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Rakesh Kumar Dutta, Ph.D. Associate Professor. CE-472(c) Geosynthetics. National Institute of Technology, Hamirpur. Department of Civil Engineering. Reinforced Earth. Basic Mechanism of Reinforced Earth. Choice of Soil.
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Rakesh Kumar Dutta, Ph.D.Associate Professor CE-472(c) Geosynthetics National Institute of Technology, Hamirpur Department of Civil Engineering
Choice of Soil • Three principal considerations in the selection of the soil for reinforced earth are • Long term stability of the complete structure • Short term stability • Physicochemical properties of materials • Granular soils compacted to densities that result in volumetric expansion during shear are ideally suited for use in reinforced earth structures.
Department of Transport recommends the use of cohesive frictional fill also provided if it corresponds to the grading and plasticity characteristics as given below
Fine grained soils are recommended as a backfill material only when the following four additional design criteria are implemented (Wayne and Han, 1998): • Internal drainage must be designed and installed properly. • Only soils with low to moderate frost-heave potential should be considered. • The internal cohesive shear strength parameter, c, is conservatively ignored for long term stability analysis. • The final design is checked by a qualified geotechnical engineer to ensure that the use of cohesive soils does not result in unacceptable, time-dependent movement of the retaining wall.
Strength Characteristics of Reinforced Sand Rupture Mode of Failure
Design Methodologies The design of a structure incorporating geosynthetics aims to ensure its strength, stability and serviceability over its intended life span. There are mainly four design methods for the geosynthetic-related structures or systems. These methods are described as follows: 1 Design-by-experience: This method is based on one’s past experience or that of other’s. This is recommended if the application is not driven by a basic function or has a nonrealistic test method.
Design-by-cost-and-availability: In this method, the maximum unit price of the geosynthetic is calculated by dividing the funds available by the area to be covered by the geosynthetic. The geosynthetic with the best quality is then selected within this unit price limit according to its availability. Being technically weak, this method is nowadays rarely recommended by the current standards of practice.
Design-by-specification: This method often consists of a property matrix where common application areas are listed along with minimum (or sometimes maximum) property values. Such a property matrix is usually prepared on the basis of local experiences and field conditions for routine applications by most of the governmental agencies and other large users of geosynthetics. For example, the AASHTO M288-00 specifications, provides the designer and field quality inspector with a very quick method of evaluating and designing geotextiles for common applications such as filters, separators, stabilizers and erosion control layers.
Design-by-function: This method is the preferred design approach for geosynthetics. The general approach of this method consists of the following steps: • Assessing the particular application, define the primary function of the geosynthetic, which can be reinforcement, separation, filtration, drainage, fluid barrier or protection. • Make the inventory of loads and constraints imposed by the application. • Define the design life of the geosynthetic. • Calculate, estimate or otherwise determine the required functional property of the geosynthetic (e.g. strength, permittivity, transmissivity, etc.) for the primary function. • Test for or otherwise obtain the allowable property (available property at the end of the design life) of the geosynthetic.
Calculate the factor of safety, FS, reproduced as below: • If this factor of safety is not acceptable, check into geosynthetics with more appropriate properties. • If acceptable, check if any other function of the geosynthetic is also critical, and repeat the above steps. • If several geosynthetics are found to meet the required factor of safety, select the geosynthetic on the basis of cost–benefit ratio, including the value of available experience and product documentation.
The design-by-function approach described above is basically the traditional working stress design approachthat aims to select allowable geosynthetic properties so that a nominated minimum total (or global) factor of safety is achieved. In geosynthetic applications, particularly reinforcement applications (e.g. geosynthetic-reinforced earth retaining walls), it is now common to use the limit state design approach, rather than the working stress design involving global safety factors.
For the purpose of geosynthetic-reinforced soil design, a limit state is deemed to be reached when one of the following occurs: • Collapse, major damage or other similar forms of structural failure • Deformations in excess of acceptable limits • Other forms of distress or minor damage, which would render the structure unsightly, require unforeseen maintenance or shorten the expected life of the structure. The condition defined in (1) is the ultimate limit state, and (2) and (3) are serviceability limit states. The practice in reinforced soil is to design against the ultimate limit state and check for the serviceability limit state.
In reinforced soil design some of these limit states may be evaluated by conventional soil mechanics approaches (e.g. settlement). Margins of safety, against attaining the ultimate limit state, are provided by the use of partial material factors and partial load factors. Limit state design for reinforced soil employs four principal partial factors all of which assume prescribed numerical values of unity or greater. Two of these are load factors applied to dead loads (external dead load – ff and soil unit weight – ffs) and to live loads (fq).
