add_filter( 'woocommerce_shipping_fields' , 'my_custom_shipping_fields' );
function my_custom_shipping_fields( $fields ) {

     $fields['shipping_address_type'] = array(
                'type'              =>  'text',
                'label'         => __('Address Type', 'woocommerce'),
                'placeholder' => _x('Address Type', 'placeholder', 'woocommerce'),
                'required'      => true,
                'class'         => array('form-row'),
                'clear'         => true,
                'options'     => array(
                        'select' => __('Select...', 'woocommerce' ),
                'House' => __('House', 'woocommerce' ),
                'Multi-Unit' => __('Apartment or Condo', 'woocommerce' ),
                'Business' => __('Business', 'woocommerce' )
                    )
                );

     return $fields;
}

add_action( 'woocommerce_checkout_process', 'my_custom_checkout_field_process');
function my_custom_checkout_field_process() {

    if ($_POST['address_type'] == "text") 
    { 
    wc_add_notice( __( 'Please tell us the Address Type we are delivering to.' ), 'error' );
    }
}

add_action( 'woocommerce_checkout_update_order_meta', 'my_custom_checkout_field_update_order_meta' ); 
        function my_custom_checkout_field_update_order_meta( $order_id ) {

            if ( ! empty( $_POST['shipping_address_type'] ) ) {
                update_post_meta( $order_id, 'Address Type', esc_attr( $_POST[ 'shipping_address_type' ]) );
            }
        }
		add_action( 'woocommerce_admin_order_data_after_shipping_address', 'my_custom_fields_display_admin_order_meta', 10, 1 ); 
function my_custom_fields_display_admin_order_meta( $order ) {
    echo '<p><strong>'.__('Address Type').':</strong> ' . get_post_meta( $order->id, 'Address Type', true ) . '</p>';
}