Elastic Modulus

An elastic modulus of 38,000 kN/m² (38 MPa) for sand can be reasonable depending on the type of sand, its density, and the stress state. Here's a breakdown: Typical Ranges for Sand's Elastic Modulus:

  • Loose sand: 10,000−25,000 kN/m210,000−25,000kN/m2
  • Medium dense sand: 25,000−50,000 kN/m225,000−50,000kN/m2
  • Dense sand: 50,000−100,000 kN/m250,000−100,000kN/m2

These values are influenced by factors such as:

  • Relative Density:
    • Denser sands exhibit higher stiffness.
    • E=38,000 kN/m2E=38,000kN/m2 corresponds to medium-dense sand.
  • Confining Pressure:
    • Elastic modulus increases with depth or under higher normal stresses.
    • For normal pressures (like the 25-100 kPa in your pullout test), this value aligns with medium-dense sand.
  • Void Ratio: Lower void ratios (more compact sands) yield higher stiffness.

Validation: #

If the referenced value of 38,000 kN/m238,000kN/m2 matches experimental or local soil conditions described in the paper you’re comparing against, it’s reasonable to use. In Plaxis:

When defining sand's stiffness in Plaxis:

  • Use the Drained Young’s Modulus for realistic deformation behavior.
  • Check the stiffness modulus’s dependency on depth if stress-dependent stiffness is enabled.

It seems you're identifying the correct relationship between the axial stiffness (EA) of the geogrid and the pullout force in your simulation. Lowering EA results in a reduced pullout force because EA directly governs the geogrid's tensile resistance, which is critical in pullout tests.

Key Observations and Suggestions: #

  1. Impact of EA on Pullout Force:
    • The pullout force depends on the interaction between the geogrid and the surrounding soil, as well as the geogrid's ability to carry the tensile load.
    • If EA is too high, the geogrid will resist elongation more effectively, increasing the mobilized pullout force.
  2. Reassessing EA:
    • The paper’s EA=1020 kN/mEA=1020kN/m value seems to come from experimental data or manufacturer specifications. However, it may represent an average or an estimated value, possibly including assumptions about how stiffness develops during the test.
  3. Adjusting EA:
    • If reducing EA leads to better agreement with the experimental pullout force, the value of EA in your model might need tuning. This can happen because:
    • Laboratory conditions (e.g., strain rate, load transfer efficiency) might differ from the assumed numerical setup.
    • The experimental EA might not account for the exact mechanical behavior at the low-strain regime seen during pullout.
  4. Check the Interface Properties:
    • The interface reduction factor (Rinter​) plays a significant role in the pullout force. Ensure Rinter​ accurately reflects the interaction between sand and geogrid.
    • Consider conducting a parametric study to see how Rinter influences results alongside EA.
  5. Sensitivity of Soil Parameters:
    • If halving the ErefEref​ of sand doesn't change the results much, it suggests the pullout mechanism is more controlled by geogrid parameters (e.g., EA) and interface properties than the bulk soil stiffness.
  1. Lower EA Gradually:
    • Experiment with reducing EA to observe its effect on pullout force. Align with the observed 37.4 kN/mkN/m target force.
  2. Verify Interface Parameters:
    • Ensure Rinter is appropriately set, as a lower Rinter​ can simulate reduced friction between sand and geogrid.
  3. Validate the Displacement:
    • Check if the displacement at maximum pullout force in your model matches the paper’s results. Discrepancies could indicate stiffness mismatches.

The observation that there is no shear stress developed on the interface surface without the geogrid, while shear stress appears at the start point of the geogrid, is an interesting aspect of the simulation. Let's explore this scenario in more detail. Possible Reasons for the Difference in Shear Stress Development

  1. Behavior of Interface Material vs. Geogrid: Interface Material (e.g., Mohr-Coulomb model): When using an interface material like Mohr-Coulomb, shear stress is typically developed due to the frictional behavior between two surfaces (soil and interface). The shear stress would usually start small at the beginning (where there is no displacement or very little) and gradually increase along the interface due to increasing shear displacement. Geogrid: In contrast, a geogrid acts as a reinforcing element. Shear stress appears immediately at the geogrid's start point because the soil particles interact with the geogrid reinforcement at that point, which leads to a more immediate shear transfer between the soil and geogrid. The distribution of shear stress along the geogrid will then depend on its interaction with the soil, which can cause higher shear stress near the start and a gradual decrease along the length, especially if there is a larger soil displacement at the beginning of the geogrid.
  2. Difference in Shear Transfer Mechanism: Without Geogrid (Interface Only): Shear stress along an interface without the geogrid should indeed appear over the entire sliding surface, gradually increasing from the starting point to the far end. However, the shear stress distribution will depend on the relative movement and interaction between the soil and the interface material. The interface might allow for some initial movement with little shear resistance, and shear stress might build up gradually as the soil moves further along the surface. With Geogrid: The geogrid acts as a reinforcement that holds the soil in place by providing resistance, which means shear stress appears immediately at the start of the geogrid, likely due to the interaction between the geogrid and the soil at that location. The geogrid may cause a more localized concentration of shear stress at the start, which decreases as the interaction with the soil diffuses further along the geogrid length.
  3. Boundary Effects in the Plaxis Model: Plaxis Model: It's possible that Plaxis is applying boundary conditions or assumptions that influence the shear stress distribution along the interface and geogrid. When the geogrid is present, it might be designed to transfer shear immediately, starting from the point where it interacts with the soil. In contrast, without the geogrid, shear stress develops more gradually because the interface material alone doesn’t have the same immediate frictional resistance as the geogrid. Geogrid Length and Interaction: As the geogrid is placed over part of the interface, the interaction at the start of the geogrid could generate an initial peak in shear stress, while the absence of geogrid in the first part of the interface would mean no shear stress is transferred at that point.
  4. Displacement at the Start of Geogrid: Initial Displacement: The initial displacement of the soil block, especially when a geogrid is present, is more localized at the start of the geogrid, which may explain the large shear stress value at the beginning of the geogrid in your Plaxis chart. In contrast, without the geogrid, the shear stress is likely to be distributed more evenly over the length of the interface as the soil starts to slide more gradually.

