ABSTRACT
A ma thema t i c a l t-echnique is h e r e b y advanced f 01: i n v e s t i -
c j ; ~ t - it13 the bearing c a p a c i t y and a s s o c i a t e d normal stress
t l I :-; tLribut.ion il t- C a i l . u r e of s o i l f o u n d a t i o n s .
'I'hc stab1 1 i t.y e q u a t i o n s are o b t a i n e d using the L i m i l:
i,:clu.i l i b r i u m ( 1,E) c o n d i t i o n s . The c o n d i t i o n s of v e r t i c n 1 ,
I I ~ J J - i z o n t aal .n d r o t a t i o n a l e q u i l i b r i a are transformed
n ~ ; ~ t . l ~ e r n a t i c a Iw. l yi t h r e s p e c t t o the s o i l s h e a r i n g s t r e n y t l l ,
leading to t h e d e r i v a t i o n of t h e e q u a t i o n o f t h e J!unctional
y, and two i n t e g r a l c o n s t r a i n t s .
Genera 1 I. y, no c o n s t i t u t i v e law beyond t h e cou.1 (.,i;lll1 s y i e l d
c 1 . i t e r i o n is i - n c o r p o r a t e d i n the f o r m u l a t i o n . Consequent.Ly,
no c o n s t r a i n t s a r e p l a c e d o n t h e c h a r a c t e r o f the c r i t i c a l s
e x c e p t t h e o v c l - a l l e q u i l i b r i u m o f t h e f a i l i n g s o i l secti-on.
The c r j - t i c a l normal. stress d i s t r i b u t i o n , Cmin, and
c o n s e q u e n t l y the load, b i n , determined as a r e s u l t o f t h e
i u i 11i.mization of t h e f u n c t i o n a l are t h e smallest stress and
Ioatl p a r a m e t e r s t h a t can cause f a i l u r e . I n o t h e r words, lor
a s o i l w i t h s t r e n g t h p a r a m e t e r s c, 6, r , hnd f o o t i n g wiLh
qeornetry 1, I i , when stress 6 4 d n ~ i n (C,fl, r, 1, H ) and l o a d
Q 4 Qrnin(c, 6 , r , I., H ) f o u n d a t i o n is s t a b l e . O t n e r w i s e Lhe
s t a h i l i t y would depend on t h e c o n s t i t u t i v e c h a r a c t e r of the
Foundatioli s o i l . I n t h e m a t h e m a t i c a l method e m p l o y x l , the
..; t a l ~ i l i t ya nalysis i s t r a n s c r i b e d a s a mi n imi z a t i 2 n probl.ern
i n t h e C a l c u l u s o f V a r i a t i o n s .
'I'hc r e s u l t of Lhe analysis shows, among others, Cllat Lhe
7'crzaghi':; st~p
, A & O., E (2021). Bearing Capacity and Critical Normal Stress Distribution of Soils by Method of Variational Calculus. Afribary. Retrieved from https://tracking.afribary.com/works/bearing-capacity-and-critical-normal-stress-distribution-of-soils-by-method-of-variational-calculus
, AKUBUIRO and Edwin O. "Bearing Capacity and Critical Normal Stress Distribution of Soils by Method of Variational Calculus" Afribary. Afribary, 02 May. 2021, https://tracking.afribary.com/works/bearing-capacity-and-critical-normal-stress-distribution-of-soils-by-method-of-variational-calculus. Accessed 14 Nov. 2024.
, AKUBUIRO, Edwin O. . "Bearing Capacity and Critical Normal Stress Distribution of Soils by Method of Variational Calculus". Afribary, Afribary, 02 May. 2021. Web. 14 Nov. 2024. < https://tracking.afribary.com/works/bearing-capacity-and-critical-normal-stress-distribution-of-soils-by-method-of-variational-calculus >.
, AKUBUIRO and O., Edwin . "Bearing Capacity and Critical Normal Stress Distribution of Soils by Method of Variational Calculus" Afribary (2021). Accessed November 14, 2024. https://tracking.afribary.com/works/bearing-capacity-and-critical-normal-stress-distribution-of-soils-by-method-of-variational-calculus