 2/3 φ for geotextiles between the wall and fill γ = 19 kN/m3 for medium dense, moist residual granite = 17 kN/m3 for medium dense, moist windblown sand w = 6 kN/m2 for blocks filled with topsoil = 8 kN/m2 for blocks filled with concrete = 12 kN/m2 for a double row of blocks filled with topsoil The combinations of property values chosen for each chart are listed in the following Table of

Design Charts:

Design Chart

i (deg)

φ (deg)

δ (deg)

γ (kN/m3)

w (kN/m2)

b (m)

Chart 101 102 103

0/20/25 0/20/30 0/20/35

25 30 35

0,9φ

19

6

0,425

111 112 113

0/20/25 0/20/30 0/20/35

25 30 35

2/3φ

19

6

0,425

121 122 123

0/20/25 0/20/30 0/20/35

25 30 35

0,9φ

17

6

0,425

131 132 133

0/20/25 0/20/30 0/20/35

25 30 35

2/3φ

17

6

0,425

141 142 143

0/20/25 0/20/30 0/20/35

25 30 35

0,9φ

17

8

0,425


Design Chart

i (deg)

φ (deg)

δ (deg)

γ (kN/m3)

w (kN/m2)

b (m)

Chart 151 152 153

0/20/25 0/20/30 0/20/35

25 30 35

2/3φ

19

8

0,425

161 162 163

0/20/25 0/20/30 0/20/35

25 30 35

0,9φ

17

8

0,425

171 172 173

0/20/25 0/20/30 0/20/35

25 30 35

2/3φ

17

8

0,425

201 202 203

0/20/25 0/20/30 0/20/35

25 30 35

0,9φ

19

12

0,850

211 212 213

0/20/25 0/20/30 0/20/35

25 30 35

2/3φ

19

12

0,850

221 222 223

0/20/25 0/20/30 0/20/35

25 30 35

0,9φ

17

12

0,850

231 232 233

0/20/25 0/20/30 0/20/35

25 30 35

2/3φ

17

12

0,850


PART 3: THEORETICAL ANALYSIS AND DESIGN PROCEDURES


PART 3: THEORETICAL ANALYSIS AND DESIGN PROCEDURES INDEX Page 3.1 Introduction .................................................................................................................. 75 3.2 System Analysis 76 3.2.1 General .................................................................................................................. 76 3.2.2 Stability .................................................................................................................. 76 3.2.3 Sliding .................................................................................................................. 79 3.2.4 Crushing ................................................................................................................. 80 3.2.5 Foundation Design ................................................................................................. 82 3.3 Foundation Design for the case where a reaction is located behind the wall ..................... 86 3.4 References .................................................................................................................. 89


PART 3: THEORETICAL ANALYSIS AND DESIGN PROCEDURES 3.1 Introduction The main objective of the analysis is to determine a safe inclination, β, of the wall for a given

height, H, and backslope, i, in accordance with the applicable theory described in Part 2, Section 2.2.

The limiting design parameters chosen for the general configuration of the wall in this context

are those stated already in Section 2.3, nl: • cohesionless backfill • no water pressure • no surcharge • excess sliding force resisted by an adequate number of shear keys • wall and embankment fill unreinforced. The approach adopted in the analysis is that the acting forces and moments, which are a function

of the site related properties, are incorporated in the formulation of the defined stability requirements.

Once the governing properties, φ, δ, γ, w and Cf have been established, the formulas can then be

evaluated. Unfortunately, there is no direct solution for the desired β in terms of the usually given H and i, since β is contained within complex trigonometric functions.

In order to prevent a longwinded iteration process for the calculation of β in each case, the

formulas can more simply be solved for H in terms of β and i. The relationship can then be displayed in graph form in the manner adopted in the generation of the enclosed charts.


3.2 System Analysis 3.2.1 General The system analysis has to begin with calculating the total active pressure, P, of the retained soil,

which is dependant on the pressure coefficient, ka, as defined by Coulomb [4]:

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

Φ•ΦΦ•

i) - ( i) - ( ) + ( + ) + (

) - ( = k

2

a

βδδβ

ββ

sinsinsinsin

sincosec

and:

3.2.2 Stability The next step is the formulation of the three stability requirements using the geometric

relationships shown in the "FORCE DIAGRAM" (Fig. 3.1) i) Stability against Sliding: Sum of vert. forces x coeff. of friction = SFS Sum of hor. Forces

SFS= P

C )P + (WH

fV •

thus:

(1.1) 90) - + ( - 90) - + (

CSFS k

w 2 = H

fa ⎥

⎦

⎤⎢⎣

⎡••

•

δβδβγ sincos

H k = P 2a ••• γ2

1


15

FIGURE 3.1: FORCE DIAGRAM


where: W=w • H and H = HO PH=P • cos(β + δ - 90) PV=P • sin(β + δ - 90) ii) Stability against Overturning: Restoring Moment = SFO Disturbing Moment

SFO= c Pa W

••

(2) SFO= 90) - + ( b -

3 H H k

2b +

2H H w

2a ⎥

⎦

⎤⎢⎣

⎡••

••••

⎥⎦

⎤⎢⎣

⎡•

••

δββδγ

β

sinsincos

21

tan

thus:

⎥⎦

⎤⎢⎣

⎡••••

•••••

βδβγ

βδγ

w +90)-+( bkSFO H-

3

kSFOH aa2

tansin

sincos

(2.1) 0 = b w- •


iii) Proof of no open joint: Sum of applied moments around toe = x Vert. reaction

x = Pv + W

c P - a W ••

(3) x = 90) - + ( Hk + Hw

90) - + (b - 3 H Hk -

2b +

2H Hw

2a

2a

δβγ

δββδγ

βsin2

1

sinsincos

21

tan•••••

⎥⎦

⎤⎢⎣

⎡•

••

•••⎥⎦

⎤⎢⎣

⎡•

•

thus:

⎥⎦

⎤⎢⎣

⎡•••

•••

• 90)-+( kx)-(b +

wH- 3

kH aa2 δβγ

ββδγ sin

tansincos

(3.1) 0 = x)2 - (b w- ••

where: x ≥ b/3 Each one of the formulas 1.1, 2.1 and 3.1 can now be solved for H, using the stipulated stability

criteria, SFS ≥ 1,30, SFO ≥ 1,5 and x ≥ b/3, the tested and established property values, φ, δ, γ, w, Cf and b, and a chosen range of values for the variables ß and i.

The lowest result for the wall height H and keyless height Ho, obtained from the solution of the

three formulas, is then plotted against the inclination ß for a fixed backslope i. Suitable charts have thus been drawn up in which safe ß and HO values can be read off for any given H and i (see Section 2.4).

