Chapter 11
Reinforced Soil

11.1 Introduction

Soil reinforcement is typically modelled using the Engineered Element material. This is a material that can be applied to Boundaries to provide essentially one dimensional (in section) objects such as soil nails, geotextiles, and sheet pile walls. The special properties of an Engineered Element allow soil to flow through or past it if required as would be expected of e.g. a soil nail. This would otherwise not be possible in a plane strain program such as LimitState:GEO.

In other modelling approaches, soil reinforcement is often only modelled by its effect such as an imposed point force on a slip surface. This makes it challenging to model complex failure mechanisms and requires the user to pre-judge to some extent the effect of the reinforcement. In LimitState:GEO the software is given full freedom to determine the critical failure mechanism involving soil reinforcement. The parameters required for the soil reinforcement may thus not be familiar to users familiar with other approaches. However these parameters are typically required when estimating e.g. an imposed point force on a slip surface.

The parameters defining the behaviour of an Engineered element are:

Pullout factor, Tc
The contribution of the material cohesion to the pullout resistance of the element.
Pullout factor, Tq
Used to determine the contribution of the overburden to the pullout resistance of the element.
Lateral factor, Nc
The contribution of the material cohesion to the lateral resistance of the element.
Lateral factor, Nq
Used to determine the contribution of the overburden to the pullout resistance of the element.
Plastic moment, Mp
The plastic moment of resistance of the element. (If rigid joints are being modelled then this parameter should be set to 1E+30).
Rupture strength, R
The maximum tensile force that can be carried by the material.
Compression strength, C
The maximum compressive force that can be carried by the material.
Advanced > Subdivide at nodes?
Specifies whether failure of the element between end vertices is permitted (e.g. plastic hinge formation and/or tensile failure). This should be set to False for compatibility with earlier versions of LimitState:GEO.

The theoretical background to these parameters is given in Section 6.1.5. Guidance on defining Engineered element geometry using LimitState:GEO is given in Section 17.9.2.

11.2 Soil Reinforcement - Predefined Types

When defining a new Engineered Element, LimitState:GEO provides five predefined parameter sets, representing different common soil reinforcement types. Dependant upon usage, each parameter set contains fixed and editable properties taken from those listed in Section 11.1.

11.2.1 Soil Nail (Rigid)

A rigid soil nail has its plastic moment (Mp) set to 1e+30 kNm/m (effectively infinite) to ensure that the element behaves as a rigid body and cannot form any plastic hinges. The rupture and compression strengths are also set to be effectively infinite (1E+30 kN/m).

The pullout properties Tc, Tq, Nc, and Nq (which are user-defined) are ideally determined by field tests. However estimates using theory may be made. For example if a nail of diameter B is embedded in a cohesive soil of undrained shear strength cu then plasticity theory could be used to estimate the ‘Pullout Factor’ Tc as πBcu and the ‘Lateral Factor’ Nc as ~ 9cuB based on laterally loaded pile theory for widely spaced piles. Both values might then be factored. For an undrained cohesive soil the pullout and lateral factors Tq and Nq are independent of depth and therefore would be set to zero.

Certain current alternative analysis methods do not take account of the lateral resistance of soil nails and so Nc and Nq could be set to zero when comparing with these analyses. However in this situation, LimitState:GEO may occasionally identify a failure mode where the nails simply ‘float’ out of the ground because they have no lateral resistance. It is therefore recommended that a small value of Nc is set, of the order of 1 kN/m2.

11.2.2 Soil Nail (Flexible)

This type of soil nail behaves in the same way as the rigid soil nail except that the plastic moment capacity is set to zero so that the nail may hinge freely at locations along the nail. These locations can either be user-defined Vertices or, if the Subdivide at nodes? material property is set to true, Nodes along the length of the element. (By default, LimitState:GEO will set Subdivide at nodes? to true when creating any material that is designated as being able to yield. This can be modified in the Property Editor)

11.2.3 Soil Nail (Can Yield)

This type of soil nail behaves in the same way as the flexible soil nail except that finite values can be set for the axial (rupture and compression) strengths.

11.2.4 Sheet Pile Wall (Rigid)

To represent a rigid sheet pile wall the values of Tc, Nc and Mp are all set to 1e+30 i.e. effectively infinity. The values of Tq and Nq are set to zero.

Setting the ‘Pullout Factor’ Tc to infinity prevents the wall pulling out by shearing along the wall/soil interface. In effect this would prevent relative shear displacement between a wall and the surrounding soil. However in reality shear may still occur just adjacent to the wall within the soil only. LimitState:GEO always models shear along a boundary such as this as potentially occurring using either the wall/soil interface strength (if specified) or the soil shear strength only. In practice the lowest strength will always be used. The effect is that the wall/soil interface strength is thus modelled as the same as the soil itself.