The principal material factor is fm applied to geosynthetic reinforcement parameters, and fms applied to soil parameters. The fourth factor fn is used to take into account the economic ramifications of failure. This factor is employed, in addition to the material factors, to produce a reduced design strength. Note that it is not feasible to uniquely define values for all these partial factors. Prescribed ranges of values are decided to take account of the type of geosynthetic application, the mode of loading and the selected design life. Partial factors are applied in a consistent manner to minimize the risk of attaining a limit state.
In limit state design of geosynthetic reinforcement applications, disturbing forces are increased by multiplying by prescribed load factors to produce design loads, whereas restoring forces (strength test values) are decreased by dividing by prescribed material factors to produce design strengths. There is deemed to be an adequate margin of safety against attaining the ultimate limit state if
In the case of drainage application of geosynthetics, this requirement can be expressed as For assessing deformations or strains to determine compliance with the appropriate serviceability limit state, the prescribed numerical values of load factors are different from those used in assessing the ultimate limit state and usually assume a value of unity. In assessing magnitudes of total and differential settlements, all partial factors are set to a value of unity, except for those pertaining to the reinforcements (BS 8006-1995). With respect to serviceability limit state, the design requirement for a geosynthetic could be expressed as
In the generalized form, it can be said that the limit state design, considering all possible failure modes and all appropriate partial factors being applied, aims to produce a soil–geosynthetic system that satisfies the following principal equation for its all design elements.
It should be noted that this equation defines the fundamental principle of limit state design. In the case of internal stability, the design resistance effect may be generated in the soil and in reinforcement, whereas it is generated in the soil only in the case of external stability. When the safety of man and environment is at great risk because of the failure of the geosynthetic used, or when a reliable method is not available to determine the requirements of the geosynthetic to be used, it becomes necessary to perform suitable practical tests. If the tests are being conducted in the laboratory, special attention must be required to get reliable data to be used for field applications. The adoption of suitable design and construction method is essential not only to reduce design and construction costs, but also to minimize long-term operation, maintenance and monitoring expenses.
Retaining Walls The design of geosynthetic-reinforced retaining walls is quite well established. A number of design approaches have been proposed; however, the most commonly used design approach is based on limit equilibrium analysis. The analysis consists of three parts: • Internal stability analysis (‘local stability analysis’ or ‘tieback analysis’): An assumed Rankine failure surface is used, with consideration of possible failure modes of geosynthetic-reinforced soil mass, such as geosynthetic rupture, geosynthetic pullout, connection (and/or facing elements) failure and excessive geosynthetic creep. The analysis is mainly aimed at determining tension and pullout resistance in the geosynthetic reinforcement, length of reinforcement, and integrity of the facing elements. • External stability analysis (‘global stability analysis’): The overall stability of the geosynthetic-reinforced soil mass is checked including sliding, overturning, load-bearing capacity failure, and deep-seated slope failure. • Analysis for the facing system, including its attachment to the reinforcement.
Internal failure modes of geosynthetic-reinforced soil retaining walls: (a) geosynthetic rupture; (b) geosynthetic pullout; (c) connection (and/or facing elements) failure.
External failure modes of geosynthetic-reinforced soil retaining walls: (a) sliding; (b) overturning; (c) load-bearing capacity failure; (d) deep-seated slope failure.
Adjoining figure shows a geotextile-reinforced retaining wall with a geotextile wraparound facing without any surcharge and live load. The backfill is a homogeneous granular soil. According to Rankine active earth pressure theory, the active earth pressure, sa, at any depth z is given by: where, Ka is the Rankine earth pressure coefficient, gb is the unit weight of the granular backfill.
The value of Ka can be estimated from where fb is the angle of shearing resistance of the granular backfill. The factor of safety against the geotextile rupture at any depth zmay be expressed as where sG is the allowable geotextile strength in kN/m, and Sv is the vertical spacing of the geotextile layers at any depth zin metre. Since for retaining walls the geosynthetic reinforcement needs to provide stability throughout the life of the structure, the long-term sustained load test data, that is, the creep test data, should be used for design purpose.