3.2.3 Sliding

Whereas the total wall height and its inclination are determined from the overall stability against overturning, and for lower heights by the proof of no open joint, the keyless height HO is controlled by the requirement of adequate stability against sliding. The latter is expressed in Formula 1, where the sliding resistance developed in HO is equal to the product of the sum of the vertical forces multiplied with the coefficient of friction, Cf, applicable to block on block sliding.


Cf = 0,54 is used throughout the analysis for inter-block friction. The relevant laboratory tests performed to establish a safe value for this friction factor are described in Part 5, "Report on Laboratory Tests".

In portion HK of the wall height, the applied horizontal forces exceed the available inter-block

sliding resistance. The additional resistance, RK, required for stability has to be provided by the appropriate shear keys placed between the blocks in the backface of the wall (see Fig. 2.3).

In this case Formula 1 is extended to

SFS P

R + C )P + (WH

Kfv

≥•

and thus (4) C )P + (W - P SFS R f

VHK ••≥

With RK known, suitably sized precast mortar or in-situ concrete keys can now be designed and

placed to satisfy the additional requirements (see "Worked Examples" and "Report on Laboratory Tests").

3.2.4 Crushing The vertical reaction on the blocks at the base of a wall for the given H and ß, as obtained from

the charts, is expressed as: Rv = w • H + Pv The inter-block bearing pressure is greatest when the units are stacked in a stretcher bond

configuration, where each block bears on the next row with 4 individual contact points of a theoretical size 50 x 50mm (see Fig. 3.2).

The average applied bearing pressure on each contact area is thus:

[ ] (5) MPa 0,05 0,05 4 3

10 )P + H (w = -3V

b ••••••

σ

which must be equal or smaller, multiplied by an appropriate safety factor, than the available

crushing strength pb of the blocks under a such load condition.


16

FIGURE 3.2: TYPICAL IN-SITU LOAD CONDITION OF INDIVIDUAL BLOCKS


p SF bb ≤•σ The safety factor, SF = 5, has to be applied to this stress to allow for the tilting of the blocks,

load shedding through the differential settlement of foundations and the increased density of the block in-fill material.

It can thus be established that a wall could safely be built up to 8m high, if pb = 8 MPa (see

"Report on Laboratory Tests"). In cases where pb has not been tested or specified, it is advised to construct walls only to a

maximum height of 6m, with the lowest 4 rows filled with concrete. If a higher wall is then still required it should be built in a terrace construction (see Part 2, Section 2.9).

3.2.5 Foundation Design The wall foundations are designed by the principles normally applied in foundation design (see Fig. 3.3). (a) Resistance against Sliding: The resistance against sliding is provided by: • the available frictional resistance between the base concrete and the founding

material, Rf • and the passive resistance of the undisturbed ground in front of the foundation. If RH > Rf/SFS, then the remainder of the applied horizontal force has to be resisted

by the passive pressure generated in the undisturbed ground in front of the foundation.

The required passive resistance is thus: Pp ≥ SFS • RH - Rf from which:

(6) )R - R (SFS k

2 D fHp

F ••

≥γ


17

FIGURE 3.3: APPLICABLE FORCES ON A TYPICAL WALL FOUNDATION


where the required design parameters • γ = the density of the undisturbed material in front of the foundation • tan μ = friction factor (= 0,5 to 0,6) • kp = the applicable coefficient of passive pressure

⎥⎦

⎤⎢⎣

⎡φφ - 1

+ 1 =sinsin

have to be assessed by a geotechnical engineer or engineering geologist. (b) Applied Bearing Pressures: First find the location of the resultant vertical reaction in relation to the toe of the

foundation:

R

M = XV

TF ∑

where MT is the applied moment around the toe of the foundation and ΣRV the sum of the vertical reactions. Where no strip foundation is required, but the bottom blocks are filled with concrete, then:

MT = W • a - P • c and ΣRV = RV Where a strip foundation has to be constructed, MT has to be recalculated taking

cognisance of the altered geometry.

ΣRV = RV + WF, where WF is the additional weight of the foundation (see Fig. 3.3).


If bF/3 ≤ xF ≤ 2bF/3, then the applied bearing pressures are given by:

(7) b

)x - 2b6(

1 bR =

F

FF

F

V

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

±∑σ

If xF > 2bF/3, then the resultant, ΣRV, falls beyond the middle third of the base. In this situation, a portion of the vertical load is carried by the fill and the reaction at the base of the wall becomes indeterminable. The recommended solution in this case is described in Section 3.3.

(c) Bearing resistance; The safe, allowable bearing pressure, qd, of the foundation material should again be

tested and assessed by a suitably experienced geotechnical engineer or engineering geologist.

Once the critical design parameters have been established, the ultimate bearing

capacity has to be calculated on the basis of Terzaghi's formulation:

The notation is that used by Terzaghi & Peck [3]. A safety factor, SF = 3, is usually chosen for this value.

If the applied bearing pressures exceed qd/SF, then a solution might be found by designing a deeper foundation. If this is still not satisfactory, the site should not be considered for the construction of a wall. This should similarly be the case where there are indications of weak substrata formations below the founding level, which could lead to a slip circle failure of the entire embankment.

N B 1/2 + N D + N C = q qfcd γγγ •••••


3.3 Foundation Design for the case where a reaction is located behind the Wall Due to the compliance with the stability requirement for overturning, the wall is designed to be

less inclined than required by the "Proof of no open Joint" for a given H and i. The effect of this condition, applicable to walls in Range 5 as shown in Fig. 2.2, is that the

resultant of the applied forces, W and P, falls beyond the middle third of the base or even in the fill behind the wall (see Fig. 3.4). The wall structure will undoubtedly now tilt towards the embankment and shed a portion of its load onto the fill. Less load will thus be transmitted to the base.

This load reduction, which is related to the degree of tilt, rotation or settlement, can however not

be established theoretically without making certain assumptions for the purpose of the analysis in this context.

For the maintenance of adequate stability, it is thus assumed that the wall rotates and settles at its

heel until ultimately a state of equilibrium is reached where there are no more open joints in the front face of the wall, i.e. that the full base width is again under compression. In this condition the resultant R' will be located at x = 2 b/3.