If it is desired to model a lower interface strength then this could be set as the value of ‘Pullout Factor’ Tc. In practice this will be the same on both sides of the wall and will only represent a cohesion. If a frictional interface strength is required that differs from the surrounding soil then it would be necessary to model the sheet pile wall as a Solid zone of narrow width rather than using an Engineered Element, or to model narrow soil zones on either side of the pile with modified shear parameters.

Setting the ‘Lateral Factor’ Nc to infinity prevents any soil flowing through or past the element as would be expected for a sheet pile wall.

Setting the ‘Plastic moment’ Mp to infinity ensures that the element behaves as a rigid body and cannot form plastic hinges along its length.

Setting the ‘Rupture strength’ R and the ‘Compression Strength’ C to infinity prevents axial failure of the element.

11.2.5 Sheet Pile Wall (Can Yield)

This type of sheet pile wall behaves as the rigid sheet pile wall except that a finite value of plastic moment can be set so that the sheet pile may form plastic hinges at locations along the length. These locations can either be user-defined Vertices or, if the Subdivide at nodes? material property is set to true, Nodes along the length of the element. (By default, LimitState:GEO will set Subdivide at nodes? to true when creating any material that is designated as being able to yield. This can be modified in the Property Editor)

The plastic moment per metre width (into the diagram) can be estimated from a knowledge of the wall thickness and the yield strength of the wall material.

11.2.6 Other

This ‘Application’ type is used for user defined reinforcement properties which do not fit the predefined values of the other types. All parameters are freely editable. By default, LimitState:GEO will set Subdivide at nodes? to true when creating a material of this type.

11.3 Example 1 - Simple Reinforcement Pullout

The simple pullout test modelled in Figure 11.1 illustrates the functioning of the parameter Tc. The input file is available in the Example Files folder.

The reinforcement (coloured red in the diagram) is embedded in both a weightless rigid block (height 1m) on the left and a body of soil of length 2m on the right (with zero tensile strength specified on the interface between block and soil). It is assumed that it has a pullout resistance of 10 kN/m2 in the soil.

The aim of the test is to determine what force is required to displace the rigid block to the left, thus pulling the reinforcement out of the soil.

To ensure the reinforcement remains embedded in the rigid block but can pull out of the soil it is necessary to define two Engineered Element materials. The first is given a high value of Tc (e.g. 1E+30 kN/m2) and is assigned to the portion of the reinforcement in the rigid block (dark red in the diagram). The second is given a value of Tc of 10 kN/m2 and is assigned to the portion of the reinforcement in the soil block (light red in the diagram). Both materials are given high values of plastic moment of resistance (e.g. 1E+30 kNm/m) and tensile rupture strength (e.g. 1E+30 kN/m).

A unit stress with Adequacy factor (red arrows) is applied to the left hand edge of the rigid block. On solving the block displaces to the left and the light red portion of the reinforcement pulls through the soil. An Adequacy factor of 20 is returned, indicating that a force of 20 kN/m is required to pull out the 2m of reinforcement, with Tc = 10 kN/m2. Displaying the tensile force diagram confirms that the maximum tensile force experienced in the soil reinforcement is 20 kN/m.


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Figure 11.1: Simple reinforcement pullout test.


11.4 Example 2 - Simple Reinforcement Tensile Rupture

The simple test modelled in Figure 11.2 illustrates the functioning of the tensile Rupture strength parameter. The input file is available in the Example Files folder.

The problem is identical to that of the pullout test (Section 11.3) except that the reinforcement embedded in the body of soil (light red) has a tensile capacity of 40 kN/m and, in order to prevent pullout, a Tc value of 1E+30 kN/m2.

The aim of the test is to show that the force required to displace the rigid block to the left and cause the reinforcement to rupture in tension is equal to the rupture strength of the nail. On solving the block displaces to the left and the light red portion of the reinforcement does not pull through the soil. Instead the nail is seen to lengthen. An Adequacy factor of 40 is returned, indicating that a force of 40 kN/m was required to rupture the reinforcement.


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Figure 11.2: Simple reinforcement tensile rupture test.


11.5 Example 3 - Simple Reinforcement Lateral Displacement

The simple lateral displacement test modelled in Figure 11.3 illustrates the functioning of the parameter Nc. The input file is available in the Example Files folder.

