Certainly, I’m sharing a link to the pmx file. This is a report for the structural analysis of a masonry vault. It’s an educational project for university purposes, but it’s based on a real case from the 13th century. The objective of the project is to determine stress distribution in the vault based on an analytical estimate of its resistance.
In the structure, no cracks or detachments are detected, so significant tensile stresses (greater than 2.5% of compressive strength) should not appear, which is subsequently confirmed by the results. Given that traditional stone and brick structures tend to operate within a stress range well below 10-15% of their capacity, I understand that complex material plasticity analyses may not be necessary to rigorously assess the structure’s stability.
I hope this can be helpful. Thank you very much for sharing the arch model; it has greatly helped me understand the possibilities of contact surface modeling. Many thanks; Best regards, Damián.
The Young’s modulus of the masonry is derived from the Young’s moduli (E) of the individual blocks and mortar, as well as the dimensions of the joints and blocks, using an analytical formulation. However, it’s important to note that this value is not highly precise and should be used with caution. It cannot be treated as precisely as the Young’s modulus of materials like steel or those manufactured using modern techniques.
To provide an example, a 15% increase in the masonry’s moisture content can result in an 80% reduction in its strength. The Young’s modulus is estimated using the formula
The parameters α and β are related to the dimensions of the blocks and joints, as well as the Young’s moduli of the blocks and mortar, respectively. The parameter ϕ varies between 1 and 2 and is indicative of the age of the masonry. Jacques Heyman’s bibliography includes these and other methods for estimating the parameters of brick and stone masonry. Thank you very much for your assistance.
As i understand, analysis of arch masonry structure can be categories in:
macro-scale
meso-scale
detailed model
each model approach have advantage/disadvantages,
Macro-scale is the simplest one in modeling geometry but required adjustment in homogeneity of material and damage/cracking detection by the solver.
Meso-scale is moderate in complexity of modeling, ignoring mortar joint spacing, separation can be directly represent by contact. Nonlinearity of plasticity/damage material is not a must.
Detailed model is the most complex in modeling, geometry represent as in actual. But contact is not required to be modeling explicitly since mortar joint have weak material and limiting in tension. Nonlinearity of plasticity/damage material of block is not a must, depending on compression stress occurs.
Another modeling which probably need to be concern are,
Soil block fill
Pavement layer and patch load
Side wall of confinement
Abutment and foundation support stiffness
Material degradation
As general rules of FEA, more detail and complex in geometry and material are better in captures behavior but have consequently in resource of modeling and computational times are high.
I completely agree with you. However, my knowledge of FEM calculations is very basic, and I’m still learning. If you allow me, using the Optima arch as an example, from the analysis of the stresses in the arch, it can be deduced that it has very low compressive stresses at the bottom of the arch keystone [orange color], very low compressive stress at the top of the arch ribs [orange color], and high compressive stresses at the top of the springers [dark blue color]. This indicates that the arch is unstable with its own weight alone, as you correctly pointed out, because it has a low Young’s modulus and constrained lateral faces that introduce tensile stresses that don’t exist in the real-world model.
A traditional masonry arch that works under compression should provide more or less uniform stress results without tension. The distribution of minimum principal stresses should ideally be more or less uniform in color and have values significantly lower than its capacity.
n the case of modeling the arch with mortar joints and bricks, the stress distribution indicates that the bottom surface transmits -1.6 to -2.15 MPa, while the top part ranges between -0.5 to +0.3 MPa.
The model suggests that the majority of the load is distributed on the bottom surface, and practically the entire section of the arch is not effectively carrying load. If you don’t mind me saying, this situation doesn’t seem realistic. Nevertheless, your model has helped me understand the surface contact typology I need for a concrete project, and I’m immensely grateful for your contribution and comments, which are greatly assisting me in my learning. Warm regards, Damian.
Indeed, i’m only taken simple test about modeling approach for capability of the solver. Material model using simple one with assumption values, boundary condition support/load, and geometry also.
Required benchmark with tested structure available to know the reliability of these model approaches, but improvement still possible by using complete actual model and material nonlinearity, also contact or separation.
The model should work better with gravity load or surface load. In this case, it’s unclear why it doesn’t converge with gravity load. I would suggest starting with a volumetric, linear elastic model to observe the stress distribution. You can try using the COMPRESSION_ONLY model or even an isotropic material model so that you can visualize the stress distributions and the behavior of the arch.
As you surely know, the arch is a statically indeterminate structure of degree three that, due to its symmetry, yields at the keystone, ribs, and springers, generating a total of 5 hinges, efore collapsing, whether due to a very low load or an excessive load.
The hinges occur due to the openings generated by tensile stresses and the high compressive stresses generated at the red points with minimal contact surface
Once the stress distribution for a specific case, whether real or hypothetical, is determined, the stress distribution of the model you provided, with mortar joints and bricks, and the numerical simulation of contact, should yield a similar distribution.
I have attempted to create several models of masonry walls, incorporating wooden lintels, foundations, and soil contact, and I haven’t obtained results that, in my view, align well with the natural behavior of the structure. I will continue experimenting, but tomorrow my children will want to eat three times, so I can’t solely devote myself to what I’m passionate about. If you believe I can assist you with anything, please don’t hesitate to let me know. It would be my pleasure to help, despite my limited knowledge in FEM. Thank you very much for sharing your knowledge.
Regards, Damian