Assuming also that P has not changed in this process, the vertical load component carried by the

base is then reduced from W + PV to W' + PV, where W' = w'• H with w'<w (see Fig. 3.4). The effect of this load reduction is that a greater horizontal resistance now has to be provided

between the blocks of the wall and at its base, resulting therefore in: • a reduced keyless height HO • an increased number of keys in HK • and a deeper foundation. These additional requirements do not change the overall height of the wall or its inclination, but

provide increased safety against sliding. The reduced wall weight W' can now be calculated using Formula 3 with x = 2b/3 and W' = w' • H:

32b =

P + Wc P - a W

V′••′


18

FIGURE 3.4: FORCE DIAGRAM FOR THE ASSUMED FINAL STATE OF EQUILIBRIUM


thus:

The new keyless height, HO

', can then be calculated using Formula 1.1:

the increased additionally required resistance, RK

', provided by shear keys from Formula 4: RK' ≥ SFS • PH - (W' + PV) • Cf

and the new depth of foundation DF' from Formula 6:

Illustrative calculations for this condition are shown in "Worked Examples No 2".

(8)

32b - a H

c P + P 3

2b

= wV

⎟⎠⎞

⎜⎝⎛

••′

⎥⎦

⎤⎢⎣

⎡•••

′•′

90) - + ( - 90) - + ( CSFS k

w 2 = H

Fa

o

δβδβγ sincos

[ ]μγ

)W + P + W( - R SFS k

2 D FV

Hp

F tan•′••

≥′


3.4 Bibliography/References [1] SABS 0400 - 1990: "The Application of the National Building Regulations" [2] SABS 0161 - 1980: "Code of Practice for the Design of Foundations for Buildings" [3] Terzaghi & Peck: "Soil Mechanics in Engineering Practice", Second Edition 1967 [4] D W Taylor: "Fundamentals of Soil Mechanics" (1948)


PART 4: WORKED EXAMPLES


PART 4: WORKED EXAMPLES INDEX Page Case I: General Case for a Medium Wall Height ............................................................. 93 Case II: The Case for a Wall of approximately 4,2 m Height ........................................... 100 Case III: Sample Analysis of a Wall with a Traffic Surcharge ........................................... 107


PART 4: WORKED EXAMPLES CASE I: GENERAL CASE FOR A MEDIUM WALL HEIGHT A Terraforce L13 wall is required for a clear embankment height of approximately 2,15 m with a backslope ratio of 5,5:1. Choose a design height: H = 2,25 m which is made up of 10 rows of blocks (10 x 0,225 = 2,25 m). backslope i = 10,3º. Stability Requirements: SFS ≥ 1,30 SFO ≥ 1,50 Wall Properties: w = 6,0 kN/m2 b = 0,425 m Cf = 0,54 Backfill straight against wall Properties of the backfill material, as assessed: φ = 30º δ = 27º γ = 19 kN/m3 Properties of foundation material similar to those of the backfill. Applicable design chart: CHART 102 Find from chart: β and HO for H = 2,25 m and i = 10,3º. ⇒ β = 67,5º and HO = 1,50 m Calculate:

0,1743 =

10,3) - (67,5 10,3)- (30 27) + (30 + 27) + (67,5

67,5 / 30) - (67,5 = k

2

a

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

sinsinsinsin

sinsin


m 0,6900 = 90) - 27 + (67,5 0,425 - 67,5 3

27 2,25 = c

m 0,6785 = 2

0,425 + 67,5 2

2,25 = a

kN/m 13,5 = 2,25 6,0 = W

kN/m 8,3814 = 252, 0,1743 19 = P 2

sinsin

costan

21

•••

•

•

•••

Check HO for SFS = 1,30 and Cf = 0,54 (Formula 1.1)

OK) m, 1,50 (> m 1,5608 = 4,5 - 4,5

0,541,30 0,1743 19,0

6,0 2 = H O

⎥⎦⎤

⎢⎣⎡ ••

•

sincos

thus: HK min = 2,25 - 1,56 = 0,69 m choose HK = 3 ⋅ 0,225 = 0,675 m Check: H for SFO = 1,5 (Formula 2.1)

0 = 0,425 6,0 -

67,5

6,0 + 4,5 0,425 0,1743 19 1,5 H - 67,5 327 0,1743 19,0 1,5 H 2

•

⎥⎦⎤

⎢⎣⎡ ••••

•••••

tansin

sincos

0 = 2,55 - 2,6509 H - 1,5967 H 2 ••

2,25 (> m 2,3317 = 1,5967 2

2,55 1,5967 4 + 65092, + 2,6509 = H2

•••

m, OK)


Check: The distance x of the reaction from toe of base (Formula 3)

m 0,2385 = 4,5 8,3814 + 13,5

0,69 8,3814 - 0,6785 2,25 6,0 = xsin•

•••

where: b/3 = 0,1417 < x < 2b/3 = 0,2833 thus: the resultant in the middle third of the base block. The Design of Shear Keys: Find the additional resistance to be provided by the shear keys at the base of HK (Formula 4): PH = 8,3814 ⋅ cos 4,5 = 8,3556 kN/m W + PV = 13,5 + 8,3814 ⋅ sin 4,5 = 14,1576 kN/m RK ≥ 1,30 ⋅ 8,3556 - 14,1576 ⋅ 0,54 = 3,2172 kN/m Find the setback of blocks for β = 67,5º and the key length:

mm 93 = 67,5

225 = SBtan

Key length = 93 - 50 = 43 mm Find the width of keys required per metre length of the wall at the base, assuming the available shear stress of Class I mortar or 15 MPa in-situ concrete = 0,30 N/mm2 :

mm/m 250 = 4,3 0,3

10 3,2172 = Key width3

••

Thus, place one key of: width = 85 mm (min) length = 43 mm depth = 75 mm (min) in every block of the bottom row, reducing the numbers proportionately to no keys at all above HK = 0,69 m.


Check block crushing: The average vertical reaction on blocks: RV = W + PV = 14,1576 kN/m or: 14,1576/3 = 4,7192 kN/block Average applied inter-block bearing pressure (Formula 5)

MPa0,47 = 0,05 0,05 410 4,7192 =

-3

b •••

σ

Thus the required crushing strength of blocks: pb ≥ 5 ⋅ 0,47 = 2,4 MPa which is acceptable since pb is generally in the order of 6 to 8 MPa. Foundation Design: The weight of the strip foundation: WF = 6,2169 kN/m RH = PH = 8,3814 ⋅ cos 4,5 = 8,3556 kN/m RV = W + PV = 13,5 + 8,3814 ⋅ sin 4,5 = 14,1576 kN/m The details of the foundation are shown in Figure 4.1. a) Resistance against sliding: (Assume μ = δ) Rf = Σ RV ⋅ tan μ = (14,1576 + 6,2169) ⋅ 0,51 = 10,3910 kN/m


19

FIGURE 4.1: FOUNDATION DETAILS


kN/m 8,3556 = R < kN/m 7,9931 = 1,30

10,3910 = /SFS R Hf

thus: the additional resistance required by the passive pressure generated by the foundation bearing horizontally against the toe material. Find the required depth of the foundation (Formula 6) assuming: kp = 3,0 γ = 16,5 kN/m3

m 0,138 = 10,3910) - 8,3556 (1,30 3,0 16,5

2 DF ••

≥

DF (design) = 0,6 > DF (required) = 0,14 b) Applied bearing pressures:

0,389 6,2169 + 0,175) + (0,6785 13,5 = M T ••

⎟⎠⎞

⎜⎝⎛

••• 0,175 + 0,425 +

67,5 32,25 4,5 8,3814 +tan

sin

m/m-kN 6,6017= 0,2 + 3

2,25 4,5 8,3814 - ⎟⎠⎞

⎜⎝⎛•• cos

m 0,233 =

30,7 > 0,3240m =

20,37456,6017 = x

kN 20,3745 = 6,2169 + 14,1576 = R

F

VΣ

thus, the reaction is located in the middle third of the foundation.