The magnitude of the FS(R) is generally taken to be 1.3–1.5. The geotextile layer at any depth, z, will fail by pullout (bond failure) if the frictional resistance developed along its surfaces is less than the force to which it is being subjected. This type of failure occurs when the length of geotextile reinforcement is not sufficient to prevent its slippage with respect to the soil. The effective length, le, of a geotextiles layer along which the frictional resistance is developed, may be conservatively taken as the length that extends beyond the limits of the Rankine active failure zone (ABC)
The factor of safety against the geosynthetic pullout at any depth zmay be expressed as where fr is the angle of shearing resistance of soil–geosynthetic interface and it is approximately equal to 2fb/3. The magnitude of the FS(P) is generally taken to be 1.3–1.5. The length, lr, of geotextile layer within the Rankine failure zone can be calculated as: where His the height of the retaining wall.
The total length of the geotextile layer at any depth zis For designing the facing system, it can be assumed that the stress at the face is equal to the maximum horizontal stress in geosynthetic-reinforced backfill. This assumption makes our design conservative because some stress reduction generally occurs near the face. In fact, the maximum stresses are usually located near the potential failure surface and then they decrease in both direction: towards the free end of the geotextile reinforcement and towards the facing.
Values of the stress near the facing depend on its flexibility. In the case of rigid facing, the stresses near the facing and those at the potential failure surface do not differ significantly. In the case of flexible facing, the stress near the facing is lower than that at the potential failure surface (Sawicki, 2000). If the wraparound facing is to be provided, then the lap length can be determined using the following expression:
Design Procedure for Geosynthetic-Reinforced Retaining Wall with Wraparound Vertical Face and without any Surcharge Step 1: Establish wall height (H). Step 2: Determine the properties of granular backfill soil, such as unit weight (gb) and angle of shearing resistance (fb). Step 3: Determine the properties of foundation soil, such as unit weight (g) and shear strength parameters (c and f). Step 4: Determine the angle of shearing resistance of the soil–geosynthetic interface (fr). Step 5: Estimate the Rankine earth pressure coefficient.
Step 6: Select a geotextile that has allowable fabric strength of sG. Step 7: Determine the vertical spacing of the geotextile layers at various levels. Step 8: Determine the length of geotextile layer, l, at various levels. Step 9: Determine the lap length, ll, at any depth z.
Step 10: Check the factors of safety against external stability including sliding, overturning, load-bearing capacity failure and deep-seated slope failure as carried out for conventional retaining wall designs assuming that the geotextile-reinforced soil mass acts as a rigid body in spite of the fact that it is really quite flexible. The minimum values of factors of safety against sliding, overturning, load bearing failure and deep-seated failure are generally taken to be 1.5, 2.0, 2.0 and 1.5, respectively. Step 11: Check the requirements for backfill drainage and surface runoff control. Step 12: Check both total and differential settlements of the retaining wall along the wall length. This can be carried out as per the conventional methods of settlement analysis.
The current design methods make a number of simplifying assumptions. It is assumed that the retaining wall moves out sufficiently for the Rankine’s state of stress to develop in the soil mass. The direction of principal stresses are assumed to coincide with the vertical and horizontal, and the vertical stress is assumed to be either uniform or varying linearly at any depth z from top. Based on the results of small scale models and theoretical analysis, the following recommendations have been made. Failure due to slipping can be prevented by keeping width to height ratio of the wall greater than 0.8. The vertical pressure in the wall close to the face can be assumed to vary linearly with depth, with maximum value at the base. The maximum traction force in strips is reached close to the face Reinforced Earth Retaining Wall
While designing a reinforced earth wall, one has to consider • External Stability • Internal Stability In the external stability analysis, it is assumed that the reinforced earth wall is an integral unit and behaves as a rigid gravity structure and conforms to the simple laws of statics. The internal stability deals with the design of reinforcement with regard to its length, cross-section against tension failure and ensuring that it has a sufficient anchorage length into the stable soil.
External Stability The possible external failure mechanisms are • Sliding • Overturning • Tilting/bearing failure • Slip failure
Sliding • Factor of safety against sliding • = Resisting force/Sliding force
Overturning • Factor of safety against overturning • = Restoring moment/Overturning moment
Internal Stability • The internal stability is essentially associated with the tension and wedge pull-out failure mechanisms as shown in figure. In general two methods used in practical design utilise one of the following • Tie Back-Wedge Analysis • Coherent Gravity Analysis • The main difference between these two analyses originate from the basic assumptions made about • The shape of the failure zone • The rotation of the wall facing • The lateral pressures acting with in the reinforced soil • Out of the two methods, Tie Back-Wedge analysis is more popular and discussed here onward.