Key Differences in Shear Stress Development:

  1. Without Geogrid (Interface Material Only): Shear stress starts small at the beginning and gradually increases as the soil continues to slide along the interface. The shear stress is spread over the entire length of the interface, and maximum shear stress develops towards the far end.
  2. With Geogrid: Shear stress appears immediately at the start of the geogrid because of the direct interaction between the soil and geogrid. The distribution of shear stress along the geogrid is typically not uniform, with higher shear stress at the start of the geogrid, which then decreases as the distance from the start increases.

Conclusion: #

In summary, the difference in shear stress development arises because the geogrid provides an immediate resistance at the start of the sliding surface, leading to instant shear stress at that location. In contrast, the interface material alone has a gradual buildup of shear stress across the entire interface as the sliding progresses, and the maximum shear stress occurs further down the length of the interface.

The shear stress distribution behavior you're observing is likely a result of these different mechanisms of shear transfer between the materials in the simulation.

  1. Shear Stress with Geogrid:
    Shear Stress Development: When you include a geogrid in the model, it acts as a reinforcement element that interacts with the soil, creating additional shear stress along the geogrid-soil interface. The shear stress distribution in this case varies along the length of the geogrid.
    Shear Stress at Start of Geogrid: The shear stress is often highest near the start of the geogrid because of the initial interaction between the soil and geogrid at the point where the sliding starts. This is typically where the soil block starts moving, and there is a peak of shear stress as the soil mobilizes its resistance at the interface.
    Shear Stress along Geogrid: As the soil continues to slide over the geogrid, the shear stress gradually decreases, reflecting the interaction along the length of the geogrid. This is often a more gradual decrease depending on the material properties and the nature of the interface.
    Calculation of Shear Stress: The shear stress can be calculated using the formula: τmax=c′+γ⋅h⋅tan⁡(ϕ)
    where c′c′ is the effective cohesion, γγ is the unit weight of the soil, hh is the height of the sliding zone, and ϕϕ is the friction angle. The shear stress is distributed along the geogrid interface, and its total value can be integrated over the length of the geogrid to get the sliding force.
  2. Shear Stress Without Geogrid (Only Interface Material):
    Shear Stress Distribution: In the case where the geogrid is replaced by a pure interface material (such as Mohr-Coulomb interface), the shear stress develops directly at the interface of the soil. This shear stress depends on the interaction between the soil and the interface material, which has its own friction angle and cohesion (e.g., ϕ=26.6∘ϕ=26.6∘, c=2.5 kN/m2c=2.5kN/m2).
    Shear Stress Along the Interface: In a pure interface-only scenario, the shear stress typically starts small at the beginning of the interface (near the sliding start) and gradually increases towards the end of the interface, where it reaches its maximum value. The frictional resistance grows as the soil starts sliding, and the shear stress mobilizes across the entire length of the interface.
    Shear Stress Calculation: In the absence of geogrid, the shear stress is calculated purely from the interaction of the soil with the interface material. The formula is similar: τ=c′+γ⋅h⋅tan⁡(ϕ)
    where γγ is the unit weight of the soil and hh is the height (depth) of the interface zone. The shear stress should be constant across the entire length of the interface once it fully develops, assuming no geogrid.

Key Differences Between Geogrid and No Geogrid:

Geogrid-Soil Interaction: With geogrid, there is an additional reinforcement effect that modifies the shear stress distribution. The geogrid essentially adds an extra layer of resistance along the interface, leading to a higher initial shear stress at the start of the geogrid and a gradual decrease towards the end. This results in a more distributed shear stress compared to the case without geogrid.

Interface-Only (No Geogrid): Without the geogrid, the shear stress develops through the soil-interface friction alone, without the additional reinforcement from the geogrid. As a result, the shear stress is distributed more evenly and gradually increases from the start to the end of the interface, reflecting the frictional resistance between the soil and the interface material.

No Shear Stress at Geogrid Start (Mistaken Initial Interpretation): Initially, you might have thought there was no shear stress on the interface without geogrid; however, after reviewing the Plaxis results, it became clear that the shear stress is uniform (constant) at a lower value across the interface (e.g., 2.5 kN/m²). This is the shear stress that develops at the interface due to the frictional resistance of the material, and it can be calculated from the soil's normal stress and interface material properties.

Summary of Calculations:

With Geogrid: The shear stress is influenced by the geogrid's reinforcement properties, creating a variable shear stress along the geogrid. It can be calculated using the cohesion and friction angle of the geogrid-soil interface, and the total sliding force is the integrated shear stress across the geogrid.

Without Geogrid (Pure Interface): The shear stress is developed by the friction between the soil and the interface material. It starts at a small value at the beginning of the interface and increases toward the end, following the Mohr-Coulomb failure criterion (with cohesion and friction angle of the interface material).