Bearing pressures under the toe and heel of the foundation:

22,6kPa =

0,70,3240) - 6(0,7/2 - 1

0,720,3745 =

kPa 35,6 = 0,7

0,3240) - 6(0,7/2 + 1 0,7

20,3745 =

H

T

⎥⎦⎤

⎢⎣⎡•

⎥⎦⎤

⎢⎣⎡•

σ

σ

c) Available Bearing Resistance The availability bearing resistance qd, is to be assessed and calculated by a suitably experienced

geotechnical engineer or engineering geologist using Terzaghi's formulation.

N B ‰ + N D + N C = q qFcd γγγ ••••••

If σT ⋅ SF < qd, then the foundation material is suitable for the wall as designed.


CASE II: THE CASE FOR A WALL OF APPROXIMATELY 4,2m HEIGHT A Terraforce L13 wall is required for a clear embankment height of approximately 4,2m with zero backslope. Choose a design height: H = 4,275 m which is made up of 19 rows of blocks, with i = 0º. Stability requirements as before. Wall Properties: w = 6,0 kN/m2 b = 0,425 m Cf = 0,6 Backfill against the geotextile membrane placed behind the wall for drainage purposes. Properties of the backfill material, as assessed: φ = 30º δ = 20º γ = 19 kN/m3 Properties of the foundation material similar to those of the backfill. Applicable design chart: CHART 112 Find from chart: β and Ho for H = 4,275 m and i = 0º. ⇒ β = 55º and Ho = 1,93m Calculate:

0,0958 =

0) - (55 0) - (30 20) + (30 + 20) + (55

55 / 30) - (55 = k

2

a

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

sinsinsinsin

sinsin


1,7447m = 90) - 20 + (55 0,425 - 55 3

20 4,275 = c

m 1,7092 = 2

0,425 + 55 2

4,275 = a

kN/m 25,65 = 4,275 6,0 = W

kN/m 16,6377 = 2754, 0,0958 19 = P 2

sinsin

costan

21

•••

•

•

•••

Check H for SFO = 1,5 (Formula 2.1)

0 = 0,425 6,0 -

55

6,0 + (-15) 0,425 0,0958 19,0 1,5 H - 55 3

20 0,0958 19,0 1,5 H 2

•

⎥⎦⎤

⎢⎣⎡ ••••

•••••

tansin

sincos

0 = 2,55 - 3,9008 H - 1,0443 H 2 ••

4,275 (> m 4,3028 = 1,0443 2

2,55 1,0443 4 + 90083, + 3,9008 = H2

•••

Check: The distance x of the reaction from the toe of the base (Formula 3)

m 0,2833 = 2b/3 >

0,6940 = 21,343814,8132 =

(-15) 16,6377 + 25,651,7447 16,6377 - 1,7092 25,65 = x

sin•••

Thus: the resultant falls beyond the middle third of the base! This condition is created by complying with the stability criteria of providing sufficient safety against overturning. If the shape of the wall is designed to the "Proof of no open joint", in this case it would bring the reaction back into the middle third of the base with a steeper wall indication for a given H and i. The safety against overturning would then not be acceptable. For this condition, find the reduced unit weight of the wall bearing on the base following the assumption which leads to Formula 8 in Section 3.3:


mkN/ 4,5619 =

)3

0,425 2 - (1,7092 4,275

1,7447 16,6377 + (-15) 16,6377 3

0,425 2 = w

2

•

••••′

sin

Check the associated keyless height HO' (Formula 9):

OK) m, 1,93( m 1,9397 = (-15) - (-15)

0,541,30 0,0958 19,0

4,5619 2 = H O ≥

⎥⎦⎤

⎢⎣⎡ ••

•′

sincos

thus: HK' = H - HO' = 4,275 - 1,9397 = 2,3353 m As a comparison, HO = 2,5512 m as derived from Formula 1.1, with HK = 4,275 - 2,5512 = 1,7238. This would then ignore the demand for the additional horizontal resistance needed in the present configuration where the total vertical reaction on the base is reduced. The Design of Shear Keys: Find the additional resistance to be provided by the shear keys at the base of HK' (Formula 4): where: PH = 16,6377 ⋅ cos (-15) = 16,0708 kN/m W' + PV = 4,5619 ⋅ 4,275 + 16,6377 ⋅ sin (-15) = 19,5021 - 4,3062 = 15,1960 kN/m RK ≥ 1,30 ⋅ 16,0708 - 15,1960 ⋅ 0,54 = 12,6862 kN/m Find the setback of the blocks for β = 55º and the key length:

mm 157,5 = 55

225 = SBtan

Key length = 157,5 - 50 = 107 mm


Find the width of the keys required per metre length of wall at the base, assuming the available shear stress of Class I mortar or 15 MPa in-situ concrete = 0,30 N/mm2 :

mm 395 = 107 0,3

10 12,6862 = Key width3

••

Thus, place one key of: width = 130 mm (min) length= 107 mm depth = 75 mm (min) in every block of the bottom row, reducing the numbers proportionately per row to no keys at all above HK' = 2,3353 m. Check block crushing: The average vertical reaction on blocks: RV = W' + PV = 15,1960 kN/m or: 15,1960/3 = 5,0653 kN/block The average applied inter-block bearing pressure (Formula 5)

MPa0,51 = 0,05 0,05 410 5,0653 =

-3

b •••

σ

Thus, the required crushing strength of blocks: pb ≥ 5 ⋅ 0,51 = 2,5 MPa (OK) Foundation Design: Weight of strip foundation: WF = 8,0544 kN/m Distance from toe of foundation = 0,4566 m RH = PH = 16,0708 kN/m RV

1 = W1 + PV = 15,1960 The details of the foundation are shown in Figure 4.2.