The reinforcement, for example a soil nail, (coloured red in the diagram) is embedded in a body of soil of width 3m and attached to two weightless rigid blocks (width 0.5m) either side of the soil body (with frictionless interface between the soil and the blocks). It is assumed that it has a lateral displacement resistance of Nc=25 kN/m2 in the soil.

The aim of the test is to determine what force is required to displace the rigid blocks upwards, thus displacing the reinforcement through the soil. To ensure that the reinforcement remains fixed to the rigid blocks but can displace through the soil it is necessary to define two Engineered Element materials. The first is given a high value of Nc (e.g. 1E+30 kN/m2) and is assigned to the portion of the reinforcement embedded within the rigid blocks (dark red in the diagram). The second is given a value of Nc of 25 kN/m2 and is assigned to the portion of the reinforcement in the soil block (light red in the diagram).

A unit stress with Adequacy factor (red arrows) is applied to the base of each rigid block (i.e. over a total width of 1m). On solving the blocks displace upwards and the light red portion of the reinforcement pulls through the soil. An Adequacy factor of 75 is returned, indicating that a force of 25 × 3 = 75 kN/m is required to displace the 3m of reinforcement upwards, with Nc = 25 kN/m2.


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Figure 11.3: Simple reinforcement lateral displacement test.


11.6 Example 4 - Simple Reinforcement Bending

The simple bending test modelled in Figure 11.4 illustrates how the parameter Mp functions. The input file is available in the Example Files folder.

A reinforcement frame surrounds a body of soil of width 1m and height 1m. On top of the frame is attached a weightless rigid block (height 0.5m) to which a lateral pressure of 2 kN/m is applied (resulting in a 1kN/m force). It is assumed that the frame has a plastic moment of resistance of 10 kN/m/m.

The aim of the test is to determine what force is required to displace the rigid block and cause bending failure in the frame.

The Engineered Element material defining the frame (red in the diagram) is set with high values of Tc and Nc (e.g. 1E+30 kN/m2) and an Mp value of 10 kNm/m. All of the soil properties are set to zero except the undrained cohesion (cu) which is assigned a value of 10 kN/m2.

The Adequacy factor is applied to the lateral load acting on the rigid block (red arrows). A coarse nodal discretization is set (target number of nodes = 250).

On solving, the block displaces to the right and reinforcement frame displaces to form a trapezoidal shape, with bending occurring at the corners. An Adequacy factor of 50.63 is returned, indicating that a stress of 50.63 kN /m/m is required to shear the soil and cause sufficient plastic hinges in the frame to form a failure mechanism. The analytical solution for this problem can be easily determined using a simple work equation:

1λ θ = 4Mp θ + 1cuθ
(11.1)

hence:

λ = 4Mp + cu = 40 + 10 = 50
(11.2)

where λ is equal to the factor on load required to cause failure and θ is equal to the rotation at the yielding positions. Therefore, using a coarse nodal discretization, the solution has an error of approximately 1.2%. Note that the higher the number of target nodes set for the problem, the closer the value will be to the analytical solution.


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Figure 11.4: Simple reinforcement bending test.


11.7 Soil Reinforcement with Specified Interface Materials

As outlined in Section 17.5 it is often appropriate, in problems of soil/structure interaction to assign properties to the interface between a solid body and the surrounding soil that are some function of the properties of the soil. Similarly, where soil reinforcement is specified in a model, it can be appropriate to specify interface properties that are distinct on either side of the element itself. This is anticipated to be useful primarily in cases where ‘flow through’ does not occur (e.g. for a sheet pile wall), as the materials applied at the interfaces will be applied across the full width of the model (and will insert a potentially unintentional ‘wound’ through the model if used in conjunction with e.g. a soil nail).

When creating a new Engineered Element material, the user specifies only those properties that relate to the element itself (see Chapter 17). This material can then be applied to 1D boundaries in the usual manner. However, when associated with a Boundary Object, the viewer will display three lines, as shown in Figure 11.5:


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Figure 11.5: Section of a reinforced soil wall problem, showing an Engineered Element material (red) on a 1D boundary. Note the dark borders to the element, which signify that edge materials have not been applied.


The inner line depicts the Engineered Element itself while the darker outer lines represent the interfaces on either side of the element. These faces can be assigned one or more materials so that the interaction of the reinforcement with its surroundings along the interfaces can be closely modelled. For example, see the sheet pile wall depicted in Figure 11.6, where the Engineered Elelment (Sheet Pile) is bordered by Frictionless and No-Tension interface materials.


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Figure 11.6: Section of a sheet pile wall problem, showing an Engineered Element material (red) on a 1D boundary with frictionless (green) and no-tension (yellow) materials applied to the two outer faces.