Strength assessment of structural masonry walls: analysis based on machine learning approaches

Figures & data

Table 1. Previous research on masonry wall testing and modeling.

Reference	Type of Study	Objectives	Main Findings
Murty and Jain (2000) [2]	Experimental	Cyclic tests of RC frame with masonry infills	The effect of masonry infill walls on stiffness, strength and overall ductility of the building has been studied. The study compared the performance of bare frame and frame with reinforced and unreinforced infill masonry walls against lateral loading. The masonry infill shows better performance even in moderate earthquakes.
Sarangapani et al., (2005) [3]	Experimental	Determine the influence of bond strength on masonry compressive strength.	A relationship between the masonry prism compressive strength and bond strength has been obtained. The brick-mortar bond has been altered by using bond-enhancing methods such as modified brick frogs and coatings on the brick surface. The study shows the importance of using either a strong mortar or a mortar with plasticizing additives to produce better bonding. The masonry prism compressive strength is more sensitive to brick-mortar bond strength than the compressive strength of the mortar.
Franzoni et al., (2015) [4]	Experimental	Investigation of compressive strength and young’s modulus of masonry triplets in dry and wet conditions.	Performance of cement and lime-based mortar prism and masonry triplets were tested under dry, water saturated and moist conditions. The results were interpreted based on microstructural features of materials (total voids amount and pore size distribution) The compressive strength and young’s modulus found to be higher in dry and saturated condition compared to moist condition
Celano et al., (2021) [5]	Numerical Analysis	Investigation of in-plane behavior of masonry wall by modeling approach.	Finite element model and discrete macro-element model were applied to investigate the in-plane resistance of masonry wall. The mechanical properties of masonry are used to study the in-plane resistance of the masonry wall. The reliability of both the models were verified with past experimental results and found good agreement in terms of failure loads and modes. The study shows the effect of compressive and tensile strength of masonry on in-plane resistance of masonry wall.
Abdulla et al., (2017) [6]	Numerical Analysis	Utilization of simplified micro modeling approach to simulate masonry wall behavior.	The combination of plasticity-based constitutive models and extended finite element models was proposed to simulate 3D nonlinear behavior of masonry. The crack pattern was captured without specifying the crack location in advance. The performance of models was compared in terms of crack pattern and failure modes obtained in past literatures. The numerical models better agreed with experimental results and the study shows that these models can be used in the development and for optimization of strengthening system without conducting expensive experimental programs.
Mohammed et al., (2011) [7]	Experimental	Discuss the effect of scale on structural behavior of masonry under compression.	Structural behavior of brick work at prototype and model scales. The performance of masonry in prototype, half, fourth and sixth scale under compression. The study shows that the compressive strength of masonry increased as the scale is reduced, and the stiffness is not significantly affected.
Keshava and Raghunath (2017) [9]	Experimental	Investigation of behavior of axially and eccentrically loaded masonry walls	Load carrying capacity of masonry units, prisms and full-scale wall specimens were experimentally tested. The behavior of walls is tested under different slenderness and eccentricity ratios. Load carrying capacity of hollow concrete block masonry was found to be higher compared to brick masonry. The masonry strength was drastically reduced by increasing slenderness and eccentricity ratios.
Perez Gavilan et al., (2015) [10]	Experimental	Study of confined masonry walls with varying aspect ratio	The study shows that neither aspect ratio nor level of axial stress had a significant effect on lateral stiffness. The normalized shear strength of wall increased with decreasing aspect ratio.
Kaushik et al., (2007) [11]	Experimental	Investigate the behavior of stress strain characteristic of unreinforced masonry under compression.	Characteristics of unreinforced masonry and its constituents, i.e. solid clay bricks and mortar, have been studied. The relationship between brick, mortar, and masonry strengths and including the effects of other factors, such as water absorption, initial rate of absorption, and addition of lime in the mortar on the strength and ductility of masonry were also studied. Masonry prism compressive strength was found to increase with increase in compressive strengths of bricks and mortar. Compressive behavior of mortar with lime was found to be better because of greater ductility.
Corradi et al., (2003) [12]	Experimental	Determine the strength of masonry wall	The exact parameters which influence masonry behavior using laboratory and in situ tests were studied. The obtained shear strength and Young's modulus were compared with different standards and found to be in agreement.
Doddamani and Keshava (2019) [13]	Experimental and Numerical	Determine the suitability of Autoclaved Aerated Concrete (AAC) blocks with ready mix concrete in masonry construction.	Behaviour of AAC block with ready mix mortar was compared with conventional blocks and mortar. Compressive strength of hollow concrete block made with ready mix mortar had higher compressive strength compared to other types. Performance of hollow concrete blocks was found to be better compared to AAC blocks.
Reboul et al., (2018) [14]	Experimental	Study of in-plane cyclic behavior of masonry wall strengthened by composite material	Behaviour of FRP or TRC composites was compared with conventional masonry under vertical compressive load and cyclic reverse horizontal displacement. Under the compression load adopted here, TRC strengthening materials contribute more effectively to an increase in ductility than FRP-composites. Cracking mechanism shows that the micro cracks are concentrated in unreinforced zones.
James et al., (2016) [16]	Experimental	Investigation of performance of OPC stabilized soil blocks with sugar cane bagasse ash (SBA).	Blocks were cast with varying OPC and SBA dosage with target density and tested under 28 days of curing. The study shows that addition of SBA to OPC in stabilized block manufacturing was capable of producing stabilized blocks at reduced OPC content that met the minimum required standards.
Sajanthan et al., (2019) [17]	Modelling	Prediction of compressive strength of cement stabilized earth block masonry	Compressive strength of masonry predicted using masonry units and joint layer mortar combinations. Predicted compressive strength was compared with different empirical equations and experimental data and found to be in good agreement.
Lulić et al., (2023) [18]	In-situ testing	Apply reliability approaches for resistance evaluation of existing masonry in a real case study	The design value method and the adjusted partial factor method can contribute to a more efficient and high-quality renovation of numerous existing masonry structures.