20

FIGURE 4.2: FOUNDATION DETAILS


a) Resistance against sliding: (μ = φ, tan μ = 0,58) Find: Rf = Σ RV ⋅ tan μ = (15,1960 + 8,0544) ⋅ 0,58 = 13,4852 kN/m

kN/m 16,0708 = R < kN/m 10,3732 = 1,30

13,4852 = /SFS R Hf

thus: additional resistance is required by the passive pressure generated through the depth of the

foundation. Find the required depth of the foundation (Formula 6) assuming: kp = 3,0 γ = 16,5 kN/m3

m 0,5471 = 13,4852) - 16,0708 (1,30 3,0 16,5

2 DF •••

≥

DF (design) = 0,7 > DF (required) = 0,55 m b) Applied bearing pressures:

0,457 8,0544 + 0,175) + (1,7092 4,275 4,5619 = M T •••

⎟⎠⎞

⎜⎝⎛

•• 0,175 + 0,425 +

55 34,275 (-15) 16,6377 +

tansin

m/m-kN 7,4314 = 0,2 + 3

4,275 (-15) 16,6377 - ⎟⎠⎞

⎜⎝⎛•• cos

m 0,2667 =

30,8 > m 0,3196 =

23,25047,4314 = x

kN/m 23,2504 = 8,0544 + 15,1960 = R

F

VΣ


thus: the reaction is in the middle third of the foundation. Bearing pressures under the toe and heel of foundations:

11,5kPa =

0,80,3196) - 6(0,8/2 - 1

0,823,2504 =

kPa 46,6 = 0,8

0,3196) - 6(0,8/2 + 1 0,8

23,2504 =

H

T

⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡

σ

σ

c) Available Bearing Resistance The available bearing resistance is similarly to be assessed as previously noted.


CASE III: SAMPLE ANALYSIS OF A WALL WITH A TRAFFIC SURCHARGE Given a case where: H = 2,7 m and po = 12 kPa, with φ = 30º; δ = 27º; i = 0; γ = 19 kN/m3; w = 6,0 kN/m2 and Cf = 0,6 Details of the wall are shown in Figure 4.3. Calculation method: If H is known, perform the calculation with trial values of β until an adequate stability against overturning is proven. Choose: β = 55º, thus (β + δ - 90) = -8º

Find:

kN/m 16,2 = 6,0_ 2,7 = W

m 1,1984 = (-8) _ 0,425 - 55

27 _ 1,0474 = c

m 1,1578 = 2

0,425 + 55 _ 2

2,7 = a

m 1,0434 = 12/19_ 2 + 2,712/19_ 3 + 2,7

32,7 =y

kN/m 9,2469 = 1,4678_ 6,2997 =

)2,7_ 1912_ 2 + (1 72,_ 0,0910_ 19_ ‰ = P 2

sinsin

costan

⎟⎟⎠

⎞⎜⎜⎝

⎛

21


FIGURE 4.3: A WALL WITH A TRAFFIC SURCHARGE


Check the overturning stability from:

OK 1,5 > 1,6926 = 1,1984 9,2469

1,1578 16,2 =

SFO c Pa W

••

≥••

More trials can be done for other β - values to achieve SFO = 1,5 if this is required. Find the keyless height HO from

SFS P

C )P + (WH

fV

≥•

thus:

1,30 = (-8)

H 1912 2 + 1 H 0,0910 19 ‰

0,54 (-8) H 1912 2 + 1 H 0,0910 19 ‰ + H 6,0

SFS= 90) - + (

H p 2

+ 1 H k ‰

C 90) - + ( H p 2

+ 1 H k ‰ + H w

O

2O

O

2OO

O

O2Oa

fO

O2OaO

cos

sin

cos

sin

•⎟⎟⎠

⎞⎜⎜⎝

⎛••

•••

•⎥⎦

⎤⎢⎣

⎡•⎟⎟

⎠

⎞⎜⎜⎝

⎛••

••••

•⎟⎟⎠

⎞⎜⎜⎝

⎛•

•••

•⎥⎦

⎤⎢⎣

⎡•⎟⎟

⎠

⎞⎜⎜⎝

⎛•

••••

δβγ

γ

δβγ

γ

⇒ HO = 1,4875 m and HK = 2,7 - 1,5 = 1,2 m The design for the shear keys, block crushing and foundations can now be done on a similar basis as in the other examples. Detailed attention must, however, be given to the stability of the top rows in the wall where the traffic load and associated point loads, through their proximity in relation to the crest, can disturb the blocks.


PART 5: REPORT ON LABORATORY TESTS


PART 5: REPORT ON LABORATORY TESTS INDEX Page 1. INTRODUCTION .............................................................................................................. 113 2. TERMS OF REFERENCE ................................................................................................ 113 3. GENERAL INFORMATION ............................................................................................ 113 4. PHYSICAL PROPERTIES OF SAMPLE BLOCKS ....................................................... 114 5. STANDARD CUBE TESTS ............................................................................................. 114 6. L13 BLOCK CRUSHING ................................................................................................. 116 7. BLOCK ON BLOCK FRICTION ..................................................................................... 118 8. SHEAR KEY TESTS ......................................................................................................... 122 9. TESTING OF TERRAFORCE L13 SAMPLES FROM DURBAN AND CAPE TOWN MANUFACTURERS ................................................................................ 125 10. CONCLUSION .................................................................................................................. 126 11. RECOMMENDATIONS ................................................................................................... 127 12. ACKNOWLEDGEMENTS ............................................................................................... 128 ANNEXURE A : ................................................................... CUBE CRUSHING RESULTS ANNEXURE B : ................................................................... BLOCK CRUSHING RESULTS


PART 5: REPORT ON LABORATORY TESTS 1. INTRODUCTION TERRAFORCE is committed to maintaining a product standard which consistently ensures the

most practical and economic usage of the L13 Block. HAWKINS, HAWKINS AND OSBORN was therefore appointed to conduct laboratory tests on

the strength and friction characteristics of the blocks and the resistance provided by shear keys to confirm the design values currently applied in the design manual.

These properties constitute the most important design parameters for the BLOCK

INTERACTION in a gravity wall. An accurate assessment of the available minimum resistance values and the appropriate application thereof in the design procedures is thus essential to produce a safe and stable wall.

For this purpose, all tests were designed to simulate as closely as possible, the most adverse field

conditions to which a wall, designed and constructed in accordance with the current guidelines, can be subjected to.

2. TERMS OF REFERENCE It was decided to conduct the tests on samples taken from one typical production batch of the

Roodepoort plant of BRICKOR PRECAST (PTY) LTD, who are licensed manufacturers of Terraforce Products. In this way a common basis of information would be available for all test samples. This was considered to be essential for a meaningful interpretation and correlation of results.

