org.apache.catalina.LifecycleException: A child container failed during start

It looks like you're missing one or more the Spring Framework jars from your web application. If you look at the stack trace here's a line:

java.lang.NoClassDefFoundError: org/springframework/context/ApplicationContextException

Which convey spring-context-XXX.jar is missing !!!

You need the Spring jars in your web app's WEB-INF/lib directory.

According to spring-webmvc 3.1.2 need following jar:

aopalliance-1.0.jar
commons-logging-1.1.1.jar
spring-webmvc-3.1.2.RELEASE.jar
spring-asm-3.1.2.RELEASE.jar
spring-beans-3.1.2.RELEASE.jar
spring-core-3.1.2.RELEASE.jar
spring-context-3.1.2.RELEASE.jar
spring-aop-3.1.2.RELEASE.jar
spring-expression-3.1.2.RELEASE.jar
spring-context-support-3.1.2.RELEASE.jar
spring-web-3.1.2.RELEASE.jar

EDIT:_24_04_2015 After looking at your pom.xml its clear that you didn't included spring-context dependency in your pom.xml file please add below code in your pom.xml

   <dependency>
        <groupId>org.springframework</groupId>
        <artifactId>spring-context</artifactId>
        <version>3.0.5.RELEASE</version>
        <type>jar</type>
        <scope>compile</scope>
    </dependency>