Figure 1. Feature selection using mutual information and F-test statistics.

Table 2. Descriptive statistics of masonry wall dataset.

TRAIN	Max	Min	Mean	STD	CV	SKEW
Eu (MPa)	16700.00	135.00	7379.32	5536.88	0.75	0.43
Fcu (MPa)	66.00	4.57	24.15	19.59	0.81	1.22
Em (MPa)	8600.00	125.00	3792.98	3093.09	0.82	0.32
Fcm (MPa)	21.00	0.60	5.38	4.62	0.86	2.32
Fc (MPa)	40.90	1.25	11.04	9.71	0.88	2.03
TEST
Eu (MPa)	15000.00	552.31	7608.03	4721.19	0.62	0.11
Fcu (MPa)	58.90	5.70	28.87	20.58	0.71	0.22
Em (MPa)	11600.00	220.00	4572.68	3707.54	0.81	0.46
Fcm (MPa)	31.10	1.16	10.45	8.91	0.85	1.22
Fc (Mpa)	37.70	1.36	16.31	14.61	0.90	0.39

Table 3. Input output (I/O) combinations arrived based on mutual information criteria.

I/O Combination	Input Parameters	Output Parameter
I – I/O	Eu(MPa), Fcu(MPa), Fcm(MPa)	Fc (MPa)
II – I/O	Eu(MPa), Fcu(MPa)	Fc (MPa)
III – I/O	Eu(MPa), Fcm(MPa)	Fc (MPa)
IV – I/O	Fcu(MPa), Fcm(MPa)	Fc (MPa)

Figure 2. Methodology flowchart.

Table 4. Model parameters optimized by trial-and-error approach.