3. GENERAL INFORMATION The information listed below, is related to the production of the specific batch from which the

test samples were taken. The information was supplied by Brickor Precast, who confirmed that this represents the standard to which Terraforce L13 Blocks are currently made in their plant.

a) Casting Date: 5, 6, & 7 August 1992 b) Plant: VB4 Moulder with 6 moulds and surcharge pressure = 10MPa c) Mix Design (for 1m3 of concrete): 125 kg Rapid Hardening Cement (RHC) 125 kg Slagment (PC 45) 600 kg 9mm Crusher Stone (reef quartzite ex. Hippo Quarries) 900 kg Crusher Sand (reef quartzite ex. Hippo Quarries) 100 kg Filler Sand (quartzite pit sand ex. Vereeniging) 50 kg Water (minimum, adjusted to the moisture content of sand) d) Curing: 12 hr minimum in closed chambers under dry conditions, then stacked in open

air for 21 days before delivery.


4. PHYSICAL PROPERTIES OF SAMPLE BLOCKS The following properties were determined by GEOPLAN LABORATORIES from a large

number of sample blocks: average mass = 34,8 kg/block average length = 340 mm average width = 427 mm average height = 220 (+ 5mm) average wall thickness = 53 mm average volume = 0,015 m3 average cross-sectional area = 0,0685 m2 average density = 2 306 kg/m3 average absorption = 4,12% 5. STANDARD CUBE TESTS The strength of the concrete in the blocks was determined by making and crushing a number of

150 x 150 x 150 test cubes of the mix. GEOPLAN LABORATORIES were commissioned to make the cubes during the casting of the

test batch. 55 Cubes were made on a vibrating table where it was attempted to obtain a compaction similar

to that applied in the actual casting process. 37 of the cubes were cured in the standard procedure by being submerged in water until crushed,

while the remaining 18 were treated in the same way as the blocks, i.e. without effective curing. The average density of the test cubes was found to be: 2403 kg/m3 for dry cubes and 2486 kg/m3 for wet cubes, indicating that a marginal greater density was achieved in this process compared to 2306 kg/3 for

the blocks obtained on average during the normal casting process. The cubes were then crushed with Geoplan's Grade B Cube Press on 7, 14, 21 and 28 days respectively. The list of results is attached as Annexure A and a summary is represented in Fig. 5.1 which shows the relationship of the average cube strength (cured and uncured) against the cube age.


22

FIGURE 5.1: RELATIONSHIP BETWEEN CUBE STRENGTH AND AGE, CURED AND UNCURED


The graphs show that the cube strength of the uncured concrete is an average 25,5 MPa after 21 days when the blocks are allowed to leave the yard for delivery. The strength increases only nominally to 28,8 MPa at 28 days which, in turn, is approximately 60% of the final 28 day strength of the concrete if cured in the prescribed manner.

6. L13 BLOCK CRUSHING The crushing strength of the blocks was tested at the PORTLAND CEMENT INSTITUTE,

Midrand, using a Grade B press, large enough to accommodate one whole block between its plattens.

Three different test procedures were followed. In the first, representing the control test, blocks

were crushed directly between full platten contact. The next two tests simulated field conditions, where the blocks were subjected to concentrated loads as in a wall built in the common stretcher bond fashion and to a defined inclination. These settings are shown in Fig. 5.2.

50 x 50 solid steel bars were used as templates to represent the individual load and bearing

points in the press for the designed settings. Further details of the procedures and results are supplied in PCI's report attached as Annexure B.

Crushing of the first lot of 24 blocks at 21 days after casting indicated that the saturated samples

gave lower crushing values than the dry samples and that the lowest crushing strength was obtained in Setting II. The blocks are subjected to a combination of crushing and splitting forces in this setting.

All samples of the second lot of 24 blocks were thus saturated and crushed 34 days after casting.

Of these blocks, 12 were again crushed between full plattens and the other 12 were crushed in Setting II.

Summarised, the average crushing strength of the saturated samples were: at 21 days: a) full platten: 11,3 MPa (only 1 reliable test) b) Setting I: 12,4 MPa (average of 5 tests) c) Setting II: 8,8 MPa (average of 5 tests) and at 34 days: a) full platten: 15,9 MPa (average of 6 tests) b) Setting II: 11,0 MPa (average of 12 tests)


FIGURE 5.2: LOAD SETTINGS FOR SIMULATED FIELD CONDITIONS


The limited number of results does not unfortunately, allow for a reliable conclusion. The following trends can, however, be observed: - the crushing strength of the blocks under full compression is approximately half

of the crushing strength of the uncured test cubes, - the crushing strength of the blocks in Setting I, with central opposing load

points, is similar to that of the blocks under full compression, - the crushing strength of the blocks in Setting II with load and bearing points

offset, is approximately one third of the crushing strength of the uncured test cubes.

It can therefore be stated with reasonable certainty that Setting II controls the crushing strength

of the blocks in the structural design and that this should be limited to 8MPa at the time of delivery.

7. BLOCK ON BLOCK FRICTION The frictional resistance characteristics of the blocks were tested with a specially designed and

constructed testing rig at the production plant of BRICKOR PRECAST in Roodepoort. Details of this rig are shown in Fig 5.3.

The rig accommodates 3 blocks, two of which are clamped tight in the lower position, while the

third is placed on these blocks with a setback representing a designed wall inclination. A static vertical load of up to 1200 kg was applied to the upper block by means of a lever arm. The steel template between the knife edge and the block simulates the actual load points on the block and also allows various settings for the wall inclination.

The horizontal force required to cause the top block to slide, is applied by a steady manual

extension of a threaded shaft and socket arrangement, held in position between frame and block. The applied force is then measured with a calibrated proving ring incorporated in the shaft arrangement. The displacement of the sliding block in relation to the fixed blocks is measured with deflection dial gauges.

A number of trial tests were carried out to establish critical procedures, settings, load application

and effects of block filling. In order to determine a reliable friction factor for inter-block sliding under the most adverse

conditions, it was consequently decided to conduct the final test in the following manner: - the sliding surfaces of the blocks be saturated prior to testing - the blocks be empty - three new blocks be used in every test


23 24

FIGURE 5.3: TERRAFORCE TESTING RIG


- the applied horizontal force be measured while sliding over a distance of approximately

10mm - every test be repeated once with the same blocks and the same setting. Nine tests were carried out in this manner on 92/09/15, 92/10/23 and 92/10/26 in settings with

four different vertical loads. The measured displacement of the top block in relation to the bottom blocks was then plotted

against the applied horizontal force required to initiate sliding under a given vertical load for each test and its re-run. A typical plot is shown in Fig 5.4.

Finally the average residual horizontal force required to maintain sliding was plotted against the

vertical force applied for all nine tests. The friction coefficient is derived from the average slope of the line which joins these points.

The results are recorded in the following table and the graphical representation is shown in Fig.

5.4. Table of Friction Test Results

Date of Test and Block Mark

vert. Force V (kN)

hor. Force H (kN)

Cf H/V

Remarks

92/09/15: F25,26,27 F28,29,30 F31,32,33

9,48 3,59 12,42

6,70 2,11 7,76

0,7068 0,5877 0,6248

n = 9 xn = 0,616 Sn = 0,0477

92/10/23: S1, 2, 3 S4, 5, 6 S7, 8, 9

3,59 6,53 9,48

2,03 4,34 6,05

0,5655 0,6646 0,6382

92/10/26: S10,11,12 S13,14,15 S16,17,18

3,59 6,53 9,48

2,02 3,94 5,60

0,5627 0,6034 0,5907

The average friction coefficient, Cf, thus found is equal to 0,62, with a standard deviation of 0,048. The value representing the 95% Confidence Level for the factor is equal to 0,54.


25 26

FIGURE 5.4: FRICTION TEST RESULTS


8. SHEAR KEY TESTS The resistance of the shear keys, which is essential for the sliding stability of the wall, was tested

by using the same friction rig. Tests were again carried out at the production plant of Brickor Precast in Roodepoort.

In these tests it was not possible to simulate the actual construction procedure, in which a shovel

full of concrete is placed and stamped between the blocks during the backfilling operation as the wall is constructed. In the in-situ condition, the concrete is subjected to the full horizontal thrust only at the time when the wall has reached its design height. The concrete in the keys therefore develops strength over some days before being fully stressed. Investigations showed that this situation generally happens at a minimum of 7 to 8 days, depending on the size of the wall and other construction restraints.

It was therefore decided to perform the shear tests on suitably aged precast samples made of a

concrete mix commonly used in the construction procedure. A number of shear blocks of size 75 x 75 x 75mm were made by Geoplan Laboratories on 92/10/26 to a mix ratio of 1:4 cement to crusher sand, with a maximum aggregate size of 6,75mm.

Three standard test cubes of size 150 x 150 x 150mm were made as a control reference at the

same time. These cubes were stored without curing and then crushed after 7 days. The average crushing strength obtained was 8,6 MPa.

The test samples were also stored without curing. The samples used in the final tests were

however saturated prior to testing on 92/11/03, 8 days after casting. This condition again proved to be governing the determination of a design value of the shear resistance provided by the keys.

After a number of trial runs with different vertical loads, wet and dry samples and various L13

friction base blocks, the final tests were carried out in the setting as shown in Fig 5.5. Saturated shear blocks were placed in the rig between three L13 blocks of which the friction characteristics were known from previous tests. A vertical load of 600kg was applied through the leverarm arrangement and the horizontal force was then gradually increased and recorded at the failure of the shear block. All samples failed in the same manner (see Fig 5.5).

The results of the final seven significant tests showed that the average shear resistance of the

sample blocks, after having subtracted the component required to overcome the frictional resistance between the L13 base blocks from the total applied force, was 3,0kN per block with a standard deviation of 0,277kN and a 95% confidence limit of 2,544kN.

Since the actual shear keys vary in size and number for walls with different heights and back

slopes, it is necessary to convert the obtained resistance, given by the chosen shear key size, to a permissible shear stress which can then be applied in the design for all keys made to the mix proportions as specified. It follows that the characteristic shear stress of the sample material is thus equal to 0,45N/mm2, which is simply derived by dividing the obtained shear resistance by the cross-sectional area of the sample blocks.


FIGURE 5.5: SECTIONAL ELEVATION OF THE RIG SHOWING THE SHEAR BLOCK IN THE TEST POSITION


The permissible design value for the available shear stress of the keys is then obtained by dividing the characteristic stress by a partial safety factor for material of 1,5.

The resultant DESIGN SHEAR STRESS in the keys derived from the outcome of the described

tests, is equal to 0,3N/mm2. This is approximately one twenty-ninth of the cube strength of the concrete. It is also similar to the principle applied in common practice, where the permissible shear stress of concrete weaker than 20MPa strength is equal to its cube strength divided by 30.


9. TESTING OF TERRAFORCE L13 SAMPLES FROM DURBAN AND CAPE TOWN

MANUFACTURERS A number of Terraforce L13 blocks had been sent for testing by other manufacturers to Brickor

Precast, Roodepoort. Three samples had come from Corocrete Natal, and three from Klapmuts Concrete Products, Cape Town. No records of aggregates, mix proportions, casting date and procedure, design concrete strength and curing were forwarded with the samples.

Since only three samples were available of each lot, it was decided to carry out two friction tests

per lot and then crush the blocks in PCI's press to determine their individual crushing strength. The friction tests were carried out in the same way as described under the main tests in Section

7, i.e. the sliding surfaces wet, the blocks empty and a total sliding displacement of approximately 10mm for each run and its repeat. In each case the first test was conducted with a vertical load of 300kg and the second one with a load of 600kg after having turned the blocks around for a fresh sliding surface.

The blocks of each lot were then crushed at PCI, having been saturated for 24 hrs prior to

testing. In each case the first block was placed between full plattens and the last two in the offset load position as given by Setting II.

The results of the tests are summarised in the following table:

Property Corocrete Blocks

Klapmuts Blocks

Remarks

Sample Mark: avg. mass (kg): measured friction coefficient: - at 300kg - at 600kg crushing strength (MPa): - full platten - offset load position

DC 1, 2, 3 29,9

0,602 0,539

18,9 8,6

CT 1, 2, 3 32,9

0,625 0,610

16,9 10,2

one block each avg. of two blocks

Due to the very limited lot size, these results have to be viewed completely on their own and

therefore allow no meaningful definition of the source properties.


10. CONCLUSION The objective of the various tests performed on the Terraforce L13 blocks of Brickor Precast was

to establish a basis for the production standards and critical design parameters pertinent to the blocks in a retaining wall.

Although the sample size was in some cases not large enough to allow for a full statistical

analysis of the results, it can be stated with reasonable confidence that the outcome of the tests is a fair representation of the properties of the blocks made in the production runs of 5, 6 and 7 August 1992 at the Roodepoort plant. The test could therefore be considered as a future means of process control during the manufacturing process.

It has also been shown clearly that the shear keys can provide the required design resistance

when produced from a mix ratio of 1 part cement to 4 parts crusher sand with a maximum aggregate size of 6,75mm. Precasting the keys as suitably sized shear blocks once the wall inclination has been determined, will certainly facilitate better quality control of the otherwise hand mixed and placed concrete/mortar lumps.