GTB Parameters	I – I/O	II – I/O	III – I/O	IV – I/O
n_estimators	200	100	100	100
learning_rate	0.1	0.11	0.11	0.1
loss	‘ls’	‘ls’	‘ls’	‘ls’
max_depth	4	5	4	2
min_samples_split	3	2	2	4
random_state	1	1	1	1
ENN Parameters	I – I/O	II – I/O	III – I/O	IV – I/O
No. of hidden layer	1	1	1	1
Nodes in hidden layer	6	3	3	4
Epochs	200	200	200	200
Transfer function in hidden layer	tansig	tansig	tansig	tansig
Transfer function in output layer	logsig	logsig	logsig	logsig
Training function	Levenberg-Marquardt backpropagation	Scaled conjugate gradient backpropagation	Levenberg-Marquardt backpropagation	Levenberg-Marquardt backpropagation
MARS Parameters	I – I/O	II – I/O	III – I/O	IV – I/O
max_degree	2	3	3	3
penalty	0.5	0.5	0.5	0.5
minspan_alpha	0.05	0.05	0.01	0.05
endspan_alpha	0.05	0.05	0.01	0.05
endspan	5	5	−1	5

Figure 3. Violin and swarm plots for comparative performance evaluation of models.

Figure 4. Scatter plots of actual v/s predicted compressive strength (test phase data).

Figure 5. Taylor diagrams to graphically indicate the performance of each model in terms of RMSD, correlation coefficient and Standard deviation statistics (test phase data).

Table 5. Performance evaluation metrics of the models developed.

Performance metrics		MAE	RMSE	RRMSE	NNSE	KGE	WI
First – I/O Combination
GTB	TRAIN	0.0860	0.2311	0.0238	0.9994	0.9996	0.9999
	TEST	2.4823	2.9524	0.2020	0.9574	0.9075	0.9877
ENN	TRAIN	1.3405	2.7649	0.2847	0.9212	0.8406	0.9807
	TEST	5.2565	6.3967	0.4377	0.8271	0.6714	0.9569
MARS	TRAIN	2.0666	2.8471	0.2932	0.9168	0.9343	0.9759
	TEST	3.3045	4.3233	0.2958	0.9128	0.8865	0.9756
Second – I/O Combination
GTB	TRAIN	0.2429	0.3889	0.0400	0.9983	0.9988	0.9996
	TEST	6.3876	8.4655	0.5793	0.7320	0.7857	0.896
ENN	TRAIN	4.6928	6.5602	0.6755	0.6749	0.7347	0.8583
	TEST	4.0500	4.4106	0.3018	0.9096	0.7768	0.9681
MARS	TRAIN	2.7871	3.5549	0.3660	0.8761	0.8962	0.9613
	TEST	5.8929	8.2357	0.5636	0.7427	0.7713	0.8936
Third – I/O Combination
GTB	TRAIN	0.0881	0.2311	0.0238	0.9994	0.9995	0.9999
	TEST	3.7574	4.9636	0.3397	0.8882	0.8616	0.9633
ENN	TRAIN	3.0653	3.8465	0.3961	0.8579	0.8497	0.9572
	TEST	6.7771	7.7167	0.5280	0.7668	0.6482	0.9314
MARS	TRAIN	3.6269	4.3016	0.4429	0.8284	0.8451	0.9406
	TEST	3.5243	4.3000	0.2942	0.9137	0.8455	0.9725
Fourth – I/O Combination
GTB	TRAIN	0.4214	0.4936	0.0508	0.9973	0.9842	0.9993
	TEST	2.3943	2.8946	0.1981	0.959	0.9054	0.9881
ENN	TRAIN	3.5042	4.5410	0.4676	0.8125	0.8445	0.9353
	TEST	3.7702	4.3582	0.2982	0.9116	0.8125	0.9751
MARS	TRAIN	1.4699	2.0677	0.2129	0.9543	0.9658	0.9877
	TEST	2.1104	2.5719	0.1760	0.9673	0.9488	0.9911

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Data availability statement

This manuscript has no associated data. Data used for model development can be shared upon reasonable request.