11. RECOMMENDATIONS The design parameters derived from the tested properties are summarised in the following table:

Description Value

- Mass of block 30 - 35 kg

- 28 day target strength of concrete (cured) 40 MPa (min)

- Storage time before delivery 21 days

- 21 day cube strength of concrete (uncured) 25 Pa (min)

- Crushing strength of blocks at 21 days: • under full platten contact • under simulated in-situ point loading

11 - 13 MPa 8 MPa (min)

- Friction Coefficient for inter-block sliding, when used in combination with a safety factor of 1,3 for stability against sliding:

• value at 95% confidence level

0,54

- Shear key properties: • 7 day cube strength of concrete (1 cement : 4 crusher sand, with a 6,75mm aggregate size.) • permissible shear stress at 7 to 8 days

8 - 9 MPa 0,3 MPa

The implications which these values have on the design of a wall in terms of its structural safety

are demonstrated satisfactorily in the "Worked Examples" of Part 4 of the Guidelines. It is therefore recommended considering the tabled values as the minimum standards for future

block production and to carry out tests on a regular basis to further confirm the set standards and to control the product quality and exclude possible variations which could have an influence on the performance of the blocks.

Finally, it is also recommended that further research should be allowed to refine testing methods

to develop the full potential of the product in a growing and competitive market.


12. ACKNOWLEDGEMENTS The assistance given by Mr N Papenfus of Brickor Precast, Mr E von der Au of Geoplan

Laboratories and Mr P A Biondi, Engineering Geologist, in the development and successful execution of the tests is gratefully acknowledged.

HAWKINS HAWKINS AND OSBORN W G Technau Pr Eng


ANNEXURE A: CUBE CRUSHING RESULTS

GEOPLAN LABORATORIES REPORT

Date: 1992-09-08


CLIENT : HAWKINS HAWKINS & OSBORN ORDER NO. : PROJECT : L 13 TERRA FORCE BLOCKS OUR REFERENCE : STRUCTURE : DATE : 1992-09-08


CLIENT : HAWKINS HAWKINS & OSBORN ORDER NO. : PROJECT : L 13 TERRA FORCE BLOCKS OUR REFERENCE : STRUCTURE : DATE : 1992-11-02


ANNEXURE B: BLOCK CRUSHING RESULTS

PORTLAND CEMENT INSTITUTE REPORT

Date: 1992-10-06 and 1992-11-16


Lab.Ref: 644/92/RJB/aa Date: 6 October 1992 Client: Hawkins Hawkins & Osborn Project: Terraforce L 13 Blocks

LABORATORY REPORT SCOPE OF WORK

Testing of Terraforce L13 blocks.

BRIEF

PCI was requested to test Terraforce L 13 blocks supplied as follows:

First Series:

• Four samples (two pre-soaked, two air-dry) were to be crushed directly between the plattens of the compressive testing machine to determine the comparable direct compressive strengths of the blocks.

• 10 samples (five pre-soaked, five air-dried) were to be crushed between load bearing points directly above each other to represent a wall inclination of 50° (see annexure).

• 10 samples (five pre-soaked, five air-dried) were to be crushed between load and bearing points offset from each other to represent a wall inclination of 61°

(see annexure).

Second Series:

• 12 samples (all pre-soaked) were to be crushed directly between the plattens of the compressive testing machine to determine the direct compressive strength.

• 12 samples (all pre-soaked) were to be crushed between load and bearing points offset from each other to represent a wall inclination of 61° (see annexure).

Page 1 of 6


Lab.Ref: 644/92/RJB/aa Date: 6 October 1992 Client: Hawkins Hawkins & Osborn Project: Terraforce L 13 Blocks Tests and results It was assumed that the samples submitted were representative of the block stockpiles.

• The bed surfaces of all blocks were rubbed down to remove high points and

protruding fins. The force was applied at approximately 15 MPa/minute (this was determined using a net block area of approximately 0,0711 m2, supplied by the client.) The blocks tested in a "wet condition" were pre-soaked for at least 24 hrs, removed from the water and allowed to drain, weighed, and crushed in a saturated surface-dry condition. New sheets of 4-mm-thick 3-ply timber were positioned between the block specimen and the bearing points in all the tests to ensure an even distribution of the applied force. Where possible, the forces were recorded, when the first visible cracking occurred and at failure.

FIRST TEST SERIES (conducted on 26 and 27 August 1992):

Direct compressive strength (no load offset)

Page 2 of 6


26



Page 3 of 6 27


Page 4 of 6 28



Page 5 of 6 29


NOTES: 1) THE PRESS CAN ONLY EXERT CENTRAL PRESSURE

2) POINT LOADS MARKED WITH * CANNOT BE REPRESENTED 3) BEARING POINTS MARKED WITH ** HAVE TO BE INTRODUCED TO ACHIEVE

CENTRAL LOADING

LOAD SETTINGS


Lab.Ref: 644N92/RJB/aa Date: 16 November 1992 Client: Hawkins Hawkins & Osborne Project: Terraforce L 13

Blocks

LABORATORY REPORT

SCOPE OF WORK

Testing of Terraforce L 13 blocks.

BRIEF

PCI was requested to test Terraforce L 13 blocks supplied as follows:

Series "CT" and "DC"

• One specimen (pre-soaked) from each series was to be crushed

directly between the plattens of the compression testing machine to determine the direct compressive strength of the blocks.

• Two specimens (pre-soaked) from each series were to be crushed between load and bearing points, offset from each other to represent a wall inclination of 610 (see the annexure in report 644/92/RJB/aa dated 6 October 1992).

SAMPLES

The following Terraforce L 13 blocks were received:

3 No marked CT 3 No marked DC

TESTS AND RESULTS

It was assumed that the samples submitted were representative of the block stockpiles.

The bed faces of all blocks were rubbed down to remove high points and protruding fins. The force was applied at approximately 15 MPa a minute (this was determined using a net block area of approximately 0,0711 m2 supplied by the client).

Page 1 of 3


Lab.Ref: 644A/92/RJB/aa Date: 16 November 1992 Client: Hawkins Hawkins & Osborne Project: Terraforce L13

Blocks

The block specimens were all pre-soaked for at least 24 hours, removed from the water and allowed to drain, weighed and crushed in a saturated surface dry condition.

New sheets of 4-mm-thick 3-ply timber were positioned between the block specimen and the bearing points in all the tests to ensure even distribution of the applied force.

Page 2 of 3


Lab.Ref: 644A/92/RJB/aa Date: 16 November 1992 Client: Hawkins Hawkins & Osborne Project: Terraforce L 13

COMMENT

Photographs of the crushed blocks were taken by the client who was present and assisted with the testing procedure.

Page 3 of 3

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